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- W4302292617 abstract "For many constraint satisfaction problems, the algorithm which chooses a random assignment achieves the best possible approximation ratio. For instance, a simple random assignment for {sc Max-E3-Sat} allows 7/8-approximation and for every $eps >0$ there is no polynomial-time ($7/8+eps$)-approximation unless P=NP. Another example is the {sc Permutation CSP} of bounded arity. Given the expected fraction $rho$ of the constraints satisfied by a random assignment (i.e. permutation), there is no $(rho+eps)$-approximation algorithm for every $eps >0$, assuming the Unique Games Conjecture (UGC). In this work, we consider the following parameterization of constraint satisfaction problems. Given a set of $m$ constraints of constant arity, can we satisfy at least $rho m +k$ constraint, where $rho$ is the expected fraction of constraints satisfied by a random assignment? {sc Constraint Satisfaction Problems above Average} have been posed in different forms in the literature cite{Niedermeier2006,MahajanRamanSikdar09}. We present a faster parameterized algorithm for deciding whether $m/2+k/2$ equations can be simultaneously satisfied over ${mathbb F}_2$. As a consequence, we obtain $O(k)$-variable bikernels for {sc boolean CSPs} of arity $c$ for every fixed $c$, and for {sc permutation CSPs} of arity 3. This implies linear bikernels for many problems under the above average parameterization, such as {sc Max-$c$-Sat}, {sc Set-Splitting}, {sc Betweenness} and {sc Max Acyclic Subgraph}. As a result, all the parameterized problems we consider in this paper admit $2^{O(k)}$-time algorithms. We also obtain non-trivial hybrid algorithms for every Max $c$-CSP: for every instance $I$, we can either approximate $I$ beyond the random assignment threshold in polynomial time, or we can find an optimal solution to $I$ in subexponential time." @default.
- W4302292617 created "2022-10-06" @default.
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- W4302292617 date "2010-08-01" @default.
- W4302292617 modified "2023-09-28" @default.
- W4302292617 title "Improved Parameterized Algorithms for Constraint Satisfaction" @default.
- W4302292617 doi "https://doi.org/10.48550/arxiv.1008.0213" @default.
- W4302292617 hasPublicationYear "2010" @default.
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