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shortest-path-nonneg-weight.html
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<title>Shortest non-negative weighted path between two vertices</title>
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<h1 id="article-title">Shortest non-negative weighted path between two vertices</h1>
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<h1 id="problem">Problem</h1>
<p>Let <span class="math inline">D=(V,A)</span> be a simple directed graph, and <span class="math inline">w:E \to S</span> be a weight function, where <span class="math inline">S</span> is an ordered semigroup with no negative elements. Find a shortest path between <span class="math inline">s,t\in V</span> with minimum weight.</p>
<h1 id="algorithms">Algorithms</h1>
<h2 id="dijkstras-algorithm">Dijkstra’s algorithm</h2>
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<li><span class="math inline">O(m+n\log n)</span> time.</li>
<li><span class="math inline">O(n)</span> space.</li>
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