Unsatissed Variables in Local Search

Slightly expanded version of a paper submitted to AISB-95. Abstract Several local search algorithms for propositional satissability have recently been proposed which are able to solve hard random problems beyond the range of conventional backtracking procedures. In this paper, we explore the impact of focusing search in these procedures on the \unsatissed variables"; that is, those variables will appear in clauses which are not yet satissed. For random problems, we show that such a focus reduces the sensitivity of these procedures to their input parameters. We also observe a simple scaling law in performance. For non-random problems, we show that whilst this focus can improve performance, many problems remain diicult. We speculate that such problems will remain hard for local search unless constraint propagation techniques can be combined with hill-climbing.