The solution of some random NP-hard problems in polynomial expected time
Journal of Algorithms
On the second eigenvalue of random regular graphs
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Algorithmic theory of random graphs
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
A Spectral Technique for Coloring Random 3-Colorable Graphs
SIAM Journal on Computing
Approximate graph coloring by semidefinite programming
Journal of the ACM (JACM)
The Lovász Theta Function and a Semidefinite Programming Relaxation of Vertex Cover
SIAM Journal on Discrete Mathematics
Finding and certifying a large hidden clique in a semirandom graph
Random Structures & Algorithms
On semidefinite programming relaxations for graph coloring and vertex cover
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
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
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
The Largest Eigenvalue of Sparse Random Graphs
Combinatorics, Probability and Computing
Graphs with Tiny Vector Chromatic Numbers and Huge Chromatic Numbers
SIAM Journal on Computing
Techniques from combinatorial approximation algorithms yield efficient algorithms for random 2k-SAT
Theoretical Computer Science
Exact and approximative algorithms for coloring G(n,p)
Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part I
Spectral techniques applied to sparse random graphs
Random Structures & Algorithms
MAX k-CUT and approximating the chromatic number of random graphs
Random Structures & Algorithms
MAX k-CUT and approximating the chromatic number of random graphs
Random Structures & Algorithms
An improved algorithm for approximating the chromatic number of Gn,p
Information Processing Letters
Finding Large Independent Sets in Polynomial Expected Time
Combinatorics, Probability and Computing
Strong Refutation Heuristics for Random k-SAT
Combinatorics, Probability and Computing
On linear and semidefinite programming relaxations for hypergraph matching
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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We study the Lovász number $\vartheta$ along with two related SDP relaxations $\vartheta_{1/2}$, $\vartheta_2$ of the independence number and the corresponding relaxations $\bar\vartheta$, $\bar\vartheta_{1/2}$, $\bar\vartheta_2$ of the chromatic number on random graphs $G_{n,p}$. We prove that $\vartheta,\vartheta_{1/2},\vartheta_2(G_{n,p})$ are concentrated about their means, and that $\bar\vartheta,\bar\vartheta_{1/2},\bar\vartheta_2(G_{n,p})$ in the case $p0$ is a constant. As an application, we give improved algorithms for approximating the independence number of $G_{n,p}$ and for deciding $k$-colourability in polynomial expected time.