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

Abstract

Abstract. In this paper, we describe Compact- Table (CT), a bitwise algorithm to enforce Generalized Arc Consistency (GAC) on table constraints. 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.

Auto-tabling for subproblem presolving in MiniZinc

“…Extensional predicates abound and their efficient propagation to domain consistency is a topic of intense research over the last decade (see [14] for the state of the art): the predicate takes the solutions in tabular form, whereas the predicate [28] takes a compression of such a table into a finite automaton defining a regular language, and the [8] and [9] predicates take a compression of such a table into a multi-valued decision diagram (MDD).…”

Making Compact-Table Compact

“…It captures the tuples in the table t that are supports for x k , v : bit i in the support bit-set is set iff t i,k = v. The support bit-sets are used to update the sparse bit-set during the filtering phase of the algorithm (discussed below). Note that the support bit-sets are created for each propagator using the same table t with respect to the initial variable domains according to [5], a design that we are going to improve on in Sect. 3.…”

“…As mentioned in Sect. 2, the latter case is not exploited in [5]. Sharing saves memory and increases spatial locality and is likely to improve cache performance.…”

“…The compact-table propagator [5] implements table constraints, where an explicit table of tuples defines the solutions to the constraint. Its basic idea is to assign a number to each tuple in the table and maintain a sparse bit-set where bit number i is set iff the tuple with number i is still considered a possible solution.…”

“…The sparse bit-set is represented as an array of words (typically, words of 64 bits) and is sparse: operations performed on it by the propagator only consider words that have at least one bit set (that is, non-zero or non-empty words), where the emptiness information is tracked by an index structure. Compact-table and its extensions have already shown great potential [5,15,14] and sparse bit-sets have also been successfully used for itemset mining constraints [12].…”