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			Home &gt; Graph Theory: Networking
					&gt; Shortest-Path Algorithms
					&gt; Problem Variations</div>
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        <a class="toc_link" href="">Shortest-Path Algorithms</a>
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        <a class="toc_link" href="">Routing</a>
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        <a class="toc_link" href="page21.xml">Designing A Routing Protocol</a>
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        <a class="toc_link" href="page30.xml">Distance-Vector Routing</a>
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    <div id="content"><h1>Problem Variations</h1>
				<h2>Variations of the Shortest Path Problem</h2>
				
				<h2>Single Pair</h2>
				
				<h2>Input</h2>
				
				<p>
				A directed weighted graph
				<m:math>
					<m:mi>G</m:mi>
					<m:mfenced>
						<m:mi>V</m:mi>
						<m:mi>E</m:mi>
					</m:mfenced>
				</m:math>
				and vertices
				<m:math>
					<m:mi>u</m:mi>
					<m:mo>,</m:mo>
					<m:mi>v</m:mi>
					<m:mo>∈</m:mo>
					<m:mi>V</m:mi>
				</m:math>
				</p>

				<h2>Output</h2>
				<p>
				A shortest
				<m:math><m:mfenced><m:mi>u</m:mi><m:mi>v</m:mi></m:mfenced></m:math>-path and its weight.
				</p>

				<h2>Single Source</h2>
				
				<h2>Input</h2>
				<p>
				A directed weighted graph
				<m:math>
					<m:mi>G</m:mi>
					<m:mo>⁡</m:mo>
					<m:mfenced>
						<m:mi>V</m:mi>
						<m:mi>E</m:mi>
					</m:mfenced>
				</m:math>
				and vertex
				<m:math>
					<m:mi>u</m:mi>
					<m:mo>∈</m:mo>
					<m:mi>V</m:mi>
				</m:math>.
				</p>
				
				<h2>Output</h2>
				<p>
				A shortest
				<m:math><m:mfenced><m:mi>u</m:mi><m:mi>v</m:mi></m:mfenced></m:math>-path
				 and its weight for all
				<m:math><m:mi>v</m:mi><m:mo>∈</m:mo><m:mi>V</m:mi></m:math>.
				</p>
				
				<h2>All Pairs</h2>
				
				<h2>Input</h2>
				<p>
				A directed weighted graph
				<m:math>
					<m:mi>G</m:mi>
					<m:mo>⁡</m:mo>
					<m:mfenced>
						<m:mi>V</m:mi>
						<m:mi>E</m:mi>
					</m:mfenced>
				</m:math>.
				</p>
				
				<h2>Output</h2>
				<p>
				For every pair
				<m:math>
					<m:mfenced>
						<m:mi>u</m:mi>
						<m:mi>v</m:mi>
					</m:mfenced>
				</m:math>
				of vertices
				<m:math>
					<m:mo>∈</m:mo>
					<m:mi>V</m:mi>
				</m:math>
				a shortest
				<m:math>
					<m:mfenced>
						<m:mi>u</m:mi>
						<m:mi>v</m:mi>
					</m:mfenced>
				</m:math>-path and its weight.
				</p>
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