A computationally intractable problem on simplicial complexes

Computational Geometry: Theory and Applications

Volumn 6, Issue 2, 1996, Pages 85-98

  Eǧecioǧlu, Ömer ^a   Gonzalez, Teofilo F ^a  

^a Santa Barbara   (United States)

Author keywords

Algorithmic complexity; Approximation algorithm; Betti number; Collapsing; Simplicial complex; Vertex cover

Indexed keywords

EID: 30244548249     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/0925-7721(95)00015-1     Document Type: Article

References (21)

1. S. Arora, C. Lund, R. Motwani, M. Sudan and M. Szegedy, Proof verification and intractability of approximation problems, Proc. 31st Symposium on Foundations of Computer Science (1992).
2. M. Bellare, S. Goldwasser, C. Lund and A. Russell, Efficient probabilistically checkable proofs and applications to approximation, Proc. 25th Annual Symposium on the Theory of Computing (1993) 294-304.
3. E. Borowsky and E. Gafni, Generalized FLP impossibility result for t-resilient asynchronous computations, Proc. 25th Annual Symposium on the Theory of Computing (1993) 91-100.
4. A. Björner and L. Lovász, Linear decision trees, subspace arrangements and Möbius functions, Preprint, 1992.
5. A. Björner, L. Lovász and A. C. Yao, Linear decision trees: volume estimates and topological bounds, Proc. 24th Annual Symposium on the Theory of Computing (1992) 170-177.
6. S.A. Cook, The complexity of theorem proving procedures, Proc. 3rd Annual Symposium on the Theory of Computing, Association for Computing Machinery, New York (1971) 151-158.
7. O. Eǧecioǧlu and T.F. Gonzalez, A computationally intractable problem on simplicial complexes, Tech. Rep. UCSB TRCS93-1, January 1993.
8. M.J. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (W.H. Freeman and Company, New York, 1979).
9. L.C. Glaser, Geometrical Combinatorial Topology, Vol. I (Van Nostrand Reinhold Company, New York, 1970).
10. T.F. Gonzalez, LP-free approximation algorithm for the minimum weight vertex cover problem, Information Processing Letters 54 (1995) 129-131.
11. D. Grigoriev, M. Karpinski and N. Vorobjov, Complexity lower bounds on testing membership to a polyhedron by algebraic decision trees, Proc. 26th Annual Symposium on the Theory of Computing (1994) 635-643.
12. M. Herlihy and N. Shavit, The asynchronous computability theorem for t-resilient tasks, Proc. 25th Annual Symposium on the Theory of Computing (1993) 111-120.
13. J.G. Hocking and G.S. Young, Topology (Addison-Wesley, Reading, MA, 1961).
14. R.M. Karp, Reducibility among combinatorial problems, in: R.E. Miller and J.W. Thatcher, eds., Complexity of Computer Computations (Plenum, 1972) 85-103.
15. S. Lefschetz, Introduction to Topology (Princeton University Press, New Jersey, 1949).
16. C. Lund and M. Yannakakis, On the hardness of approximating minimization problems, Proc. 25th Annual Symposium on the Theory of Computing (1993) 286-293.
17. W.S. Massey, Algebraic Topology: An Introduction (Harcourt-Brace, New York, 1967).
18. J.R. Munkres, Elements of Algebraic Topology (Addison-Wesley, Menlo Park, 1984).
19. M. Saks and F. Zaharoglou, Wait-free k-set agreement is impossible: the topology of public knowledge, Proc. 25th Annual Symposium on the Theory of Computing (1993) 101-110.
20. A.C. Yao, Algebraic decision trees and Euler characteristics, Proc. 33rd Symposium on Foundations of Computer Science (1992) 268-277.
21. A.C. Yao, Decision tree complexity and Betti numbers, Proc. 26th Annual Symposium on the Theory of Computing (1994) 615-624.