Backbone Fragility and the Local Search Cost Peak
I. P. Gent, J. Singer, A. Smaill

TL;DR
This paper analyzes the relationship between backbone structure and search cost in SAT problems, introducing backbone fragility as a key factor influencing local search difficulty.
Contribution
It introduces the concept of backbone fragility and demonstrates its strong correlation with search cost in high-cost SAT instances, advancing understanding of local search pathologies.
Findings
Large backbones correlate with higher search costs.
Backbone fragility predicts instance hardness for local search.
Clauses affecting the backbone are most often unsatisfied during search.
Abstract
The local search algorithm WSat is one of the most successful algorithms for solving the satisfiability (SAT) problem. It is notably effective at solving hard Random 3-SAT instances near the so-called `satisfiability threshold', but still shows a peak in search cost near the threshold and large variations in cost over different instances. We make a number of significant contributions to the analysis of WSat on high-cost random instances, using the recently-introduced concept of the backbone of a SAT instance. The backbone is the set of literals which are entailed by an instance. We find that the number of solutions predicts the cost well for small-backbone instances but is much less relevant for the large-backbone instances which appear near the threshold and dominate in the overconstrained region. We show a very strong correlation between search cost and the Hamming distance to the…
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