NDLI: Probe Order Backtracking

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Probe Order Backtracking

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Haven, G. Neil Purdom, Paul Walton
Copyright Year	1997
Abstract	The algorithm for constraint-satisfaction problems, Probe Order Backtracking, has an average running time much faster than any previously analyzed algorithm under conditions where solutions are common. The algorithm uses a probing assignment (a preselected test assignment to unset variables) to help guide the search for a solution. If the problem is not satisfied when the unset variables are temporarily set to the probing assignment, the algorithm selects one of the relations which is not satisfied by the probing assignment and selects an unset variable which affects the value of that relation. It then does a backtracking (splitting) step, where it generates subproblems by setting the selected variable each possible way. Each subproblem is simplified and then solved recursively. For random problems with v variables, t clauses, and probability p that a literal appears in a clause, the average time for Probe Order Backtracking is no more than $v^n$ when $p\geq(\ln t)/v$ plus lower-order terms. The best previous result was $p\geq\sqrt{(\ln t)/v}$. When the algorithm is combined with an algorithm of Franco that makes selective use of resolution, the average time for solving random problems is no more than $v^n$ for all values of p when $t\leq O(n^{1/3}(v/\ln v)^{2/3})$. The best previous result was $t\leq O(n^{1/3}(v/\ln v)^{1/6})$. Probe Order Backtracking also runs in polynomial average time when $p\leq 1/v$, compared with the best previous result of $p\leq 1/(2v)$. With Probe Order Backtracking, the range of p that leads to more than polynomial time is much smaller than that for previously analyzed algorithms.
Starting Page	456
Ending Page	483
Page Count	28
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539793256053
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	2
Volume Number	26
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-28
Access Restriction	Subscribed
Subject Keyword	Analysis of algorithms and problem complexity Classical propositional logic average time satisfiability Theorem proving searching backtracking NP-complete combinatorial search Asymptotic enumeration
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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