The solution of some random NP-hard problems in polynomial expected time
Journal of Algorithms
The greedy coloring is a bad probabilistic algorithm
Journal of Algorithms
Sudden emergence of a giant k-core in a random graph
Journal of Combinatorial Theory Series B
Algorithmic theory of random graphs
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
Information Processing Letters
Smallest-last ordering and clustering and graph coloring algorithms
Journal of the ACM (JACM)
Heuristics for semirandom graph problems
Journal of Computer and System Sciences
Finding Sparse Induced Subgraphs of Semirandom Graphs
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Coloring Random Graphs in Polynomial Expected Time
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
Finding Large Independent Sets in Polynomial Expected Time
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Zero Knowledge and the Chromatic Number
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
3-coloring in time 0(1.3446^n): a no-MIS algorithm
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
The analysis of a list-coloring algorithm on a random graph
FOCS '97 Proceedings of the 38th 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
Solving Sparse Random Instances of Max Cut and Max 2-CSP in Linear Expected Time
Combinatorics, Probability and Computing
Solving random satisfiable 3CNF formulas in expected polynomial time
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Max k-cut and approximating the chromatic number of random graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
A spectral method for MAX2SAT in the planted solution model
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Simple and efficient greedy algorithms for hamilton cycles in random intersection graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Average-case non-approximability of optimisation problems
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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We investigate the problem of colouring random graphs G 驴 G(n, p) in polynomial expected time. For the case p n, we present an algorithm that finds an optimal colouring in linear expected time. For sufficiently large values of p, we give algorithms which approximate the chromatic number within a factor of O(驴np). As a byproduct, we obtain an O(驴np/ ln(np))-approximation algorithm for the independence number which runs in polynomial expected time provided p 驴 ln6 n/n.