Analyses of load stealing models based on differential equations
Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures
Rigorous results for random (2 + p)-SAT
Theoretical Computer Science - Phase transitions in combinatorial problems
Results related to threshold phenomena research in satisfiability: lower bounds
Theoretical Computer Science - Phase transitions in combinatorial problems
Lower bounds for random 3-SAT via differential equations
Theoretical Computer Science - Phase transitions in combinatorial problems
The Power of Two Choices in Randomized Load Balancing
IEEE Transactions on Parallel and Distributed Systems
Almost all graphs with average degree 4 are 3-colorable
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Random graphs, random triangle-free graphs, and random partial orders
Computational Discrete Mathematics
The phase transition in random horn satisfiability and its algorithmic implications
Random Structures & Algorithms
Colouring Random Graphs in Expected Polynomial Time
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Efficient Recognition of Random Unsatisfiable k-SAT Instances by Spectral Methods
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
The Probabilistic Analysis of a Greedy Satisfiability Algorithm
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Almost all graphs with average degree 4 are 3-colorable
Journal of Computer and System Sciences - STOC 2002
Studying Balanced Allocations with Differential Equations
Combinatorics, Probability and Computing
The pure literal rule threshold and cores in random hypergraphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Annals of Mathematics and Artificial Intelligence
The resolution complexity of random graphk-colorability
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Typical case complexity of satisfiability algorithms and the threshold phenomenon
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
A novel giant-subgraph phase-transition in sparse random k-partite graphs
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
The probabilistic analysis of a greedy satisfiability algorithm
Random Structures & Algorithms
A novel giant-subgraph phase-transition in sparse random k-partite graphs
Discrete Applied Mathematics
The resolution complexity of random graph k-colorability
Discrete Applied Mathematics
Typical case complexity of Satisfiability Algorithms and the threshold phenomenon
Discrete Applied Mathematics
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
On independent sets in random graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The freezing threshold for k-colourings of a random graph
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Average-case complexity of backtrack search for coloring sparse random graphs
Journal of Computer and System Sciences
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We introduce a natural k-coloring algorithm and analyze its performance on random graphs with constant expected degree c (G/sub n,p=c/n/). For k=3 our results imply that almost all graphs with n vertices and 1.923 n edges are 3-colorable. This improves the lower bound on the threshold for random 3-colorability significantly and settles the last case of a long-standing open question of Bollobas. We also provide a tight asymptotic analysis of the algorithm. We show that for all k/spl ges/3, if c/spl les/k In k-3/2k then the algorithm almost surely succeeds, while for any /spl epsiv/0, and k sufficiently large, if c/spl ges/(1+/spl epsiv/)k In k then the algorithm almost surely fails. The analysis is based on the use of differential equations to approximate the mean path of certain Markov chains.