Compact-Table: Efficiently Filtering Table Constraints with Reversible Sparse Bit-Sets

TL;DR

This paper introduces Compact-Table (CT), a bitwise algorithm for enforcing Generalized Arc Consistency on table constraints, optimized with reversible sparse bit-sets, and demonstrates its superior performance over existing algorithms.

Contribution

The paper presents a novel bitwise algorithm, Compact-Table, with a reversible sparse bit-set data structure, for efficient GAC enforcement on table constraints.

Findings

CT outperforms state-of-the-art algorithms on standard benchmarks.

Reversible sparse bit-sets enable incremental invalidation of tuples.

The algorithm is implemented in publicly available CP solvers.

Abstract

In this paper, we describe Compact-Table (CT), a bitwise algorithm to enforce Generalized Arc Consistency (GAC) on table con- straints. Although this algorithm is the default propagator for table constraints in or-tools and OscaR, two publicly available CP solvers, it has never been described so far. Importantly, CT has been recently improved further with the introduction of residues, resetting operations and a data-structure called reversible sparse bit-set, used to maintain tables of supports (following the idea of tabular reduction): tuples are invalidated incrementally on value removals by means of bit-set operations. The experimentation that we have conducted with OscaR shows that CT outperforms state-of-the-art algorithms STR2, STR3, GAC4R, MDD4R and AC5-TC on standard benchmarks.