Shortest path methods: A unifying approach

Abstract

A survey of shortest path methods is presented. All the algorithms described are shown to derive from one single prototype method, the difference between them depending only on the particular data structure used in their implementation. This analysis suggests a new classification of the shortest path algorithms. Both the single shortest path tree problem and the all-pairs shortest path problem are considered. One section is dedicated to reoptimization procedures.

Average-case complexity of single-source shortest-paths algorithms: lower and upper bounds

“…It implements the set of candidate nodes Q as a FIFO-Queue and achieves running time O(n · m). There are many more ways to maintain Q and select nodes from it (see [6,27] for an overview). For example, the algorithms of Pallottino [54], Goldberg and Radzik [34], and Glover et al [29][30][31] subdivide Q into two sets Q 1 and Q 2 each of which is implemented as a list.…”

Differential Space-Time Network Coding for Multi-Source Cooperative Communications

“…The minimization of Φ in (40) is the shortest-path problem [32] and can be solved by using the idea of Dijkstra's algorithm [20], [32] as follows.…”

The all-to-all alternative route problem

“…Dijkstra's algorithm or, preferably, a labelcorrecting algorithm [5]) applied to find the shortest route from every node to node L Then the alternative path is found by 'removing' the first are of 7T and applying Nemhauser's algorithm with the zero-intensity function providing a consistent function.…”

“…Phase (1) may be effected by using a Dijkstra-like algorithm or, preferably, a label-correcting algorithm based on deques (Gallo and Pallottino, [5]) applied for each node x Alternatively, an integrated scheme may be used [4]. However» whatever the overall scheme used, the effort of finding all first shortest paths must be embedded somewhere in the calculations.…”