A generating function method for the average-case analysis of DPLL

Rémi Monasson

doi:10.1007/11538462_34

A generating function method for the average-case analysis of DPLL

Rémi Monasson

École Polytechnique

Research output: Contribution to journal › Conference article › peer-review

Abstract

A method to calculate the average size of Davis-Putnam-Loveland-Logemann (DPLL) search trees for random computational problems is introduced, and applied to the satisfiability of random CNF formulas (SAT) and the coloring of random graph (COL) problems. We establish recursion relations for the generating functions of the average numbers of (variable or color) assignments at a given height in the search tree, which allow us to derive the asymptotics of the expected DPLL tree size, 2^Nwω+o(N) where N is the instance size, ω is calculated as a function of the input distribution parameters (ratio of clauses per variable for SAT, average vertex degree for COL), and the branching heuristics.

Original language	English
Pages (from-to)	402-413
Number of pages	12
Journal	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3624
DOIs	https://doi.org/10.1007/11538462_34
Publication status	Published - 1 Jan 2005
Event	8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and 9th International Workshop on Randomization and Computation, RANDOM 2005 - Berkeley, CA, United States Duration: 22 Aug 2005 → 24 Aug 2005

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title = "A generating function method for the average-case analysis of DPLL",

abstract = "A method to calculate the average size of Davis-Putnam-Loveland-Logemann (DPLL) search trees for random computational problems is introduced, and applied to the satisfiability of random CNF formulas (SAT) and the coloring of random graph (COL) problems. We establish recursion relations for the generating functions of the average numbers of (variable or color) assignments at a given height in the search tree, which allow us to derive the asymptotics of the expected DPLL tree size, 2Nwω+o(N) where N is the instance size, ω is calculated as a function of the input distribution parameters (ratio of clauses per variable for SAT, average vertex degree for COL), and the branching heuristics.",

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doi = "10.1007/11538462\_34",

language = "English",

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note = "8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and 9th International Workshop on Randomization and Computation, RANDOM 2005 ; Conference date: 22-08-2005 Through 24-08-2005",

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T1 - A generating function method for the average-case analysis of DPLL

AU - Monasson, Rémi

PY - 2005/1/1

Y1 - 2005/1/1

N2 - A method to calculate the average size of Davis-Putnam-Loveland-Logemann (DPLL) search trees for random computational problems is introduced, and applied to the satisfiability of random CNF formulas (SAT) and the coloring of random graph (COL) problems. We establish recursion relations for the generating functions of the average numbers of (variable or color) assignments at a given height in the search tree, which allow us to derive the asymptotics of the expected DPLL tree size, 2Nwω+o(N) where N is the instance size, ω is calculated as a function of the input distribution parameters (ratio of clauses per variable for SAT, average vertex degree for COL), and the branching heuristics.

AB - A method to calculate the average size of Davis-Putnam-Loveland-Logemann (DPLL) search trees for random computational problems is introduced, and applied to the satisfiability of random CNF formulas (SAT) and the coloring of random graph (COL) problems. We establish recursion relations for the generating functions of the average numbers of (variable or color) assignments at a given height in the search tree, which allow us to derive the asymptotics of the expected DPLL tree size, 2Nwω+o(N) where N is the instance size, ω is calculated as a function of the input distribution parameters (ratio of clauses per variable for SAT, average vertex degree for COL), and the branching heuristics.

U2 - 10.1007/11538462_34

DO - 10.1007/11538462_34

M3 - Conference article

AN - SCOPUS:26944450049

SN - 0302-9743

VL - 3624

SP - 402

EP - 413

JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

JF - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

T2 - 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and 9th International Workshop on Randomization and Computation, RANDOM 2005

Y2 - 22 August 2005 through 24 August 2005

ER -

A generating function method for the average-case analysis of DPLL

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