Dominating Set Reconfiguration with Answer Set Programming
Masato Kato, Torsten Schaub, Takehide Soh, Naoyuki Tamura, Mutsunori Banbara
TL;DR
This work tackles Dominating Set Reconfiguration (DSRP), the problem of determining if one dominating set can reach another through a sequence of adjacent dominating sets. It advances a declarative solution based on Answer Set Programming (ASP) and the multi-shot solver recongo, converting DSRP instances into ASP facts and solving via a high-level encoding under token jumping, with extensions to token addition-removal and a domain-specific hint (token destination) to prune invalid moves. Empirical results on a newly created 442-instance benchmark show substantial reachability decisions, with the best ASP approach solving 363 instances and outperforming a ZDD-based method (ddreconf) in overall coverage. The work demonstrates the effectiveness of ASP-based combinatorial reconfiguration for DSRP and positions recongo as a robust tool for practical, large-scale reconfiguration problems, while offering rich benchmarks for future comparison and development.
Abstract
The dominating set reconfiguration problem is defined as determining, for a given dominating set problem and two among its feasible solutions, whether one is reachable from the other via a sequence of feasible solutions subject to a certain adjacency relation. This problem is PSPACE-complete in general. The concept of the dominating set is known to be quite useful for analyzing wireless networks, social networks, and sensor networks. We develop an approach to solve the dominating set reconfiguration problem based on Answer Set Programming (ASP). Our declarative approach relies on a high-level ASP encoding, and both the grounding and solving tasks are delegated to an ASP-based combinatorial reconfiguration solver. To evaluate the effectiveness of our approach, we conduct experiments on a newly created benchmark set.