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キーワード:
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要旨:
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 a simple algorithm for arbitrary directed graphs
with random edge weights uniformly distributed in $\left[0,1\right]$
and show that it needs linear time ${\cal O}(n+m)$ with high probability.
