Improved algorithms for 3-coloring, 3-edge-coloring, and constraint satisfaction
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Journal of Algorithms
Techniques from combinatorial approximation algorithms yield efficient algorithms for random 2k-SAT
Theoretical Computer Science
A spectral heuristic for bisecting random graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
The Lovász Number of Random Graphs
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
The resolution complexity of random graphk-colorability
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Strong Refutation Heuristics for Random k-SAT
Combinatorics, Probability and Computing
The diameter of randomly perturbed digraphs and some applications
Random Structures & Algorithms
Spectral clustering by recursive partitioning
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Spectral clustering with limited independence
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On the Expansion of the Giant Component in Percolated (n, d,λ) Graphs
Combinatorics, Probability and Computing
A discriminative framework for clustering via similarity functions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Complexity analysis of a decentralised graph colouring algorithm
Information Processing Letters
On the tractability of coloring semirandom graphs
Information Processing Letters
Expansion and Lack Thereof in Randomly Perturbed Graphs
Algorithms and Models for the Web-Graph
Network analysis of collaboration structure in Wikipedia
Proceedings of the 18th international conference on World wide web
Group-Level Analysis and Visualization of Social Networks
Algorithmics of Large and Complex Networks
Data reductions, fixed parameter tractability, and random weighted d-CNF satisfiability
Artificial Intelligence
Small Clique Detection and Approximate Nash Equilibria
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
A spectral approach to analysing belief propagation for 3-colouring
Combinatorics, Probability and Computing
On the random satisfiable process
Combinatorics, Probability and Computing
The resolution complexity of random graph k-colorability
Discrete Applied Mathematics
3-coloring in time O (1.3289n)
Journal of Algorithms
Graph partitioning via adaptive spectral techniques
Combinatorics, Probability and Computing
Why almost all k-colorable graphs are easy
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A spectral method for MAX2SAT in the planted solution model
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Finding Planted Partitions in Random Graphs with General Degree Distributions
SIAM Journal on Discrete Mathematics
MCPR'11 Proceedings of the Third Mexican conference on Pattern recognition
Finding a maximum independent set in a sparse random graph
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
The spectral gap of random graphs with given expected degrees
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
An adaptive spectral heuristic for partitioning random graphs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Coloring random 3-colorable graphs with non-uniform edge probabilities
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Coloring sparse random k-colorable graphs in polynomial expected time
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Complete convergence of message passing algorithms for some satisfiability problems
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Multi-way spectral partitioning and higher-order cheeger inequalities
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Recognizing 3-colorings cycle-patterns on graphs
Pattern Recognition Letters
| Hi-index | 0.00 |
Let G3n,p,3 be a random 3-colorable graph on a set of 3n vertices generated as follows. First, split the vertices arbitrarily into three equal color classes, and then choose every pair of vertices of distinct color classes, randomly and independently, to be edges with probability p. We describe a polynomial-time algorithm that finds a proper 3-coloring of G3n,p,3 with high probability, whenever p $\geq$ c/n, where c is a sufficiently large absolute constant. This settles a problem of Blum and Spencer, who asked if an algorithm can be designed that works almost surely for p $\geq$ polylog(n)/n [J. Algorithms, 19 (1995), pp. 204--234]. The algorithm can be extended to produce optimal k-colorings of random k-colorable graphs in a similar model as well as in various related models. Implementation results show that the algorithm performs very well in practice even for moderate values of c.