Computing H-Partitions in ASP and Datalog

TL;DR

This paper demonstrates that algorithms for computing H-partitions in graphs can be expressed in Datalog with stratified negation, and compares their performance with guess-and-check programs using Clingo.

Contribution

It shows how polynomial-time algorithms for H-partitions can be encoded in Datalog and provides an experimental comparison with guess-and-check approaches.

Findings

Guess-and-check programs run faster than Datalog programs in Clingo.

Polynomial-time algorithms for H-partitions can be expressed in Datalog with stratified negation.

Experimental results compare different logic programming approaches for H-partitions.

Abstract

A $H$-partition of a finite undirected simple graph $G$ is a labeling of $G$'s vertices such that the constraints expressed by the model graph $H$ are satisfied. For every model graph $H$, it can be decided in non-deterministic polynomial time whether a given input graph $G$ admits a $H$-partition. Moreover, it has been shown by Dantas et al. that for most model graphs, this decision problem is in deterministic polynomial time. In this paper, we show that these polynomial-time algorithms for finding $H$-partitions can be expressed in Datalog with stratified negation. Moreover, using the answer set solver Clingo, we have conducted experiments to compare straightforward guess-and-check programs with Datalog programs. Our experiments indicate that in Clingo, guess-and-check programs run faster than their equivalent Datalog programs.