A Spectral Technique for Coloring Random 3-Colorable Graphs
SIAM Journal on Computing
Algorithms for graph partitioning on the planted partition model
Random Structures & Algorithms
Some optimal inapproximability results
Journal of the ACM (JACM)
A spectral technique for random satisfiable 3CNF formulas
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Colouring Random Graphs in Expected Polynomial Time
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Spectral Partitioning of Random Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
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
Solving random satisfiable 3CNF formulas in expected polynomial time
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Why almost all k-colorable graphs are easy
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
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 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
Average-case analysis for the MAX-2SAT problem
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
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We propose an algorithm using a spectral method, and analyze its average-case performance for MAX2SAT in the planted solution model. In [16], they proposed a distribution Gn,p,r for MAX2SAT in the planted solution model, as well as a message-passing algorithm. They showed that it solves, whp, MAX2SAT on Gn,p,r for rather dense formulas, i.e., the expected number of clauses is Ω(n1.5 √log n). In this paper, we propose an algorithm using a spectral method and a variant of message-passing algorithms, and show that it solves, whp, MAX2SAT on Gn,p,r for sparser formulas, i.e., the expected number of clauses is Ω(n log n).