S$^*$: A Heuristic Information-Based Approximation Framework for Multi-Goal Path Finding

TL;DR

This paper introduces S$^*$, a heuristic approximation framework for multi-goal path finding that guarantees a solution within twice the optimal cost, combining search strategies and TSP approximations.

Contribution

The paper presents a novel 2-approximation framework for multi-goal path finding, integrating heuristic search and TSP approximation techniques.

Findings

Reduces number of expanded nodes compared to traditional methods.

Achieves faster run times in numerical experiments.

Guarantees a solution within twice the optimal cost.

Abstract

We combine ideas from uni-directional and bi-directional heuristic search, and approximation algorithms for the Traveling Salesman Problem, to develop a novel framework for a Multi-Goal Path Finding (MGPF) problem that provides a 2-approximation guarantee. MGPF aims to find a least-cost path from an origin to a destination such that each node in a given set of goals is visited at least once along the path. We present numerical results to illustrate the advantages of our framework over conventional alternates in terms of the number of expanded nodes and run time.