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The first algorithm, motivated by the attempt to design efficient algorithms for the All Pairs Shortest Path problem using fast matrix multiplication, solves the problem of computingwitnesses for the Boolean product of two matrices. That is, ifA andB are twon byn matrices, andC=AB is their Boolean product, the algorithm finds for every entryC\n\n                  ij\n                =1 a witness: an indexk so thatA\n\n                  ik\n                =B\n\n                  kj\n                =1. Its running time exceeds that of computing the product of twon byn matrices with small integer entries by a polylogarithmic factor. The second algorithm is a nearly linear time deterministic procedure for constructing a perfect hash function for a givenn-subset of {1,...,m}.",{"EN":237},"Derandomization, witnesses for Boolean matrix multiplication and construction of perfect hash functions",{"VOID":239},"[\"4631906804426848663\"]",{"VOID":241},"10.1007\u002FBF01940874","PUBLICATION","VERIFIED","2024-05-02T22:09:32.234+00:00","Auto Verify","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002FBF01940874",[248,266],{"id":249,"sortIndex":21,"researcher":20,"roles":250,"affiliations":252,"properties":261,"displayName":263,"givenName":20,"familyName":20},"113a5ef4-741a-4e14-95ea-348cb34186c7",[251],"AUTHOR",[253],{"id":254,"sortIndex":21,"affiliation":255,"properties":20},"b81fa9f5-90fb-4416-afaf-44c888ee17c9",{"id":254,"createTime":20,"updateTime":20,"relativeEntities":256,"slug":20,"properties":257,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":260,"statistic":20},[],{"title":258},{"VI":259},"Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel",[],{"title":262,"gsAuthor":264},{"VI":263},"N. 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Alon, L. Babai, and A. Itai, A fast and simple randomized parallel algorithm for the maximal independent set problem,Journal of Algorithms,7 (1986), 567–583.","https:\u002F\u002Flinkinghub.elsevier.com\u002Fretrieve\u002Fpii\u002F0196677486900192",{"doi":353},"10.1016\u002F0196-6774(86)90019-2",{"id":355,"text":356,"url":357,"identifiers":358},"4c68646b-0035-4279-8000-0006b275d4fa","N. Alon, J. Brusck, J. Naor, M. Naor, and R. Roth, Construction of asymptotically good, low-rate error-correcting codes through pseudo-random graphs,IEEE Transactions on Information Theory,38 (1992), 509–516.","https:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs10440-022-00541-7",{"doi":359},"10.1007\u002Fs10440-022-00541-7",{"id":355,"text":361,"url":357,"identifiers":362},"N. Alon, Z. Galil, and O. Margalit, On the exponent of the All Pairs Shortest Path problem,Proc. 32nd IEEE Annual Symposium on Foundations of Computer Science, 1991, pp. 569–575. AlsoJournal of Computer and System Sciences, to appear.",{"doi":359},{"id":355,"text":364,"url":357,"identifiers":365},"N. Alon, Z. Galil, O. Margalit. and M. Naor, Witnesses for Boolean matrix multiplication and for shortest paths,Proc. 33rd IEEE Annual Symposium on Foundations of Computer Science, 1992, pp. 417–426.",{"doi":359},{"id":355,"text":367,"url":357,"identifiers":368},"N. Alon, O. Goldreich, J. Hastad, and R. Peralta, Simple constructions of almostk-wise independent random variables,Proc. 31st IEEE Symposium on Foundations of Computer Science, 1990, pp. 544–553. AlsoRandom Structures and Algorithms,3 (1992), 289–304.",{"doi":359},{"id":355,"text":370,"url":357,"identifiers":371},"N. Alon and J. Spencer,The Probabilistic Method, Wiley, New York, 1991.",{"doi":359},{"id":355,"text":373,"url":357,"identifiers":374},"B. Berger and J. Rompel, Simulating (logc n)-wise independence in NC,Journal of the ACM,38 (1991), 1026–1046.",{"doi":359},{"id":355,"text":376,"url":357,"identifiers":377},"D. Coppersmith and S. Winograd, Matrix multiplication via arithmetic progressions,Journal of Symbolic Computation,9 (1990), 251–280.",{"doi":359},{"id":20,"text":379,"url":20,"identifiers":380},"A. Fiat and M. Naor, ImplicitO(1) probe search,SIAM Journal on Computing,22 (1993), 1–10.",{},{"id":355,"text":382,"url":357,"identifiers":383},"A. Fiat, M. Naor, J. P. Schmidt, and A. Siegel, Non-oblivious hashing,Journal of the ACM,31 (1992), 764–782.",{"doi":359},{"id":355,"text":385,"url":357,"identifiers":386},"M. L. Fredman and J. Komlós, On the size of separating systems and families of perfect hash functions.SIAM Journal on Algebraic and Discrete Methods,5 (1) (1984), 61–68.",{"doi":359},{"id":355,"text":388,"url":357,"identifiers":389},"M. L. Fredman, J. Komlós, and E. Szemerédi, Storing a sparse table withO(1) worst case access time,Journal of the ACM,31 (1984), 538–544.",{"doi":359},{"id":20,"text":391,"url":20,"identifiers":392},"Z. Galil and O. Margalit, A faster algorithm for the all pairs shortest path problem for undirected graphs, Manuscript, August 1991.",{},{"id":355,"text":394,"url":357,"identifiers":395},"Z. Galil and O. Margalit, Witnesses for Boolean matrix multiplication and for transitive closure,Journal of Complexity,9 (1993), 201–221.",{"doi":359},{"id":355,"text":397,"url":357,"identifiers":398},"R. M. Karp and A. Wigderson, A fast parallel algorithm for the maximal independent set problem,Journal of the ACM,32 (1985), 762–773.",{"doi":359},{"id":355,"text":400,"url":357,"identifiers":401},"J. Körner, Fredman-Komlós bounds and information theory,SIAM Journal on Algebraic and Discrete Methods,7 (1986), 560–570.",{"doi":359},{"id":355,"text":403,"url":357,"identifiers":404},"M. Luby, A simple parallel algorithm for the maximal independent set problem,SIAM Journal on Computing,15 (1986), 1036–1053.",{"doi":359},{"id":406,"text":407,"url":408,"identifiers":409},"7687452b-b123-49fb-9a48-042f9345e416","M. Luby, Removing randomness in parallel computation without a processor penalty,Journal of Computer Systems and Science,47 (1993), 250–286.","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002F002200009390033S",{"doi":410},"10.1016\u002F0022-0000(93)90033-S",{"id":355,"text":412,"url":357,"identifiers":413},"H. Mairson, The effect of table expansion on the program complexity of perfect hash functions,BIT,32 (1992), 430–440.",{"doi":359},{"id":20,"text":415,"url":20,"identifiers":416},"O. Margalit, Ph.D. Dissertation, Tel Aviv University, 1993.",{},{"id":20,"text":418,"url":20,"identifiers":419},"K. Mehlhorn,Data Structure and Algorithms 1: Sorting and Searching, Springer-Verlag, Berlin, 1984.",{},{"id":421,"text":422,"url":423,"identifiers":424},"25136b8f-a858-43e1-b6a7-a64500a8da68","R. Motwani, J. Naor and M. Naor, The probabilistic method yields deterministic parallel algorithms,Proc. 30th IEEE Symposium on Foundations of Computer Science, 1989, pp. 8–13.","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0022000005800698",{"doi":425},"10.1016\u002Fs0022-0000(05)80069-8",{"id":355,"text":427,"url":357,"identifiers":428},"J. Naor and M. Naor, Small-bias probability spaces: efficient constructions and applications,SIAM Journal on Computing,22 (1993), 838–856.",{"doi":359},{"id":355,"text":430,"url":357,"identifiers":431},"A. Nilli, Perfect hashing and probability,Combinatorics, Probability and Computing,3 (1994), 407–419.",{"doi":359},{"id":355,"text":433,"url":357,"identifiers":434},"P. Raghavan, Probabilistic construction of deterministic algorithms: approximating packing integer programs,Journal of Computer Systems and Science,37 (1988), 130–143.",{"doi":359},{"id":355,"text":436,"url":357,"identifiers":437},"T. J. Sager, A polynomial time generator for minimal perfect hash functions,Communications of the ACM,28 (1985).",{"doi":359},{"id":20,"text":439,"url":20,"identifiers":440},"J. Schmidt and A. Siegel, The spatial complexity of obliviousk-probe hash functions,SIAM Journal on Computing,19 (1990), 775–786.",{},{"id":355,"text":442,"url":357,"identifiers":443},"R. Seidel, On the all-pairs-shortest-path problem,Proc. 24th Annual ACM Symposium on Theory of Computing, 1992, pp. 745–749.",{"doi":359},{"id":355,"text":445,"url":357,"identifiers":446},"J. Spencer,Ten Lectures on the Probabilistic Method, SIAM, Philadelphia, PA, 1987.",{"doi":359},{"id":20,"text":448,"url":20,"identifiers":449},"R. E. Tarjan and A. C. Yao, Storing a Sparse Table,Communications of the ACM,22 (1979), 606–611.",{},false,{"id":452,"createTime":453,"updateTime":454,"relativeEntities":455,"slug":456,"properties":457,"entityType":242,"verifyStatus":243,"verifyTime":466,"verifyNote":245,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":467,"fullTextUrl":20,"authors":468,"publicationType":283,"publisherRelationship":532,"citationCount":21,"citationInfo":588,"publishDate":591,"publishYear":589,"citationAnalyzeStatus":344,"lastCitationAnalyze":454,"indexDatabases":592,"openAccess":20,"references":593,"isForceReanalyzing":450},"455aadbc-cef9-4e4d-8064-b0b9e241c219","2024-01-28T18:36:01.248+00:00","2026-08-24T14:47:45.766+00:00",[],"Permutation-Betting-Markets-Singleton-Betting-with-Extra-Information",{"abstract":458,"title":460,"gsPaper":462,"doi":464},{"EN":459},"We study permutation betting markets, introduced by Chen et al. (Proceedings of the ACM Conference on Electronic Commerce, 2007). For these markets, we consider subset bettings in which each trader can bet on a subset of candidates ending up in a subset of positions. We consider the revenue maximization problem for the auctioneer in two main frameworks: the risk-free revenue maximization (studied in Chen et al., Proceedings of the ACM Conference on Electronic Commerce, 2007), and the probabilistic revenue maximization. We also explore the use of some certain knowledge or extra information about the possible outcomes of the market. We first show that finding the optimal revenue in the risk-free model for the subset betting problem is inapproximable. This resolves an open question posed by Chen et al. (Proceedings of the ACM Conference on Electronic Commerce, 2007). In order to identify solvable variants of the problem, we propose the singleton betting language which allows traders to bet an arbitrary value on one candidate for one position. For singleton bettings, we first provide a linear-time implementable necessary and sufficient condition for existence of a solution with positive revenue for any possible outcome. Furthermore, we develop an LP-based polynomial-time algorithm to find the optimum solution of this problem. In addition, we show how to extend this LP-based method to handle some extra information about the possible outcomes. Finally, we consider the revenue maximization problem in a probabilistic setting. For this variant, we observe that the problem of maximizing the expected revenue is polynomial-time solvable, but we show that maximizing the probability of achieving a pre-specified revenue is #P-Complete.",{"EN":461},"Permutation Betting Markets: Singleton Betting with Extra Information",{"VOID":463},"[\"9472816150258532178\"]",{"VOID":465},"10.1007\u002Fs00453-009-9378-0","2024-05-05T12:26:17.009+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs00453-009-9378-0",[469,486,501,519],{"id":470,"sortIndex":21,"researcher":20,"roles":471,"affiliations":472,"properties":481,"displayName":483,"givenName":20,"familyName":20},"417bd1da-f089-410f-ba55-ed75302a333b",[251],[473],{"id":474,"sortIndex":21,"affiliation":475,"properties":20},"05fbed6b-b1ca-402f-ad07-f6800fedd7c9",{"id":474,"createTime":20,"updateTime":20,"relativeEntities":476,"slug":20,"properties":477,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":480,"statistic":20},[],{"title":478},{"VI":479},"Department of Computer Engineering, Sharif University of Technology, Tehren, Iran",[],{"title":482,"gsAuthor":484},{"VI":483},"Mohammad Ghodsi",{"VOID":485},"[\"70Rmp1oAAAAJ\"]",{"id":487,"sortIndex":180,"researcher":20,"roles":488,"affiliations":489,"properties":496,"displayName":498,"givenName":20,"familyName":20},"2924aedc-fae0-493c-8cce-e7d8582fe451",[251],[490],{"id":474,"sortIndex":21,"affiliation":491,"properties":20},{"id":474,"createTime":20,"updateTime":20,"relativeEntities":492,"slug":20,"properties":493,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":495,"statistic":20},[],{"title":494},{"VI":479},[],{"title":497,"gsAuthor":499},{"VI":498},"Hamid Mahini",{"VOID":500},"[\"q3EGms8AAAAJ\"]",{"id":502,"sortIndex":503,"researcher":20,"roles":504,"affiliations":505,"properties":514,"displayName":516,"givenName":20,"familyName":20},"e3e4a58f-52b3-4187-b73d-4070afa32d79",2,[251],[506],{"id":507,"sortIndex":21,"affiliation":508,"properties":20},"47b536e7-fcce-420c-b16c-8e53146065bf",{"id":507,"createTime":20,"updateTime":20,"relativeEntities":509,"slug":20,"properties":510,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":513,"statistic":20},[],{"title":511},{"VI":512},"Microsoft Research, Redmond, USA",[],{"title":515,"gsAuthor":517},{"VI":516},"Vahab S. 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In: Proceedings of the ACM Conference on Electronic Commerce (2007)",{"doi":359},{"id":355,"text":598,"url":357,"identifiers":599},"Plott, C., Sunder, S.: Efficiency of experimental security markets with insider information: An application of rational expectations models. J. Polit. Econ. 90, 663–698 (1982)",{"doi":359},{"id":355,"text":601,"url":357,"identifiers":602},"Plott, C., Sunder, S.: Rational expectations and the aggregation of diverse information in laboratory security markets. Econometrica 56, 1085–1118 (1988)",{"doi":359},{"id":355,"text":604,"url":357,"identifiers":605},"Berg, J.E., Forsythe, R., Nelson, F.D., Rietz, T.A.: Results from a dozen years of election futures markets research. In: Plott, C.A., Smith, V. (eds.) Handbook of Experimental Economic Results. Elsevier, North-Holland (2001)",{"doi":359},{"id":355,"text":607,"url":357,"identifiers":608},"Forsythe, R., Rietz, T.A., Ross, T.W.: Wishes, expectations, and actions: A survey on price formation in election stock markets. J. Econ. Behav. Organ. 39, 83–110 (1999)",{"doi":359},{"id":20,"text":610,"url":20,"identifiers":611},"Pennock, D.M., Lawrence, S., Giles, C.L., Nielsen, F.A.: The real power of artificial markets. Science 291, 987–988 (2002)",{},{"id":355,"text":613,"url":357,"identifiers":614},"Dhamdhere, K., Goyal, V., Ravi, R., Singh, M.: How to pay, come what may: Approximation algorithms for demand-robust covering problems. In: Proceedings of the Annual Symposium on Foundations of Computer Science (FOCS) (2005)",{"doi":359},{"id":355,"text":616,"url":357,"identifiers":617},"Ghodsi, M., Mahini, H., Mirrokni, V.S., Zadimoghaddam, M.: Permutation betting markets: singleton betting with extra information. In: Proceedings of the ACM Conference on Electronic Commerce (2008)",{"doi":359},{"id":355,"text":619,"url":357,"identifiers":620},"Nikulin, Y.: Robustness in combinatorial optimization and scheduling theory: An annotated bibliography. Technical Report SOR-91-13, Statistics and Operation Research (2004)",{"doi":359},{"id":20,"text":622,"url":20,"identifiers":623},"Feige, U., Jain, K., Mahdian, M., Mirrokni, V.S: Robust combinatorial optimization with exponential number of scenarios. In: Proceedings of the Conference on Integer Programming and Combinatorial Optimization (2007)",{},{"id":355,"text":625,"url":357,"identifiers":626},"Immorlica, N., Karger, D., Minkoff, M., Mirrokni, V.S.: On the costs and benefits of procrastination: Approximation algorithms for stochastic combinatorial optimization problems. In: Proceedings Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (2004)",{"doi":359},{"id":20,"text":628,"url":20,"identifiers":629},"Gupta, A., Pal, M., Ravi, R., Sinha, A.: Boosted sampling: Approximation algorithms for stochastic optimization. In: Proceedings of the Annual ACM Symposium on Theory of Computing (STOC) (2004)",{},{"id":355,"text":631,"url":357,"identifiers":632},"Shmoys, D., Swamy, S.: Stochastic optimization is (almost) as easy as deterministic optimization. In: Proceedings of the Annual Symposium on Foundations of Computer Science (FOCS) (2004)",{"doi":359},{"id":20,"text":634,"url":20,"identifiers":635},"Pennock, D.: Personal communications",{},{"id":637,"text":638,"url":639,"identifiers":640},"d362e9a9-9f5e-4329-897b-46331f9fb8de","Fortnow, L., Kilian, J., Pennock, D., Wellman, M.P.: Betting boolean-style: A framework for trading in securities based on logical formulas. Decis. Support Syst. 39(1), 87–104 (2004)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0167923604001770",{"doi":641},"10.1016\u002Fj.dss.2004.08.010",{"id":643,"text":644,"url":645,"identifiers":646},"3aa502a6-16c6-4dad-8775-d7cb781f7e71","Hanson, R.D.: Combinatorial information market design. Inf. Syst. Front. 5(1), 107–119 (2003)","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1023\u002FA:1022058209073",{"doi":647},"10.1023\u002FA:1022058209073",{"id":20,"text":649,"url":20,"identifiers":650},"Cramton, P., Shoham, Y., Steinberg, R.: Combinatorial Auctions. MIT Press, Cambridge (2005)",{},{"id":652,"text":653,"url":654,"identifiers":655},"c606fd10-8050-4303-8847-d7f336df1937","Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.: Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)","https:\u002F\u002Fwww.emerald.com\u002Finsight\u002Fcontent\u002Fdoi\u002F10.1108\u002F03684920810884423\u002Ffull\u002Fhtml",{"doi":656},"10.1108\u002F03684920810884423",{"id":658,"text":659,"url":660,"identifiers":661},"4a92e964-6644-41a4-8553-3225a8db28ee","Lehmann, B., Lehmann, D., Nisan, N.: Combinatorial auctions with decreasing marginal utilities. In: Proceedings of the ACM Conference on Electronic Commerce (EC) (2001)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS089982560500028X",{"doi":662},"10.1016\u002Fj.geb.2005.02.006",{"id":664,"text":665,"url":666,"identifiers":667},"aba76646-582a-4500-ab1c-3756d75658f2","Sandholm, T.: Algorithm for optimal winner determination in combinatorial auctions. Artif. Intell. 135, 1–54 (2002)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS000437020100159X",{"doi":668},"10.1016\u002Fs0004-3702(01)00159-x",{"id":355,"text":670,"url":357,"identifiers":671},"Feige, U.: On maximizing welfare when utility functions are subadditive. In: Proceedings of the Annual ACM Symposium on Theory of Computing (STOC) (2006)",{"doi":359},{"id":355,"text":673,"url":357,"identifiers":674},"Schrijver, A.: Total dual integrality of matching forest constraints. Combinatorica 20, 575–588 (2000)",{"doi":359},{"id":676,"text":677,"url":678,"identifiers":679},"eb0ef371-82f2-4c0f-92a5-e6f7f9ca6f51","Papadimitriou, C., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Dover, New York (1998)","https:\u002F\u002Fwww.goodreads.com\u002Fbook\u002Fshow\u002F138564.Combinatorial_Optimization",{"isbn":680,"isbn13":681},"0486402584","9780486402581",{"id":355,"text":683,"url":357,"identifiers":684},"Schrijver, A.: Combinatorial Optimization—Polyhedra and Efficiency. Springer, Berlin (2003)",{"doi":359},{"id":20,"text":686,"url":20,"identifiers":687},"Heller, I., Tompkins, C.B.: An extension of a theorem of Dantzig’s. In: Kuhn, H.W., Tucker, A.W. (eds.) Linear Inequalities and Related Systems, pp. 247–254. Princeton University Press, Princeton (1956)",{},{"id":689,"createTime":690,"updateTime":691,"relativeEntities":692,"slug":693,"properties":694,"entityType":242,"verifyStatus":243,"verifyTime":707,"verifyNote":245,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":708,"fullTextUrl":20,"authors":709,"publicationType":283,"publisherRelationship":752,"citationCount":803,"citationInfo":804,"publishDate":809,"publishYear":805,"citationAnalyzeStatus":344,"lastCitationAnalyze":810,"indexDatabases":811,"openAccess":20,"references":20,"isForceReanalyzing":450},"7f5dd778-4f9c-43aa-8143-13d5c94c0dbb","2024-04-09T04:58:07.294+00:00","2026-08-18T06:16:30.778+00:00",[],"Finding-all-periods-and-initial-palindromes-of-a-string-in-parallel",{"abstract":695,"title":697,"gsPaper":699,"keywords":701,"references":703,"doi":705},{"EN":696},"An optimalO(log logn)-time CRCW-PRAM algorithm for computing all period lengths of a string is presented. Previous parallel algorithms compute the period only if it is shorter than half of the length of the string. The algorithm can be used to find all initial palindromes of a string in the same time and processor bounds. Both algorithms are the fastest possible over a general alphabet. We derive a lower bound for finding initial palindromes by modifying a known lower bound for finding the period length of a string [9]. Whenp processors are available the bounds become Θ(⌈n\u002Fp⌉+log⌈1+p\u002Fn⌉2p).",{"EN":698},"Finding all periods and initial palindromes of a string in parallel",{"VOID":700},"[\"5056765032105495457\"]",{"EN":702},"",{"VOID":704},"A. Apostolico and D. Breslauer. An optimalO(log logn) time parallel algorithm for detecting all squares in a string.SIAM J. Comput., to appear.\nA. Apostolico, D. Breslauer, and Z. Galil. Optimal parallel algorithms for periods, palindromes and squares.Proc. 19th Internat. Colloq. on Automata, Languages, and Programming. Lecture Notes in Computer Science, Vol. 623. Springer-Verlag, Berlin, 1992, pages 296–307.\nH. W. Bergerson.Palindromes and Anagrams. Dover. New York, 1973.\nR. P. Brent. Evaluation of general arithmetic expressions.J. Assoc. Comput. Mach., 21:201–206, 1974.\nD. Breslauer. Efficient String Algorithmics. Ph.D. thesis, Department of Computer Science, Columbia University, New York, 1992.\nD. Breslauer. Fast parallel string prefix-matching.Theoret. Comput. Sci., 137(2):269–278, 1995.\nD. Breslauer. Testing string superprimitivity in parallel.Inform. Process. Lett., 49:5 235–241, 1994.\nD. Breslauer and Z. Galil. An optimalO(log logn) time parallel string matching algorithm.SIAM J. Comput., 19(6): 1051–1058, 1990.\nD. Breslauer and Z. Galil. A lower bound for parallel string matching.SIAM J. Comput., 21(5):856–862. 1992.\nM. Crochemore and W. Rytter. Usefulness of the Karp-Miller-Rosenberg algorithm in parallel computations on strings and arrays.Theoret. Comput. Sci., 88:59–82, 1991.\nF. E. Fich, R. L. Radge, and A. Wigderson. Relations between concurrent-write models of parallel computation.Proc. 3rd ACM Symp. on Principles of Distributed Computing, 1984, pages 179–189.\nM. J. Fischer and M. S. Paterson. Sring matching and other produces. In R. M. Karp, editor,Complexity of Computation. American Mathematical Society, Providence, RI, 1974, pages 113–125.\nG. Galil. Optimal parallel algorithms for string matching.Inform. and Control. 67:144–157, 1985.\nJ. E. Hopcroft and J. D. Ullman.Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading, MA, 1979.\nR. M. Karp, R. E. Miller, and A. L. Rosenberg. Rapid identification of repeated patterns in strings, trees and arrays.Proc. 4th ACM Symp. on Theory of Computing, 1972, pages 125–136.\nZ. Kedem, G. M. Landau, and K. Palem. Optimal parallel suffix-prefix matching algorithm and applications.Proc. 1st ACM Symp. on Parallel Algorithms and Architectures, 1989, pages 388–398.\nD. E. Knuth, J. H. Morris, and V. R. Pratt. Fast pattern matching in strings.SIAM J. Comput., 6:322–350, 1977.\nM. Lothaire.Combinatorics on Words. Addison-Wesley, Reading, MA, 1983.\nR. C. Lyndon and M. P. Schutzenberger. The equation am=bncp in a free group.Michigan Math. J., 9:289–298, 1962.\nG. Manacher. A new linear-time “On-line” algorithm for finding the smallest initial palindrome of a string.J. Assoc. Comput. Mach., 22:346–351, 1975.\nL. G. Valiant. Parallelism in comparison models.SIAM J. Comput., 4:348–355, 1975.\nU. Vishkin. 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present a bijection between the set of plane triangulations (aka maximal planar graphs) and a simple subset of the set of plane trees with two leaves adjacent to each node. The construction takes advantage of Schnyder tree decompositions of plane triangulations. This bijection yields an interpretation of the formula for the number of plane triangulations with n vertices. Moreover, the construction is simple enough to induce a linear random sampling algorithm, and an explicit information theory optimal encoding. Finally, we extend our bijection approach to triangulations of a polygon with k sides with m inner vertices, and develop in passing new results about Schnyder tree decompositions for these objects.",{"EN":822},"Optimal Coding and Sampling of 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the Subset Feedback Vertex Set (Subset-FVS) problem the input is a graph G on n vertices, a subset T of vertices of G called the “terminal” vertices, and an integer k. The task is to determine whether there exists a subset of vertices of cardinality at most k which together intersect all cycles which pass through the terminals. Subset-FVS generalizes several well studied problems including Feedback Vertex Set and Multiway Cut. This problem is known to be NP-Complete, even in split graphs. Cygan et al. (SIAM J Discrete Math 27(1):290–309, 2013) proved that Subset-FVS is fixed parameter tractable (\n                  \n                    \n                  \n                  $$\\mathsf {FPT}$$\n                  \n                    \n                  \n                ) in general graphs when parameterized by k. In split graphs a simple observation reduces the problem to an equivalent instance of the 3-Hitting Set problem with the same solution size. This directly implies, for Subset-FVSrestricted to split graphs, (i) an \n                  \n                    \n                  \n                  $$\\mathsf {FPT}$$\n                  \n                    \n                  \n                 algorithm which solves the problem in \n                  \n                    \n                  \n                  $$\\mathcal {O}^{\\star } (2.076^k)$$\n                  \n                    \n                  \n                 time (The \n                  \n                    \n                  \n                  $$\\mathcal {O}^{\\star } ()$$\n                  \n                    \n                  \n                 notation hides polynomial factors.) (Wahlström in Algorithms, measures and upper bounds for satisfiability and related problems. Ph.D. Thesis, Department of Computer and Information Science, Linköpings universitet, 2007), and (ii) a kernel of size \n                  \n                    \n                  \n                  $$\\mathcal {O}(k^3)$$\n                  \n                    \n                  \n                . We improve both these results for Subset-FVS on split graphs; we derive (i) a kernel of size \n                  \n                    \n                  \n                  $$\\mathcal {O}(k^2)$$\n                  \n                    \n                  \n                 which is the best possible unless \n                  \n                    \n                  \n                  $$\\textsf {NP}\\subseteq {\\mathsf {coNP}}\u002F{\\textsf {poly}}$$\n                  \n                    \n                  \n                , and (ii) an algorithm which solves the problem in time \n                  \n                    \n                  \n                  $$\\mathcal {O}^*(2^k)$$\n                  \n                    \n                  \n                . Our algorithm, in fact, solves Subset-FVS on the more general class of chordal graphs, also in \n                  \n                    \n                  \n                  $$\\mathcal {O}^*(2^k)$$\n                  \n                    \n                  \n                 time. To the best of our knowledge, the fastest known exact algorithm for Subset-FVS on chordal graphs is based on the 3-Hitting Set algorithm of Fomin et al. (JACM 66(2):8, 2019) which runs in \n                  \n                    \n                  \n                  $$\\mathcal {O}^*(1.5182^n)$$\n                  \n                    \n                  \n                 time. Applying the results of Fomin et al. \n(2019) to our \n                  \n                    \n                  \n                  $$\\mathsf {FPT}$$\n                  \n                    \n                  \n                 algorithm yields two exact exponential-time algorithms for Subset-FVS on chordal graphs: a randomized algorithm which runs in \n                  \n                    \n                  \n                  $$\\mathcal {O}^*(1.5^{n})$$\n                  \n                    \n                  \n                 time, and a deterministic algorithm which runs in \n                  \n                    \n                  \n                  $$\\mathcal {O}^*((1.5+\\varepsilon )^{n})$$\n                  \n                    \n                  \n                 time for any fixed \n                  \n                    \n                  \n                  $$\\varepsilon >0$$\n                  \n                    \n                  \n                .",{"EN":935},"Subset Feedback Vertex Set in Chordal and Split Graphs",{"VOID":937},"[\"2218153369156090815\"]",{"VOID":939},"Abu-Khzam, F.N.: A kernelization algorithm for d-hitting set. J. Comput. Syst. Sci. 76(7), 524–531 (2010). https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.jcss.2009.09.002\nBlair, J.R., Peyton, B.: An introduction to chordal graphs and clique trees. In: Graph Theory and Sparse Matrix Computation, pp. 1–29. Springer (1993)\nChitnis, R., Fomin, F.V., Lokshtanov, D., Misra, P., Ramanujan, M., Saurabh, S.: Faster exact algorithms for some terminal set problems. J. Comput. Syst. Sci. 88, 195–207 (2017)\nChitnis, R.H., Cygan, M., Hajiaghayi, M.T., Marx, D.: Directed subset feedback vertex set is fixed-parameter tractable. ACM Trans. Algorithms (TALG) 11(4), 28:1–28:28 (2015)\nCygan, M., Fomin, F.V., Kowalik, L., Lokshtanov, D., Marx, D., Pilipczuk, M., Pilipczuk, M., Saurabh, S.: Parameterized Algorithms. Springer, Berlin (2015)\nCygan, M., Pilipczuk, M., Pilipczuk, M., Wojtaszczyk, J.O.: Subset feedback vertex set is fixed-parameter tractable. SIAM J. Discrete Math. 27(1), 290–309 (2013)\nDell, H., Van Melkebeek, D.: Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses. J. ACM 61(4), 23:1–23:27 (2014)\nDiestel, R.: Graph Theory, 5th edn. Springer, Berlin (2016)\nEven, G., Naor, J., Zosin, L.: An 8-approximation algorithm for the subset feedback vertex set problem. SIAM J. Comput. 30(4), 1231–1252 (2000)\nFomin, F., Kratsch, D.: Exact Exponential Algorithms. Texts in Theoretical Computer Science. An EATCS Series. Springer, Berlin Heidelberg (2010)\nFomin, F.V., Gaspers, S., Lokshtanov, D., Saurabh, S.: Exact algorithms via monotone local search. JACM 66(2), 8 (2019)\nFomin, F.V., Heggernes, P., Kratsch, D., Papadopoulos, C., Villanger, Y.: Enumerating minimal subset feedback vertex sets. Algorithmica 69(1), 216–231 (2014)\nFomin, F.V., Le, T.N., Lokshtanov, D., Saurabh, S., Thomassé, S., Zehavi, M.: Subquadratic kernels for implicit 3-hitting set and 3-set packing problems. ACM Trans. Algorithms (TALG) 15(1), 13 (2019)\nFomin, F.V., Lokshtanov, D., Misra, N., Philip, G., Saurabh, S.: Hitting forbidden minors: approximation and kernelization. SIAM J. Discrete Math. 30(1), 383–410 (2016)\nFomin, F.V., Lokshtanov, D., Saurabh, S., Zehavi, M.: Kernelization: Theory of Parameterized Preprocessing. Cambridge University Press, Cambridge (2019)\nGalinier, P., Habib, M., Paul, C.: Chordal graphs and their clique graphs. In: International Workshop on Graph-Theoretic Concepts in Computer Science, pp. 358–371. Springer (1995)\nGolovach, P.A., Heggernes, P., Kratsch, D., Saei, R.: Subset feedback vertex sets in chordal graphs. J. Discrete Algorithms 26, 7–15 (2014)\nGolumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs, vol. 57. Elsevier, Amsterdam (2004)\nHammer, P.L., Simeone, B.: The splittance of a graph. Combinatorica 1(3), 275–284 (1981)\nHols, E.M.C., Kratsch, S.: A randomized polynomial kernel for subset feedback vertex set. Theory Comput. Syst. 62(1), 63–92 (2018)\nKawarabayashi, Ki, Kobayashi, Y.: Fixed-parameter tractability for the subset feedback set problem and the s-cycle packing problem. J. Comb. Theory Ser. B 102(4), 1020–1034 (2012)\nLokshtanov, D., Ramanujan, M., Saurabh, S.: Linear time parameterized algorithms for subset feedback vertex set. ACM Trans. Algorithms (TALG) 14(1), 7 (2018)\nThomassé, S.: A \\(4k^{{2}}\\) kernel for feedback vertex set. ACM Trans. Algorithms (TALG) 6(2), 32:1–32:8 (2010)\nWahlström, M.: Algorithms, measures and upper bounds for satisfiability and related problems. Ph.D. Thesis, Department of Computer and Information Science, Linköpings universitet (2007)\nWahlström, M.: Half-integrality, LP-branching and FPT algorithms. In: Proceedings of the Twenty-fifth Annual ACM-SIAM symposium on Discrete algorithms, pp. 1762–1781. 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Steiner Tree (DST) is a central problem in combinatorial optimization and theoretical computer science: Given a directed graph \n                \n                  \n                \n                $$G=(V, E)$$\n                \n               with edge costs \n                \n                  \n                \n                $$c \\in {\\mathbb {R}}_{\\ge 0}^E$$\n                \n              , a root \n                \n                  \n                \n                $$r \\in V$$\n                \n               and k terminals \n                \n                  \n                \n                $$K\\subseteq V$$\n                \n              , we need to output the minimum-cost arborescence in G that contains an \n                \n                  \n                \n                $$r \\rightarrow t$$\n                \n               path for every \n                \n                  \n                \n                $$t \\in K$$\n                \n              . Recently, Grandoni, Laekhanukit and Li, and independently Ghuge and Nagarajan, gave quasi-polynomial time \n                \n                  \n                \n                $$O(\\log ^2k\u002F\\log \\log k)$$\n                \n              -approximation Algorithms for the problem, which are tight under popular complexity assumptions. In this paper, we consider the more general Degree-Bounded Directed Steiner Tree (DB-DST) problem, where we are additionally given a degree bound \n                \n                  \n                \n                $$d_v$$\n                \n               on each vertex \n                \n                  \n                \n                $$v \\in V$$\n                \n              , and we require that every vertex v in the output tree has at most \n                \n                  \n                \n                $$d_v$$\n                \n               children. We give a quasi-polynomial time \n                \n                  \n                \n                $$(O(\\log n \\log k), O(\\log ^2 n))$$\n                \n              -bicriteria approximation: The Algorithm produces a solution with cost at most \n                \n                  \n                \n                $$O(\\log n\\log k)$$\n                \n               times the cost of the optimum solution that violates the degree constraints by at most a factor of \n                \n                  \n                \n                $$O(\\log ^2n)$$\n                \n              . This is the first non-trivial result for the problem. While our cost-guarantee is nearly optimal, the degree violation factor of \n                \n                  \n                \n                $$O(\\log ^2n)$$\n                \n               is an \n                \n                  \n                \n                $$O(\\log n)$$\n                \n              -factor away from the approximation lower bound of \n                \n                  \n                \n                $$\\Omega (\\log n)$$\n                \n               from the set-cover hardness. The hardness result holds even on the special case of the Degree-Bounded Group Steiner Tree problem on trees (DB-GST-T). With the hope of closing the gap, we study the question of whether the degree violation factor can be made tight for this special case. We answer the question in the affirmative by giving an \n                \n                  \n                \n                $$(O(\\log n\\log k), O(\\log n))$$\n                \n              -bicriteria approximation Algorithm for DB-GST-T.",{"EN":1091},"On Approximating Degree-Bounded Network Design Problems",{"VOID":1093},"[\"17486595449712144114\"]",{"VOID":1095},"Bartal, Yair: Probabilistic approximations of metric spaces and its algorithmic applications. In: 37th Annual Symposium on Foundations of Computer Science, FOCS ’96, Burlington, Vermont, USA, 14-16 October, 1996, pp. 184–193, (1996)\nCharikar, Moses, Chekuri, Chandra, Cheung, To-Yat., Dai, Zuo, Goel, Ashish, Guha, Sudipto, Li, Ming: Approximation algorithms for directed steiner problems. J. Algorithms 33(1), 73–91 (1999)\nDehghani, Sina, Ehsani, Soheil, Hajiaghayi, Mohammad Taghi, Liaghat, Vahid, Räcke, Harald, Seddighin, Saeed: Online weighted degree-bounded steiner networks via novel online mixed packing\u002Fcovering. In: 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016, July 11-15, 2016, Rome, Italy, pp. 42:1–42:14, (2016)\nDehghani, Sina, Ehsani, Soheil, Hajiaghayi, MohammadTaghi, Liaghat, Vahid: Online degree-bounded steiner network design. In: Proceedings of the Twenty-seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’16, pp. 164–175, Philadelphia, PA, USA, Society for Industrial and Applied Mathematics. (2016)\nDehghani, Sina, Ehsani, Soheil, Hajiaghayi, MohammadTaghi, Liaghat, Vahid, Seddighin, Saeed: Greedy algorithms for online survivable network design. In: 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018, July 9-13, 2018, Prague, Czech Republic, pp. 152:1–152:14 (2018)\nFakcharoenphol, Jittat, Rao, Satish, Talwar, Kunal: A tight bound on approximating arbitrary metrics by tree metrics. J. Comput. Syst. Sci. 69(3), 485–497 (2004)\nFriggstad, Zachary, Könemann, Jochen, Kun-Ko, Young, Louis, Anand, Shadravan, Mohammad, Tulsiani, Madhur: Linear programming hierarchies suffice for directed steiner tree. In: Integer Programming and Combinatorial Optimization - 17th International Conference, IPCO 2014, Bonn, Germany, June 23-25, 2014. Proceedings, pp. 285–296 (2014)\nFürer, Martin, Raghavachari, Balaji: Approximating the minimum-degree steiner tree to within one of optimal. J. Algorithms 17(3), 409–423 (1994)\nGarg, Naveen, Konjevod, Goran, Ravi, R.: A polylogarithmic approximation algorithm for the group steiner tree problem. J. Algorithms 37(1), 66–84 (2000)\nGhuge, Rohan, Nagarajan, Viswanath: A quasi-polynomial algorithm for submodular tree orienteering in directed graphs. CoRR, arXiv:abs\u002F1812.01768, (2018)\nGoemans, Michel X.: Minimum bounded degree spanning trees. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, FOCS ’06, pp. 273–282, Washington, DC, USA, IEEE Computer Society (2006)\nGrandoni, Fabrizio, Laekhanukit, Bundit, Li, Shi: O(log\\({}^{\\text{2}}\\)k \u002F log log k)-approximation algorithm for directed steiner tree: a tight quasi-polynomial-time algorithm. In: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019, Phoenix, AZ, USA, June 23-26, 2019, pp. 253–264 (2019)\nHajiaghayi, Mohammad Taghi: Open problems on bounded-degree network design from 8-th workshop on flexible network design, amsterdam, 2016. Announcement, (2016)\nHalperin, Eran, Krauthgamer, Robert: Polylogarithmic inapproximability. In: Lawrence L. Larmore and Michel X. Goemans (eds.) Proceedings of the 35th Annual ACM Symposium on Theory of Computing. San Diego, CA, USA, ACM. pp. 585–594 (2003)\nKönemann, Jochen, Ravi, R.: A matter of degree: Improved approximation algorithms for degree-bounded minimum spanning trees. SIAM J. Comput. 31(6), 1783–1793 (2002)\nKönemann, Jochen, Ravi, R.: Quasi-polynomial time approximation algorithm for low-degree minimum-cost steiner trees. In: FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science, 23rd Conference, Mumbai, India, December 15-17, 2003, Proceedings, pp. 289–301, (2003)\nKönemann, Jochen, Ravi, R.: Primal-dual meets local search: Approximating msts with nonuniform degree bounds. SIAM J. Comput. 34(3), 763–773 (2005)\nKortsarz, Guy, Nutov, Zeev: Bounded degree group steiner tree problems. In: IWOCA’20, to appear, (2020)\nLau, Lap Chi, Naor, Joseph, Salavatipour, Mohammad R., Singh, Mohit: Survivable network design with degree or order constraints. SIAM J. Comput. 39(3), 1062–1087 (2009)\nLau, Lap Chi, Singh, Mohit: Additive approximation for bounded degree survivable network design. SIAM J. Comput. 42(6), 2217–2242 (2013)\nRavi, R., Marathe, Madhav V., Ravi, S. S., Rosenkrantz, Daniel J., Hunt III, Harry B.: Many birds with one stone: multi-objective approximation algorithms. In: Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, May 16-18, 1993, San Diego, CA, USA, pp. 438–447, (1993)\nRothvoß, Thomas: Directed steiner tree and the lasserre hierarchy. CoRR, arXiv:abs\u002F1111.5473, (2011)\nSingh, Mohit, Lau, Lap Chi: Approximating minimum bounded degree spanning trees to within one of optimal. J. ACM 62(1), 1.1-1.19 (2015)\nZelikovsky, Alexander: A series of approximation algorithms for the acyclic directed steiner tree problem. 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In: IFIP Congress, pp. 839–842 (1977)",{},{"id":20,"text":1536,"url":20,"identifiers":1537},"Gronemeier, A.: Asymptotically optimal lower bounds on the NIH-multi-party information complexity of the AND-function and disjointness. In: Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science, pp. 505–516 (2009)",{},{"id":20,"text":1539,"url":20,"identifiers":1540},"Harsha, P., Jain, R., McAllester, D., Radhakrishnan, J.: The communication complexity of correlation. In: Proceedings of the 22nd Annual IEEE Conference on Computational Complexity, pp. 10–23 (2007)",{"doi":1541},"10.1109\u002FCCC.2007.32",{"id":20,"text":1543,"url":20,"identifiers":1544},"Håstad, J., Wigderson, A.: The randomized communication complexity of set disjointness. Theory Comput. 3(1), 211–219 (2007)",{"doi":1545},"10.4086\u002Ftoc.2007.v003a011",{"id":20,"text":1547,"url":20,"identifiers":1548},"Jain, R.: New strong direct product results in communication complexity. Electron. Colloq. Comput. Complex. (ECCC) 18, 24 (2011)",{},{"id":20,"text":1550,"url":20,"identifiers":1551},"Jain, R., Pereszlényi, A., Yao, P.: A direct product theorem for the two-party bounded-round public-coin communication complexity. In: Proceedings of the 53rd Annual IEEE Symposium on Foundations of Computer Science, pp. 167–176 (2012)",{"doi":1552},"10.1109\u002FFOCS.2012.42",{"id":20,"text":1554,"url":20,"identifiers":1555},"Jain, R., Sen, P., Radhakrishnan, J.: Optimal direct sum and privacy trade-off results for quantum and classical communication complexity. CoRR (2008). arXiv:0807.1267",{},{"id":20,"text":1557,"url":20,"identifiers":1558},"Kalyanasundaram, B., Schnitger, G.: The probabilistic communication complexity of set intersection. SIAM J. Discret. Math. 5(4), 547–557 (1992)",{"doi":1559},"10.1137\u002F0405044",{"id":20,"text":1561,"url":20,"identifiers":1562},"Kane, D.M., Nelson, J., Woodruff, D.P.: On the exact space complexity of sketching and streaming small norms. 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ACM 32(3), 652–686, 1985] roughly states that searching for an element is fast if the element was accessed recently. Binary search trees, such as splay trees, can achieve this property in the amortized sense, while data structures that are not binary search trees are known to have this property in the worst case. We close this gap and present a binary search tree called a layered working-set tree that guarantees the working-set property in the worst case. The unified bound [Bădoiu et al. in Theor. Comput. Sci. 382(2), 86–96, 2007] roughly states that searching for an element is fast if it is near (in terms of rank distance) to a recently accessed element. We show how layered working-set trees can be used to achieve the unified bound to within a small additive term in the amortized sense while maintaining in the worst case an access time that is both logarithmic and within a small multiplicative factor of the working-set bound.",{"EN":1640},"Layered Working-Set Trees",{"VOID":1642},"[\"13925496893220304098\"]",{"VOID":1644},"Bădoiu, M., Cole, R., Demaine, E.D., Iacono, J.: A unified access bound on comparison-based dynamic dictionaries. Theor. Comput. Sci. 382(2), 86–96 (2007)\nBayer, R.: Symmetric binary B-trees: Data structures and maintenance algorithms. Acta Inform. 1, 290–306 (1972)\nCole, R.: On the dynamic finger conjecture for splay trees. Part II: The proof. SIAM J. Comput. 30(1), 44–85 (2000)\nCole, R., Mishra, B., Schmidt, J., Siegel, A.: On the dynamic finger conjecture for splay trees. Part I: Splay sorting log n-block sequences. SIAM J. Comput. 30(1), 1–43 (2000)\nCormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)\nDerryberry, J.C., Sleator, D.D.: Skip-splay: Toward achieving the unified bound in the BST model. In: WADS ’09: Proceedings of the 16th Annual International Workshop on Algorithms and Data Structures (2009)\nGuibas, L.J., Sedgewick, R.: A dichromatic framework for balanced trees. In: FOCS ’78: Proceedings of the 19th Annual IEEE Symposium on Foundations of Computer Science, pp. 8–21 (1978)\nSleator, D.D., Tarjan, R.E.: Self-adjusting binary search trees. J. ACM 32(3), 652–686 (1985)\nTarjan, R.E.: Data Structures and Network Algorithms. Society for Industrial and Applied Mathematics, Philadelphia (1983)\nWilber, R.: Lower bounds for accessing binary search trees with rotations. SIAM J. 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maximal common subsequence (MCS) between two strings X and Y is an inclusion-maximal subsequence of both X and Y. MCSs are a natural generalization of the classical concept of longest common subsequence (LCS), which can be seen as a longest MCS. We study the problem of efficiently listing all the distinct MCSs between two strings. As discussed in the paper, this problem is algorithmically challenging as the same MCS cannot be listed multiple times: for example, dynamic programming [Fraser et al., CPM 1998] incurs in an exponential waste of time, and a recent algorithm for finding an MCS [Sakai, CPM 2018] does not seem to immediately extend to listing. We follow an alternative and novel graph-based approach, proposing the first output-sensitive algorithm for this problem: it takes polynomial time in n per MCS found, where $$n = \\max \\{ |X|, |Y|\\}$$ , with polynomial preprocessing time and space.",{"EN":1780},"Enumeration of Maximal Common Subsequences Between Two 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