New bounds for old algorithms: on the average-case behavior of classic single-source shortest-paths approaches

Authors:
Ulrich Meyer;Andrei Negoescu;Volker Weichert
Affiliations:
Institut für Informatik, Goethe-Universität Frankfurt am Main, Germany;Institut für Informatik, Goethe-Universität Frankfurt am Main, Germany;Institut für Informatik, Goethe-Universität Frankfurt am Main, Germany
Venue:
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Year:
2011

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Abstract

Despite disillusioning worst-case behavior, classic algorithms for single-source shortest-paths (SSSP) like Bellman-Ford are still being used in practice, especially due to their simple data structures. However, surprisingly little is known about the average-case complexity of these approaches. We provide new theoretical and experimental results for the performance of classic label-correcting SSSP algorithms on graph classes with non-negative random edge weights. In particular, we prove a tight lower bound of Ω(n2) for the running times of Bellman-Ford on a class of sparse graphs with O(n) nodes and edges; the best previous bound was Ω(n4/3-ε). The same improvements are shown for Pallottino's algorithm. We also lift a lower bound for the approximate bucket implementation of Dijkstra's algorithm from Ω(n log n/ log log n) to Ω(n1.2-ε). Furthermore, we provide an experimental evaluation of our new graph classes in comparison with previously used test inputs.