A generalized best-first search method in graphs

Abstract

This paper is addressed to the problem of finding a ”good” path P from a start node s to some goal node γ within a graph G; this means that for all subpaths Q of P starting with s, the costs c(Q) shall not exceed a limit C(Q).

In order to find such a path P, the search algorithm BF** is introduced, which is based on two decision functions F and G: BF** expands that path P for which F(P) ε ℝ is minimal, and it redirects paths such that G(P) ε ℝ becomes as small as possible. In contrast to the procedure BF* (see [3]), the functions F and G may be different.

The main result of this paper says that BF** actually finds a path P described above if F and G satisfy four conditions; this theorem implies some assertions of [3]. Two further results deal with the possibility of replacing F and G by new decision functions $\tilde F$ and $\tilde G$ (resp.) with some additional properties.