## Abstract

A valued constraint satisfaction problem (VCSP) instance (V;Πω) is a set of variables V with a set of constraints Π weighted by ω. Given a VCSP instance, we are interested in a reweighted subinstance (V;Π'⊃ Π, ω') that preserves the value of the given instance (under every assignment to the variables) within factor 1 ± ∈. A well-studied special case is cut sparsification in graphs, which has found various applications. We show that a VCSP instance consisting of a single boolean predicate P(x, y) (e.g., for cut, P = XOR) can be sparsified into O(|V|=∈^{2}) constraints iff the number of inputs that satisfy P is anything but one (i.e., |P^{-1}(1)| ≠ 1). Furthermore, this sparsity bound is tight unless P is a relatively trivial predicate. We conclude that also systems of 2SAT (or 2LIN) constraints can be sparsified.

Original language | English |
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Pages (from-to) | 1263-1276 |

Number of pages | 14 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 31 |

Issue number | 2 |

DOIs | |

State | Published - 1 Jan 2017 |

## Keywords

- Boolean predicates
- Cut sparsification
- MAX-CSP
- Valued constraint satisfaction problem

## All Science Journal Classification (ASJC) codes

- Mathematics(all)