Coloring random and semi-random k-colorable graphs
Journal of Algorithms
Approximating the independence number via the j -function
Mathematical Programming: Series A and B
Heuristics for semirandom graph problems
Journal of Computer and System Sciences
Minimum coloring random and semi-random graphs in polynomial expected time
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Derandomizing semidefinite programming based approximation algorithms
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximate graph coloring by semidefinite programming
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Finding Large Independent Sets in Polynomial Expected Time
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
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The analysis of algorithms on semirandom graph instances intermediates smoothly between the analysis in the worst case and the average case. The aim of this paper is to present an algorithm for finding a large independent set in a semirandom graph in polynomial expected time, thereby extending the work of Feige and Kilian [4]. In order to preprocess the input graph, the algorithm makes use of SDP-based techniques. The analysis of the algorithm shows that not only is the expected running time polynomial, but even arbitrary moments of the running time are polynomial in the number of vertices of the input graph. The algorithm for the independent set problem yields an algorithm for k-coloring semirandom k-colorable graphs, and for the latter algorithm a similar result concerning its running time holds, as also for the independent set algorithm. The results on both problems are essentially best-possible, by the hardness results obtained in [4].