Finding Optimal Solutions to Token Swapping by Conflict-based Search and Reduction to SAT

TL;DR

This paper introduces the first optimal algorithms for the token swapping problem by adapting conflict-based search and SAT reduction methods from multi-agent path finding, demonstrating better scalability of SAT-based solutions.

Contribution

It presents novel optimal solving algorithms for TSWAP using CBS and SAT reduction, bridging techniques from MAPF and addressing a previously unexplored problem.

Findings

SAT-based approach scales better than CBS for TSWAP

First optimal algorithms for TSWAP problem

Experimental results validate effectiveness of proposed methods

Abstract

We study practical approaches to solving the token swapping (TSWAP) problem optimally in this short paper. In TSWAP, we are given an undirected graph with colored vertices. A colored token is placed in each vertex. A pair of tokens can be swapped between adjacent vertices. The goal is to perform a sequence of swaps so that token and vertex colors agree across the graph. The minimum number of swaps is required in the optimization variant of the problem. We observed similarities between the TSWAP problem and multi-agent path finding (MAPF) where instead of tokens we have multiple agents that need to be moved from their current vertices to given unique target vertices. The difference between both problems consists in local conditions that state transitions (swaps/moves) must satisfy. We developed two algorithms for solving TSWAP optimally by adapting two different approaches to MAPF - CBS and MDD- SAT. This constitutes the first attempt to design optimal solving algorithms for TSWAP. Experimental evaluation on various types of graphs shows that the reduction to SAT scales better than CBS in optimal TSWAP solving.