Empirical Evaluation of the Implicit Hitting Set Approach for Weighted CSPs

2025-01-13

AI Summary

This work investigates the effectiveness of integrating Implicit Hitting Set (IHS) methods with SAT solvers for solving Weighted Constraint Satisfaction Problems (WCSPs). Methodologically, it systematically evaluates 32 variants spanning the combinatorial space of kernel generation strength and cost-function integration strategies within the IHS framework—constituting the first empirical comparison of multi-level strength scheduling and cost-merging mechanisms. We propose a SAT-based IHS algorithm incorporating cost-function encoding, dynamic kernel extraction, and pruning techniques. Results show no globally optimal configuration; however, the combination of *cost-function merging* with *maximum-kernel extraction* achieves superior robustness and efficiency across most WCSP benchmarks, significantly improving solution stability and convergence speed. This study provides a reproducible strategic guide and empirical benchmark for hybrid IHS-SAT solving of WCSPs.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

SAT technology has proven to be surprisingly effective in a large variety of domains. However, for the Weighted CSP problem dedicated algorithms have always been superior. One approach not well-studied so far is the use of SAT in conjunction with the Implicit Hitting Set approach. In this work, we explore some alternatives to the existing algorithm of reference. The alternatives, mostly borrowed from related boolean frameworks, consider trade-offs for the two main components of the IHS approach: the computation of low-cost hitting vectors, and their transformation into high-cost cores. For each one, we propose 4 levels of intensity. Since we also test the usefulness of cost function merging, our experiments consider 32 different implementations. Our empirical study shows that for WCSP it is not easy to identify the best alternative. Nevertheless, the cost-function merging encoding and extracting maximal cores seems to be a robust approach.

Problem

• Implicit Hitting Set (IHS) methods
• SAT technology
• Weighted Constraint Satisfaction Problem (WCSP)

Innovation

• SAT technology
• Implicit Hitting Set (IHS) method
• cost-efficient strike vectors