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

Remi Monasson (1)

1 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]

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^{N w + o(N)}, where N is the instance size. w 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.

Mots clés: Average-case analysis; backtracking; constrained satisfaction; coloring; generating function

Domaines: Complexité [cs.CC]; Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]

Remi Monasson. A generating function method for the average-case analysis of DPLL. RANDOM 2005, 2005, United States. pp.3624, 402. ⟨hal-00005399⟩