Improving the Performance of maxRPC

TL;DR

This paper introduces optimized maxRPC algorithms that significantly improve pruning efficiency and runtime performance over previous methods, making maxRPC more practical for constraint satisfaction problems.

Contribution

The paper proposes two new maxRPC algorithms with improved time complexities and practical performance, incorporating data structures and heuristics to reduce redundant checks.

Findings

New algorithms outperform previous maxRPC methods in experiments.

The algorithms are efficient during search with restricted complexity.

MaxRPC can be a viable alternative to arc consistency in many cases.

Abstract

Max Restricted Path Consistency (maxRPC) is a local consistency for binary constraints that can achieve considerably stronger pruning than arc consistency. However, existing maxRRC algorithms suffer from overheads and redundancies as they can repeatedly perform many constraint checks without triggering any value deletions. In this paper we propose techniques that can boost the performance of maxRPC algorithms. These include the combined use of two data structures to avoid many redundant constraint checks, and heuristics for the efficient ordering and execution of certain operations. Based on these, we propose two closely related algorithms. The first one which is a maxRPC algorithm with optimal O(end^3) time complexity, displays good performance when used stand-alone, but is expensive to apply during search. The second one approximates maxRPC and has O(en^2d^4) time complexity, but a restricted version with O(end^4) complexity can be very efficient when used during search. Both algorithms have O(ed) space complexity. Experimental results demonstrate that the resulting methods constantly outperform previous algorithms for maxRPC, often by large margins, and constitute a more than viable alternative to arc consistency on many problems.