A New Polynomially Bounded Shortest Path Algorithm

Abstract

This paper develops a new polynomially bounded shortest path algorithm, called the partitioning shortest path (PSP) algorithm, for finding the shortest path from one node to all other nodes in a network containing no cycles with negative lengths. This new algorithm includes as variants the label setting algorithm, many of the label correcting algorithms, and the apparently computationally superior threshold algorithm.

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

“…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. Intuitively, Q 1 represents the "more promising" candidate nodes.…”

“…Average-case time Bellman-Ford algorithm [3,21] Ω(n 4/3−ε ) Pallottino's Incremental Graph algorithm [54] Ω(n 4/3−ε ) Basic Topological Ordering algorithm [34] Ω(n 4/3−ε ) Threshold algorithm [29][30][31] Ω(n · log n/ log log n) ABI-Dijkstra [6] Ω(n · log n/ log log n) ∆-Stepping [48] Ω(n · √ log n/ log log n) Finally, we present a general method to construct sparse input graphs with random edge weights for which several label-correcting SSSP algorithms require superlinear averagecase running-time: we consider the "Bellman-Ford algorithm" [3,21], "Pallottino's Incremental Graph algorithm" [54], the "Threshold approach" by Glover et al [29][30][31], the basic version of the "Topological Ordering SSSP algorithm" by Goldberg and Radzik [34], the "Approximate Bucket implementation" of Dijkstra's algorithm (ABI-Dijkstra) [6], and its refinement, the "∆-Stepping algorithm" [48]. The obtained lower bounds are summarized in Fig.…”

“…Glover et al suggested several variants [29][30][31] of a method which combines ideas lying behind the algorithms of Bellman-Ford and Dijkstra: the set of queued nodes is partitioned into two subsets, NOW and NEXT. These sets are implemented by FIFO queues.…”

A Review of Dynamic Traffic Assignment Computer Packages

“…Sherali et al (2003) developed an effective method for implicitly working with the composite graphs rather than constructing the full composite graphs a priori. This model is based on the partitioned shortest-path algorithmic developed by Glover et al (1985) and its dynamic programming (DP) interpretation developed by Sherali (1991). Furthermore, to reduce the search effort, Sherali et al (2003) proposed several heuristic curtailing schemes by focusing the search to systematically proceed toward the destination from the origin while avoiding the searching of paths that are beyond a defined boundary.…”

Comparaison d'algorithmes de plus courts chemins sur des graphes routiers de grande taille

“…Elle fait monter x en le permutant avec son père, tant qu'on n'est pas à la racine et que x est inférieur à son père. Sur la figure, si l'élément 9 voit sa valeur 49 passer à 29, on n'a plus un tas puisque que W [9] est inférieur à la valeur du père. En permutant 9 avec 3, puis 7, l'élément 9 devient la racine du tas (ce qui est normal puisqu'il est devenu le minimum).…”