Shortest path problem in rectangular complexes of global nonpositive curvature

Ahuja, 1993 Bandelt, 1985, Networks with Condorcet solutions, European J. Oper. Res., 20, 314, 10.1016/0377-2217(85)90004-9 Bandelt, 2008, Metric graph theory and geometry: a survey, vol. 453, 49 Bandelt, 2010, Combinatorics and geometry of finite and infinite squaregraphs, SIAM J. Discrete Math., 24, 1399, 10.1137/090760301 Bandelt Bandelt, 1983, Median algebras, Discrete Math., 45, 1, 10.1016/0012-365X(83)90173-5 Bandelt, 1989, Embedding topological median algebras in products of dendrons, Proc. Lond. Math. Soc., 58, 439, 10.1112/plms/s3-58.3.439 Billera, 2001, Geometry of the space of phylogenetic trees, Adv. in Appl. Math., 27, 733, 10.1006/aama.2001.0759 Birkhoff, 1937, Rings of sets, Duke Math. J., 3, 443, 10.1215/S0012-7094-37-00334-X Birkhoff, 1947, A ternary operation in distributive lattices, Bull. Amer. Math. Soc., 52, 749, 10.1090/S0002-9904-1947-08864-9 Bridson, 1999 Chazelle, 1991, Triangulating a simple polygon in linear time, Discrete Comput. Geom., 6, 485, 10.1007/BF02574703 Chakerian Chatterji, 2010, Kazhdan and Haagerup properties from the median viewpoint, Adv. Math., 225, 882, 10.1016/j.aim.2010.03.012 Chepoi, 2000, Graphs of some CAT(0) complexes, Adv. in Appl. Math., 24, 125, 10.1006/aama.1999.0677 V. Chepoi, F. Dragan, Y. Vaxès, Center and diameter problem in planar quadrangulations and triangulations, in: Proc. 13th Annu. ACM–SIAM Symp. on Discrete Algorithms (SODA 2002), pp. 346–355. Chepoi, 2006, Distance and routing problems in plane graphs of non-positive curvature, J. Algorithms, 61, 1, 10.1016/j.jalgor.2004.07.011 Cheng, 2012, A poset-based approach to embedding median graphs in hypercubes and lattices, Order, 29, 147, 10.1007/s11083-011-9203-7 Cheng, 2011, Weak sense of direction labellings and graph embeddings, Discrete Appl. Math., 159, 303, 10.1016/j.dam.2010.12.012 de Berg, 2008 Dilworth, 1950, A decomposition theorem for partially ordered sets, Ann. of Math., 51, 161, 10.2307/1969503 Eppstein, 2005, The lattice dimension of a graph, European J. Combin., 26, 585, 10.1016/j.ejc.2004.05.001 Eppstein, 2007 Fletcher Ghrist, 2006, Nonpositive curvature and Pareto-optimal coordination of robots, SIAM J. Control Optim., 45, 1697, 10.1137/040609860 Ghrist, 2007, The geometry and topology of reconfiguration, Adv. in Appl. Math., 38, 302, 10.1016/j.aam.2005.08.009 Gromov, 1987, Hyperbolic groups, vol. 8, 75 Guibas, 1989, Optimal shortest path queries in a simple polygon, J. Comput. System Sci., 39, 126, 10.1016/0022-0000(89)90041-X Guibas, 1987, Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons, Algorithmica, 2, 209, 10.1007/BF01840360 Harel, 1984, Fast algorithms for finding nearest common ancestors, SIAM J. Comput., 13, 338, 10.1137/0213024 Hershberger, 1994, Computing minimum length paths of a given homotopy class, Comput. Geom. Theory Appl., 4, 63, 10.1016/0925-7721(94)90010-8 Hershberger, 1999, An optimal algorithm for Euclidean shortest paths in the plane, SIAM J. Comput., 28, 2215, 10.1137/S0097539795289604 Imrich, 2000 Larson, 1998, Embeddings of finite distributive lattices into products of chains, Semigroup Forum, 56, 70, 10.1007/s00233-002-7005-3 Lee, 1984, Euclidean shortest paths in the presence of rectilinear barriers, Networks, 14, 393, 10.1002/net.3230140304 Mitchell, 1996, Shortest paths among obstacles in the plane, Internat. J. Comput. Geom. Appl., 6, 309, 10.1142/S0218195996000216 Mitchell, 2000, Geometric shortest paths and network optimization, 633 Mulder, 1978, The structure of median graphs, Discrete Math., 24, 197, 10.1016/0012-365X(78)90199-1 Mulder, 1980, The Interval Function of a Graph, vol. 132 Nica, 2004, Cubulating spaces with walls, Algebr. Geom. Topol., 4, 297, 10.2140/agt.2004.4.297 Owen, 2011, A fast algorithm for computing geodesic distances in tree space, IEEE/ACM Trans. Comput. Biol. Bioinf., 8, 2, 10.1109/TCBB.2010.3 Reif, 1994, Shortest paths in the plane with polygonal obstacles, J. ACM, 41, 982, 10.1145/185675.185795 M. Roller, Poc sets, median algebras and group actions, preprint, Univ. of Southampton, 1998. Sageev, 1995, Ends of group pairs and non-positively curved cube complexes, Proc. Lond. Math. Soc., 71, 585, 10.1112/plms/s3-71.3.585 van de Vel, 1993