S$^*$: A Heuristic Information-Based Approximation Framework for Multi-Goal Path Finding
This provides an efficient solution for path planning in domains like robotics or logistics, though it is incremental as it builds on existing search and approximation methods.
The paper tackles the Multi-Goal Path Finding problem by developing a framework that combines heuristic search and approximation algorithms to find a path visiting all goals, achieving a 2-approximation guarantee and showing advantages in expanded nodes and run time.
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.