Shortest-Route Methods: 1. Reaching, Pruning, and Buckets

Abstract

We present a new family of shortest-route methods, which reduce an upper bound on running time, and make empirical comparisons for a certain class of networks. These methods also allow for exploitation of structure by pruning arcs and/or nodes.

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

“…Therefore, subsequent approaches have been designed to avoid the sorting complexity; they identified label-setting criteria that allow to scan nodes in nonsorted order. Dinitz [16] and Denardo and Fox [10] observed the following:…”

“…Hence, at first glance, label-setting algorithms seem to be the better choice. However, several independent case studies [6,10,13,28,29,44,50,70] showed that SSSP implementations of label-correcting approaches frequently outperform labelsetting algorithms. Thus, worst-case analysis sometimes fails to bring out the advantages of algorithms that perform well in practice.…”

“…By Lemma 5 there is a node z ∈ Q, z = v, lying on a shortest path from s to v with tent(z) = dist(z) M. However, since all edges into v have weight at least tent(v) − M, this implies dist(v) dist(z) + tent(v) − M tent(v), a contradiction. ✷ Lemma 8 was already implicit in [10,16]. However, for a long time, the IN-criterion has not been exploited in its full strength to derive better SSSP algorithms.…”

“…In Section 4 we will review some basic implementations of Dijkstra's algorithm with bucket based priority queues [1,10,12,16]. Alternative bucket approaches include nested (multiple levels) buckets and/or buckets of different widths [2,10].…”

“…Alternative bucket approaches include nested (multiple levels) buckets and/or buckets of different widths [2,10]. So far, the best bound for SSSP on arbitrary directed graphs with nonnegative integer edge-weights in {1, .…”