Annotating simplices with a homology basis and its applications

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 7357 LNCS, Issue , 2012, Pages 189-200

  Busaryev, Oleksiy ^a   Cabello, Sergio ^b   Chen, Chao ^c   Dey, Tamal K ^a   Wang, Yusu ^a  

^a The Ohio State University   (United States)

^b UNIVERSITY OF LJUBLJANA   (Slovenia)

^c INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA   (Austria)

Author keywords

homology basis; matrix multiplication; optimal cycles; Simplicial complex; topology

Indexed keywords

ANSWERING QUERIES; BINARY VECTORS; COORDINATE VECTORS; HOMOLOGY BASIS; MATRIX MULTIPLICATION; NP-HARD; OPTIMAL BASIS; OPTIMAL CYCLES; P-CYCLES; SIMPLICIAL COMPLEX; TIME COMPLEXITY;

OPTIMIZATION; TOPOLOGY;

ALGORITHMS;

EID: 84863084755     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-31155-0_17     Document Type: Conference Paper

References (13)

1. Cabello, S., Colin de Verdière, É., Lazarus, F.: Finding cycles with topological properties in embedded graphs. SIAM J. Disc. Math. 25(4), 1600-1614 (2011)
2. Chambers, E., Erickson, J., Nayyeri, A.: Minimum cuts and shortest homologous cycles. In: Proc. ACM Symp. on Computational Geometry (SOCG), pp. 377-385 (2009)
3. Chen, C., Freedman, D.: Hardness results for homology localization. Discrete and Computational Geometry 45(3), 425-448 (2011)
4. Dey, T.K., Sun, J., Wang, Y.: Approximating loops in a shortest homology basis from point data. In: Proc. ACM Symp. on Computational Geometry (SOCG), pp. 166-175 (2010)
5. Erickson, J., Nayyeri, A.: Minimum cuts and shortest non-separating cycles via homology covers. In: Proc. ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 1166-1176 (2011)
6. Erickson, J., Whittlesey, K.: Greedy optimal homotopy and homology generators. In: Proc. ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 1038-1046 (2005)
7. Dey, T.K., Hirani, A., Krishnamoorthy, B.: Optimal homologous cycles, total unimodularity, and linear programming. SIAM J. Comput. 40, 1026-1044 (2011)
8. Coppersmith, D., Winograd, S.: Matrix multiplication via arithmetic progressions. J. Symb. Comput. 9(3), 251-280 (1990)
9. Chen, C., Freedman, D.: Quantifying homology classes. In: Proc. Symp. on Theoretical Aspects of Computer Science (STACS), pp. 169-180 (2008)
10. Italiano, G.F., Nussbaum, Y., Sankowski, P.,Wulff-Nilsen, C.: Improved algorithms for min cut and max flow in undirected planar graphs. In: Proc. ACM Symp. on Theory of Computing (STOC), pp. 313-322 (2011)
11. Bunch, J., Hopcroft, J.: Triangular factorization and inversion by fast matrix multiplication. Math. Comp. 28, 231-236 (1974)
12. Ibarra, O., Moran, S., Hui, R.: A generalization of the fast LUP matrix decomposition algorithm and applications. Journal of Algorithms 3(1), 45-56 (1982)
13. Jeannerod, C.: LSP matrix decomposition revisited (2006), http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2006/RR2006-28.pdf