Computing optimal Morse matchings

SIAM Journal on Discrete Mathematics

Volumn 20, Issue 1, 2006, Pages 11-25

  Joswig, Michael ^a   Pfetsch, Marc E ^b  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

^b ZUSE INSTITUTE BERLIN   (Germany)

Author keywords

Discrete Morse function; Morse matching

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; INTEGER PROGRAMMING; OPTIMAL SYSTEMS; PROBLEM SOLVING;

DISCRETE MORSE FUNCTIONS; MORSE FUNCTIONS; MORSE MATCHING; POLYHEDRAL RESULTS;

FUNCTIONAL ANALYSIS;

EID: 33847612091     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480104445885     Document Type: Article

References (31)

1. T. ACHTERBERG, SCIP-A framework to integrate constraint and mixed integer programming, ZIB-Report 04-19, Zuse Institute Berlin, Berlin, Germany, 2004.
2. T. ACHTERBERG, T. KOCH, AND A. MARTIN, Branching rules revisited, Oper. Res. Lett., 33 (2005), pp. 42-54.
3. E. BABSON, A. BJÖRNER, S. LINUSSON, J. SHARESHIAN, AND V. WELKER, Complexes of not i-connected graphs, Topology, 38 (1999), pp. 271-299.
4. E. BATZIES AND V. WELKER, Discrete Morse theory for cellular resolutions, 3. Reine Angew. Math., 543 (2002), pp. 147-168.
5. M. K. CHARI, On discrete Morse functions and combinatorial decompositions, Discrete Math., 217 (2000), pp. 101-113.
6. M. K. CHARI AND M. JOSWIG, Complexes of discrete Morse functions, Discrete Math., 302 (2005), pp. 39-51.
7. Ö. EǦECIOG̀LU AND T. F. GONZALEZ, A computationally intractable problem on simplicial complexes, Comput. Geom., 6 (1996), pp. 85-98.
8. R. FORMAN, Morse theory for cell complexes, Adv. Math., 134 (1998), pp. 90-145.
9. R. FORMAN, Morse theory and evasiveness, Combinatorica, 20 (2000), pp. 489-504.
10. R. FORMAN, A user's guide to discrete Morse theory, Sém. Lothar. Combin., 48 (2002), pp. Art. B48c, 35 pp.
11. E. GAWRILOW AND M. JOSWIG, polymake: a framework for analyzing convex polytopes, in Polytopes-Combinatorics and Computation, G. Kalai and G. M. Ziegler, eds., DMV Sem. 29, Birkhäuser, Basel, Switzerland, 2000, pp. 43-73.
12. E. GAWRILOW AND M. JOSWIG, polymake: Version 2.1.0, http://www.math.tu-berlin.de/polymake, 2004. With contributions by T. Schröder and N. Witte.
13. M. GRÖTSCHEL, M. JÜNGER, AND G. REINELT, A cutting plane algorithm for the linear ordering problem, Oper. Res., 32 (1984), pp. 1195-1220.
14. M. GRÖTSCHEL, M. JÜNGER, AND G. REINELT, On the acyclic subgraph polytope, Math. Programing, 33 (1985), pp. 28-42.
15. M. HACHIMORI, Simplicial complex library. Available online from http://infoshako.sk.tsukuba.ac.jp/hachi/math/library/index_eng.html, 2001.
16. P. L. HAMMER, E. L. JOHNSON, AND U. N. PELED, Facets of regular 0-1 polytopes, Math. Programing, 8 (1975), pp. 179-206.
17. P. HERSH, On optimizing discrete Morse functions, Adv. in Appl. Math., 35 (2005), pp. 294-322.
18. C. S. ILIOPOULOS, Worst-case complexity bounds on algorithms for computing the canonical structure of finite Abelian groups and the Hermite and Smith normal forms of an integer matrix, SIAM J. Comput., 18 (1989), pp. 658-669.
19. J. JONSSON, On the topology of simplicial complexes related to 3-connected and Hamiltonian graphs, J. Combin. Theory Ser. A, 104 (2003), pp. 169-199.
20. M. JOSWIG, Computing invariants of simplicial manifolds, preprint. Available online from math.AT/0401176, 2004.
21. M. JÜNGER, Polyhedral Combinatorics and the Acyclic Subdigraph Problem, Research and Exposition in Mathematics, 7, Heldermann Verlag, Berlin, 1985.
22. B. KORTE AND J. VYGEN, Combinatorial optimization. Theory and algorithms, 2nd ed., Algorithms and Combinatorics, 21, Springer-Verlag, Berlin, 2002.
23. T. LEWINER, H. LOPES, AND G. TAVARES, Optimal discrete Morse functions for 2-manifolds, Comput. Geom., 26 (2003), pp. 221-233.
24. T. LEWINER, H. LOPES, AND G. TAVARES, Towards optimality in discrete Morse theory, Experiment Math., 12 (2003), pp. 271-285.
25. F. H. LUTZ, Small examples of nonconstructible simplicial balls and spheres, SIAM J. Discrete Math, 18 (2004), pp. 103-109.
26. F. H. LUTZ, A vertex-minimal nonshellable simplicial 3-ball with 9 vertices and 18 facets, Electronic Geometry Models, (2004). Available online from www.eg-models.de.
27. J. R. MUNKRES, Elements of Algebraic Topology, Addison-Wesley, Menlo Park, CA, 1984.
28. G. REINELT, The Linear Ordering Problem: Algorithms and Applications, Research and Exposition in Mathematics, 8, Heldermann Verlag, Berlin, 1985.
29. A. SCHRIJVER, Combinatorial Optimization: Polyhedra and Efficiency, Algorithms and Combinatorics, 24, Springer-Verlag, Berlin, 2003.
30. J. SHARESHIAN, Discrete Morse theory for complexes of 2-connected graphs, Topology, 40 (2001), pp. 681-701.
31. D. M. WARME, P. WINTER, AND M. ZACHARIASEN, Exact solutions to large-scale plane steiner tree problems, in Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 1999, pp. 979-980.