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arXiv · 1404.3675

On Backdoors To Tractable Constraint Languages

Clement Carbonnel·Martin C. Cooper·Emmanuel Hebrard
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Abstract

In the context of CSPs, a strong backdoor is a subset of variables such that every complete assignment yields a residual instance guaranteed to have a specified property. If the property allows efficient solving, then a small strong backdoor provides a reasonable decomposition of the original instance into easy instances. An important challenge is the design of algorithms that can find quickly a small strong backdoor if one exists. We present a systematic study of the parameterized complexity of backdoor detection when the target property is a restricted type of constraint language defined by means of a family of polymorphisms. In particular, we show that under the weak assumption that the polymorphisms are idempotent, the problem is unlikely to be FPT when the parameter is either r (the constraint arity) or k (the size of the backdoor) unless P = NP or FPT = W[2]. When the parameter is k+r, however, we are able to identify large classes of languages for which the problem of finding a small backdoor is FPT.

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Clement Carbonnel, Martin C. Cooper, Emmanuel Hebrard. 2014-10-10. On Backdoors To Tractable Constraint Languages. https://arxiv.org/abs/1404.3675

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