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Directed single-source shortest-paths in linear average-case time

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45038

Meyer,  Ulrich
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Volltexte (frei zugänglich)

2001-1-002
(beliebiger Volltext), 11KB

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Zitation

Meyer, U.(2001). Directed single-source shortest-paths in linear average-case time (MPI-I-2001-1-002). Saarbrücken: Max-Planck-Institut für Informatik.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0014-6D44-5
Zusammenfassung
The quest for a linear-time single-source shortest-path (SSSP) algorithm on directed graphs with positive edge weights is an ongoing hot research topic. While Thorup recently found an ${\cal O}(n+m)$ time RAM algorithm for undirected graphs with $n$ nodes, $m$ edges and integer edge weights in $\{0,\ldots, 2^w-1\}$ where $w$ denotes the word length, the currently best time bound for directed sparse graphs on a RAM is ${\cal O}(n+m \cdot \log\log n)$. In the present paper we study the average-case complexity of SSSP. We give simple label-setting and label-correcting algorithms for arbitrary directed graphs with random real edge weights uniformly distributed in $\left[0,1\right]$ and show that they need linear time ${\cal O}(n+m)$ with high probability. A variant of the label-correcting approach also supports parallelization. Furthermore, we propose a general method to construct graphs with random edge weights which incur large non-linear expected running times on many traditional shortest-path algorithms.