ZDD-Based Algorithmic Framework for Solving Shortest Reconfiguration Problems

TL;DR

This paper introduces a ZDD-based algorithmic framework to efficiently solve reconfiguration problems, enabling shortest solution transformations and detailed analysis of the solution space, even when exponential in size.

Contribution

The paper presents a novel ZDD-based framework that efficiently explores and analyzes the solution space of reconfiguration problems, including shortest transformation paths.

Findings

Efficiently finds shortest reconfiguration sequences using ZDDs.

Provides detailed information on solution space connectivity.

Demonstrates applicability to various reconfiguration problems.

Abstract

This paper proposes an algorithmic framework for various reconfiguration problems using zero-suppressed binary decision diagrams (ZDDs), a data structure for families of sets. In general, a reconfiguration problem checks if there is a step-by-step transformation between two given feasible solutions (e.g., independent sets of an input graph) of a fixed search problem such that all intermediate results are also feasible and each step obeys a fixed reconfiguration rule (e.g., adding/removing a single vertex to/from an independent set). The solution space formed by all feasible solutions can be exponential in the input size, and indeed many reconfiguration problems are known to be PSPACE-complete. This paper shows that an algorithm in the proposed framework efficiently conducts the breadth-first search by compressing the solution space using ZDDs, and finds a shortest transformation between two given feasible solutions if exists. Moreover, the proposed framework provides rich information on the solution space, such as the connectivity of the solution space and all feasible solutions reachable from a specified one. We demonstrate that the proposed framework can be applied to various reconfiguration problems, and experimentally evaluate their performances.