Shortest Path Problem Algorithms

Abstract The shortest path problem (SPP) is a fundamental combinatorial optimization problem that concerns finding the shortest paths between a source and a destination; it is also referred to as a single‐source shortest path problem (SSPP). In some problem settings, shortest paths between all pairs of nodes are desired; these are referred to as all‐pairs shortest path problems (ASPP). The SPP arises in a number of applications, both as a stand‐alone problem and as a subproblem in more complex scenarios. Several applications have been described in the last chapter. In this article, we describe algorithmic methods to solve the SSPP, as well as the ASPP. In real‐life applications, networks vary in their characteristics such as in the presence of negative arcs, directed cycles, and so forth. We present both customized and the most extensively studied algorithms for each scenario, with an analysis of their individual complexities.