Abstract
We consider instances of the maximum independent set problem that are constructed according to the following semirandom model. First, let G n,p be a random graph, and let S be a set consisting of k vertices, chosen uniformly at random. Then, let G 0 be the graph obtained by deleting all edges connecting two vertices in S. Adding to G 0 further edges that do not connect two vertices in S, an adversary completes the instance G = G. n,p,k . We propose an algorithm that in the case k ≥C(n/p) 1/2 on input G within polynomial expected time finds an independent set of size ≥ k.
Research supported by the Deutsche Forschungsgemeinschaft (grant DFG FOR 413/1-1)
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References
Alon, N., Kahale, N.: Approximating the independence number via the φ-function. Math. Programming 80 (1998) 253–264.
Alon, N., Krivelevich, M., Sudakov, B.: Finding a large hidden clique in a random graph. Random Structures & Algorithms 13 (1998) 457–466
Alon, N., Krivelevich, M., Vu, V.H.: On the concentration of the eigenvalues of random symmetric matrices. to appear in Israel J. of Math.
Blum, A., Spencer, J.: Coloring random and semirandom k-colorable graphs. J. of Algorithms 19(2) (1995) 203–234
Bollobás, B.: Random graphs, 2nd edition. Cambridge University Press (2001)
Coja-Oghlan, A.: Finding sparse induced subgraphs of semirandom graphs. Proc. 6. Int. Workshop RANDOM (2002) 139–148
Coja-Oghlan, A.: Coloring k-colorable semirandom graphs in polynomial expected time via semidefinite programming, Proc. 27th Int. Symp. on Math. Found. of Comp. Sci. (2002) 201–211
Coja-Oghlan, A., Taraz, A.: Colouring random graphs in expected polynomial time. To appear in STACS 2003.
Feige, U., Kilian, J.: Heuristics for semirandom graph problems. J. Comput. and System Sci. 63 (2001) 639–671
Feige, U., Krauthgamer, J.: Finding and certifying a large hidden clique in a semirandom graph. Random Structures & Algorithms 16 (2000) 195–208
Frieze, A., McDiarmid, C.: Algorithmic theory of random graphs. Random Structures & Algorithms 10 (1997) 5–42
Füredi, Z., Komloś, J.: The eigenvalues of random symmetric matrices, Combinatorica 1 (1981) 233–241
Grötschel, M., Lovász, L., Schrijver, A.: Geometric algorithms and combinatorial optimization. Springer (1988) ai]14._Håstad, J.: Clique is hard to approximate within n 1-∈. Proc. 37th Annual Symp. on Foundations of Computer Science (1996) 627–636
Janson, S., Luczak, T., Ruciński, A.: Random Graphs. Wiley (2000)
Jerrum, M.: Large cliques elude the metropolis process. Random Structures & Algorithms 3 (1992) 347–359
Juhász, F.: The asymptotic behaviour of Lovász. function for random graphs. Combinatorica 2 (1982) 269–280
Karger, D., Motwani, R., Sudan, M.: Approximate graph coloring by semide finite programming. J. Assoc. Comput. Mach. 45 (1998) 246–265
Karp, R.: Reducibility among combinatorial problems. Miller, R.E., Thatcher, J.W. (eds.): Complexity of Computer Computations. Plenum Press (1972) 85–103
Karp, R.: Probabilistic analysis of some combinatorial search problems. Traub, J.F. (ed.): Algorithms and complexity: New Directions and Recent Results. Academic Press (1976) 1–19
Knuth, D.: The sandwich theorem, Electron. J. Combin. 1 (1994)
Kuĉera, L.: Expected complexity of graph partitioning problems. Discrete Applied Math. 57 (1995) 193–212
Krivelevich, M., Vu, V.H.: Approximating the independence number and the chromaticnumber in expected polynomial time. J. of Combinatorial Optimization 6 (2002) 143–155
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Coja-Oghlan, A. (2003). Finding Large Independent Sets in Polynomial Expected Time. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_45
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DOI: https://doi.org/10.1007/3-540-36494-3_45
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