Performance of algorithms minimizing violated clauses in random k-XORSAT

Investigate the performance of greedy, message-passing, and local-search algorithms that seek assignments minimizing the number of violated clauses in random k-XORSAT, including in the regime above the satisfiability threshold.

Background

The paper focuses on algorithms that find satisfying assignments, especially Belief Propagation Guided Decimation, in the satisfiable regime. It concludes by pointing to a different unresolved direction: analyzing algorithms that optimize the number of violated clauses rather than necessarily finding a fully satisfying assignment.

This optimization question is relevant even when the clause density exceeds the random k-XORSAT satisfiability threshold, where satisfying assignments typically do not exist. The authors mention greedy, message-passing, and local-search methods and identify a heuristic dynamical-cavity analysis as an initial step, but do not resolve the broader algorithmic-performance question.