论文信息 - NP-Completeness of Non-Adjacency Relations on Some 0-1 Polytopes

NP-Completeness of Non-Adjacency Relations on Some 0-1 Polytopes

In this paper, we discuss the adjacency structures of some classes of 0-1 polytopes including knapsack polytopes, set covering polytopes and 0-1 polytopes represented by complete sets of implicants. We show that for each class of 0-1 polytope, non-adjacency test problems are NP-complete. For equality constrained knapsack polytopes, we can solve adjacency test problems in pseudo polynomial time.

Tomomi Matsui | Tomomi Matsui

[1] R. Bellman. Notes on the theory of dynamic programming IV ‐ Maximization over discrete sets , 1955 .

[2] Egon Balas,et al. On the Set-Covering Problem , 1972, Oper. Res..

[3] M. R. Rao,et al. The travelling salesman problem and a class of polyhedra of diameter two , 1974, Math. Program..

[4] Egon Balas,et al. On the Set-Covering Problem: II. An Algorithm for Set Partitioning , 1972, Oper. Res..

[5] V. Chvátal. On certain polytopes associated with graphs , 1975 .

[6] Richard A. Brualdi,et al. The assignment polytope , 1976, Math. Program..

[7] E. Balas,et al. Set Partitioning: A survey , 1976 .

[8] Christos H. Papadimitriou,et al. The adjacency relation on the traveling salesman polytope is NP-Complete , 1978, Math. Program..

[9] Bernhard Korte,et al. Colouring criteria for adjacency on 0–1-polyhedra , 1978 .

[10] David S. Johnson,et al. Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[11] Dirk Hausmann. Adjacency on Polytopes in Combinatorial Optimization , 1980 .

[12] George L. Nemhauser,et al. Simplex pivots on the set packing polytope , 1985, Math. Program..

[13] Tomomi Matsui,et al. Adjacency on Combinatorial Polyhedra , 1995, Discret. Appl. Math..

[14] Akihisa Tamura,et al. Ideal polytopes and face structures of some combinatorial optimization problems , 1995, Math. Program..