Approximation algorithms for Median Hub Location Problems
Tóm tắt
In Hub Location Problems, an input is composed of sets of clients, locations and a pairs of clients; a solution is a subset of locations to open hubs and an assignment for each pair of clients to a route starting in the first client, passing through one or more hubs and ending in the second client. The objective is to find a solution that minimizes the length of all routes plus the cost of opening hubs. The currently known approximation algorithms consider only the case in which the set of hubs is given as part of the input and the problem is assigning clients to hubs. For a metric space setting, this work presents the first constant-factor approximation algorithms for the problem of, simultaneously, selecting hubs and allocating clients. A few variants are considered, depending on whether the number of open hubs is given in the input or a client must be assigned to a single hub. In particular, we give an LP-rounding
$$2.48$$
-approximation algorithm for the Single-Allocation Median Hub Location Problem, using a new formulation and exploiting its symmetries.
Tài liệu tham khảo
Ando R, Matsui T (2011) Algorithm for single allocation problem on hub-and-spoke networks in 2-dimensional plane. In: Algorithms and computation, pp 474–483
Byrka J, Aardal K (2010) An optimal bifactor approximation algorithm for the metric uncapacitated facility location problem. SIAM J Comput 39(6):2212–2231
Byrka J, Pensyl T, Rybicki B, Srinivasan A, Trinh K (2014) An improved approximation for \(k\)-median, and positive correlation in budgeted optimization. In: Proceedings of the twenty-sixth annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, pp 737–756
Chen L-H, Cheng D-W, Hsieh S-Y, Hung L-J, Lee C-W, Wu BY (2016) Approximation algorithms for the star \(k\)-hub center problem in metric graphs. Springer, Cham, pp 222–234
Farahani RZ, Hekmatfar M, Arabani AB, Nikbakhsh E (2013) Hub location problems: a review of models, classification, solution techniques, and applications. Comput Ind Eng 64(4):1096–1109
Ge D, He S, Ye Y, Zhang J (2010) Geometric rounding: a dependent randomized rounding scheme. J Comb Optim 22(4):699–725
Iwasa M, Saito H, Matsui T (2009) Approximation algorithms for the single allocation problem in hub-and-spoke networks and related metric labeling problems. Discrete Appl Math 157(9):2078–2088
Li S (2013) A 1.488 approximation algorithm for the uncapacitated facility location problem. Inf Comput 222(0):45–58
Liang H (2013) The hardness and approximation of the star-hub center problem. Oper Res Lett 41(2):138–141
Lin J-H, Vitter JS (1992) Approximation algorithms for geometric median problems. Inf Process Lett 44(5):245–249
O’Kelly ME (1986) The location of interacting hub facilities. Transp Sci 20(2):92–106
O’Kelly ME (1987) A quadratic integer program for the location of interacting hub facilities. Eur J Oper Res 32(3):393–404
Sohn J, Park S (2000) The single allocation problem in the interacting three-hub network. Networks 35(1):17–25
Zhang P (2007) A new approximation algorithm for the \(k\)-facility location problem. Theor Comput Sci 384(1):126–135