  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.
