Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis

Peter Jonsson; Victor Lagerkvist; Johannes Schmidt; Hannes Uppman

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arXiv · 1406.3247

Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis

Peter Jonsson·Victor Lagerkvist·Johannes Schmidt·Hannes Uppman

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Abstract

Obtaining lower bounds for NP-hard problems has for a long time been an active area of research. Recent algebraic techniques introduced by Jonsson et al. (SODA 2013) show that the time complexity of the parameterized SAT($\cdot$) problem correlates to the lattice of strong partial clones. With this ordering they isolated a relation $R$ such that SAT($R$) can be solved at least as fast as any other NP-hard SAT($\cdot$) problem. In this paper we extend this method and show that such languages also exist for the max ones problem (MaxOnes($\Gamma$)) and the Boolean valued constraint satisfaction problem over finite-valued constraint languages (VCSP($\Delta$)). With the help of these languages we relate MaxOnes and VCSP to the exponential time hypothesis in several different ways.

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Peter Jonsson, Victor Lagerkvist, Johannes Schmidt, Hannes Uppman. 2014-06-12. Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis. https://arxiv.org/abs/1406.3247

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