Local optimization on graphs. (English) Zbl 0675.90085

This paper is devoted to the study of the complexity of finding a local optimum of an arbitrary function over a neighborhood graph. Some kind of two-person game is introduced to yield an estimation of the amount of work needed to find a local optimum.
Reviewer: W.-X.Li


90C35 Programming involving graphs or networks
05C99 Graph theory
68Q25 Analysis of algorithms and problem complexity
91A05 2-person games
68W99 Algorithms in computer science
91A80 Applications of game theory
68R10 Graph theory (including graph drawing) in computer science
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[1] Aldous, D., Minimization algorithms and random walk on the \(d\)-cube, Tech. Rept., University of California, Berkeley, CA (1981)
[2] Beineke, L. W.; Harary, F., The genus of the \(n\)-cube, Canad. J. Math., 17, 494-496 (1965) · Zbl 0127.13801
[3] Danzer, L.; Klee, V., Lengths of snakes in boxes, J. Combinat. Theory, 2, 258-265 (1967) · Zbl 0153.54202
[4] Djidjev, H., On the problem of partitioning planar graphs, SIAM J. Alg. Dis. Meth., 229-240 (1982) · Zbl 0503.05057
[5] Dobkin, D.; Lipton, R., Multidimensional searching problems, SIAM J. Comput., 5, 2, 181-186 (1976) · Zbl 0333.68031
[6] Feller, W., (An Introduction to Probability Theory and Its Applications, 1 (1971), Wiley: Wiley New York) · Zbl 0138.10207
[7] Garey, M.; Johnson, D., Computers and Intractibility: A Guide to the Theory of NP-Completeness (1979), Freeman: Freeman San Francisco, CA
[8] Gilbert, J. R.; Hutchinson, J. P.; Tarjan, R. E., A separator theorem for graphs of bounded genus, J. Algorithms, 5, 3, 391-407 (1984) · Zbl 0556.05022
[9] Hausmann, D.; Korte, B., Lower bounds on the worst-case complexity of some oracle algorithms, Discrete Math., 24, 261-276 (1978) · Zbl 0392.68036
[10] Johnson, D.; Papadimitriou, C.; Yannakakis, M., How easy is local search?, (Proceeding IEEE Symposium on the Foundations of Computer Science (1985)), 39-42
[12] Lipton, R.; Rose, D.; Tarjan, R., Generalized nested dissection, SIAM J. Numer. Anal., 16, 2, 346-358 (1979) · Zbl 0435.65021
[13] Murty, K. G.; Kabadi, S. N., Some NP-complete problems in quadratic and nonlinear programming, Math. Programming, 39, 2, 117-130 (1987) · Zbl 0637.90078
[14] Nemhauser, G.; Wolsey, L., Best algorithms for approximating the maximum of a submodular set function, Math. Oper. Res., 3, 177-188 (1978) · Zbl 0395.90072
[15] Papadimitriou, C.; Steiglitz, K., Combinatorial Optimization: Algorithms and Complexity (1982), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0503.90060
[16] Ringel, G., Das Geschlecht des Vollständigen Paaren Graphen, A.B.H. Math. Sem. Univ. Hamburg, 28, 139-150 (1965) · Zbl 0132.21203
[17] Tovey, C. A., A simplified NP-complete satisfiability problem, Discrete Appl. Math., 8, 85-89 (1984) · Zbl 0534.68028
[18] Tovey, C. A., Low order polynomial bounds on the expected performance of local improvement algorithms, Math. Programming, 35, 2, 193-224 (1986) · Zbl 0613.90065
[19] Wood, G. R., Multidimensional bisection and global minimization, Tech. Rept., University of Canterbury (1985)
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