Approximability of Bounded Occurrence Max Ones

TL;DR

This paper investigates how well the Max Ones problem can be approximated when each variable appears only a limited number of times, providing a complete classification for certain cases and relating others to known problems.

Contribution

It offers a comprehensive classification of the approximability of Max Ones with bounded variable occurrences, especially for conservative constraint languages.

Findings

Complete classification for three or more occurrences in conservative cases

Partial classification for two occurrences in conservative cases

Non-conservative cases are either trivial or reducible to conservative cases

Abstract

We study the approximability of Max Ones when the number of variable occurrences is bounded by a constant. For conservative constraint languages (i.e., when the unary relations are included) we give a complete classification when the number of occurrences is three or more and a partial classification when the bound is two. For the non-conservative case we prove that it is either trivial or equivalent to the corresponding conservative problem under polynomial-time many-one reductions.