A theoretical analysis of backtracking in the graph coloring problem
Journal of Algorithms
Almost all k-colorable graphs are easy to color
Journal of Algorithms
Improvements to graph coloring register allocation
ACM Transactions on Programming Languages and Systems (TOPLAS)
The hardest constraint problems: a double phase transition
Artificial Intelligence
On-line coloring of sparse random graphs and random trees
Journal of Algorithms
Boosting combinatorial search through randomization
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
The Complexity of Near-Optimal Graph Coloring
Journal of the ACM (JACM)
New methods to color the vertices of a graph
Communications of the ACM
Frozen development in graph coloring
Theoretical Computer Science - Phase transitions in combinatorial problems
Heavy-Tailed Phenomena in Satisfiability and Constraint Satisfaction Problems
Journal of Automated Reasoning
The analysis of a list-coloring algorithm on a random graph
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Almost all graphs with average degree 4 are 3-colorable
Journal of Computer and System Sciences - STOC 2002
The two possible values of the chromatic number of a random graph
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Exact and approximative algorithms for coloring G(n,p)
Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part I
Algorithmic Barriers from Phase Transitions
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Where the really hard problems are
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Why Almost All k-Colorable Graphs Are Easy to Color
Theory of Computing Systems - Special Issue: Theoretical Aspects of Computer Science; Guest Editors: Wolgang Thomas and Pascal Weil
Evaluating the Kernighan-Lin Heuristic for Hardware/Software Partitioning
International Journal of Applied Mathematics and Computer Science
Improved Bounds on the Complexity of Graph Coloring
SYNASC '10 Proceedings of the 2010 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
The Nature of Computation
A generating function method for the average-case analysis of DPLL
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
Hi-index | 0.00 |
We investigate asymptotically the expected number of steps taken by backtrack search for k-coloring random graphs G"n","p"("n") or proving non-k-colorability, where p(n) is an arbitrary sequence tending to 0, and k is constant. Contrary to the case of constant p, where the expected runtime is known to be O(1), we prove that here the expected runtime tends to infinity. We establish how the asymptotic behavior of the expected number of steps depends on the sequence p(n). In particular, for p(n)=d/n, where d is a constant, the runtime is always exponential, but it can be also polynomial if p(n) decreases sufficiently slowly, e.g. for p(n)=1/lnn.