Geodesics in CAT(0) cubical complexes
作者： Federico Ardila , Megan Owen , Seth Sullivant
DOI: 10.1016/J.AAM.2011.06.004
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摘要: We describe an algorithm to compute the geodesics in arbitrary CAT(0) cubical complex. A key tool is a correspondence between complexes of global non-positive curvature and posets with inconsistent pairs. This also gives explicit realization such complex as state reconfigurable system, way embed any interval integer lattice cubing its dimension.
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birs.ca 参考文章(23)
Nathan Reading, Order Dimension, Strong Bruhat Order and Lattice Properties for Posets Order. ,vol. 19, pp. 73- 100 ,(2002) , 10.1023/A:1015287106470
J. Scott Provan, Megan Owen, Ezra Miller, Averaging metric phylogenetic trees arXiv: Metric Geometry. ,(2012)
Joseph S. B. Mitchell, Valentin Polishchuk, Touring Convex Bodies - A Conic Programming Solution. canadian conference on computational geometry. pp. 290- 293 ,(2005)
S. M. Gersten, Essays in Group Theory ,(2011)
Fajie Li, Reinhard Klette, Shortest Paths in a Cuboidal World Lecture Notes in Computer Science. pp. 415- 429 ,(2006) , 10.1007/11774938_33
Joseph S.B. Mitchell, Chapter 15 – Geometric Shortest Paths and Network Optimization Handbook of Computational Geometry. pp. 633- 701 ,(2000) , 10.1016/B978-044482537-7/50016-4
Louis J. Billera, Karen Vogtmann, Susan P. Holmes, Geometry of the space of phylogenetic trees ,(2000)
Robert Ghrist, Steven M. Lavalle, Nonpositive Curvature and Pareto Optimal Coordination of Robots Siam Journal on Control and Optimization. ,vol. 45, pp. 1697- 1713 ,(2006) , 10.1137/040609860
Michah Sageev, Ends of Group Pairs and Non-Positively Curved Cube Complexes Proceedings of the London Mathematical Society. ,vol. s3-71, pp. 585- 617 ,(1995) , 10.1112/PLMS/S3-71.3.585
R. P. Dilworth, A Decomposition Theorem for Partially Ordered Sets Classic Papers in Combinatorics. ,vol. 51, pp. 139- 144 ,(2009) , 10.1007/978-0-8176-4842-8_10