When does the Physarum Solver Distinguish the Shortest Path from other Paths: the Transition Point and its Applications

TL;DR

This paper introduces the concept of the transition point and dominant path to accurately identify when the Physarum solver finds the shortest path, leading to an accelerated algorithm that outperforms existing methods.

Contribution

It proposes a novel termination criterion based on D-Path and T-Point, improving the Physarum solver's efficiency and clarifying misconceptions about acceleration in related algorithms.

Findings

The OPPA-D algorithm outperforms baseline methods in speed.

The proposed termination criterion accurately detects the shortest path.

The method clarifies issues with previous claims of acceleration.

Abstract

Physarum solver, also called the physarum polycephalum inspired algorithm (PPA), is a newly developed bio-inspired algorithm that has an inherent ability to find the shortest path in a given graph. Recent research has proposed methods to develop this algorithm further by accelerating the original PPA (OPPA)'s path-finding process. However, when does the PPA ascertain that the shortest path has been found? Is there a point after which the PPA could distinguish the shortest path from other paths? By innovatively proposing the concept of the dominant path (D-Path), the exact moment, named the transition point (T-Point), when the PPA finds the shortest path can be identified. Based on the D-Path and T-Point, a newly accelerated PPA named OPPA-D using the proposed termination criterion is developed which is superior to all other baseline algorithms according to the experiments conducted in this paper. The validity and the superiority of the proposed termination criterion is also demonstrated. Furthermore, an evaluation method is proposed to provide new insights for the comparison of different accelerated OPPAs. The breakthrough of this paper lies in using D-path and T-point to terminate the OPPA. The novel termination criterion reveals the actual performance of this OPPA. This OPPA is the fastest algorithm, outperforming some so-called accelerated OPPAs. Furthermore, we explain why some existing works inappropriately claim to be accelerated algorithms is in fact a product of inappropriate termination criterion, thus giving rise to the illusion that the method is accelerated.