205 lines
6.7 KiB
HTML
205 lines
6.7 KiB
HTML
<HTML>
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<!--
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Copyright (c) Matyas Egyhazy 2008
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt)
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-->
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<Head>
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<Title>Boost Graph Library: Metric Traveling Salesperson Approximation</Title>
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<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
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ALINK="#ff0000">
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<IMG SRC="../../../boost.png"
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ALT="C++ Boost" width="277" height="86">
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<BR Clear>
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<H1><A NAME="sec:metric_tsp_approx"></A>
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<TT>metric_tsp_approx</TT>
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</H1>
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<P>
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<PRE>
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template <typename VertexListGraph,
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typename WeightMap,
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typename VertexIndexMap,
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typename TSPVertexVisitor>
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void metric_tsp_approx_from_vertex(
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const VertexListGraph& g,
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typename graph_traits<VertexListGraph>::vertex_descriptor start,
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WeightMap weightmap,
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VertexIndexMap indexmap,
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TSPVertexVisitor vis)
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<i>// Overloads</i>
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template<typename VertexListGraph, typename OutputIterator>
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void metric_tsp_approx_tour(VertexListGraph& g, OutputIterator o)
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template<typename VertexListGraph, typename WeightMap, typename OutputIterator>
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void metric_tsp_approx_tour(VertexListGraph& g, WeightMap w,
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OutputIterator o)
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template<typename VertexListGraph, typename OutputIterator>
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void metric_tsp_approx_tour_from_vertex(VertexListGraph& g,
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typename graph_traits<VertexListGraph>::vertex_descriptor start,
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OutputIterator o)
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template<typename VertexListGraph, typename WeightMap,
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typename OutputIterator>
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void metric_tsp_approx_tour_from_vertex(VertexListGraph& g,
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typename graph_traits<VertexListGraph>::vertex_descriptor start,
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WeightMap w, OutputIterator o)
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<i>// visitor versions</i>
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template<typename VertexListGraph, typename TSPVertexVisitor>
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void metric_tsp_approx(VertexListGraph& g, TSPVertexVisitor vis)
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template<typename VertexListGraph, typename Weightmap,
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typename VertexIndexMap, typename TSPVertexVisitor>
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void metric_tsp_approx(VertexListGraph& g, Weightmap w,
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TSPVertexVisitor vis)
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template<typename VertexListGraph, typename WeightMap,
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typename VertexIndexMap, typename TSPVertexVisitor>
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void metric_tsp_approx(VertexListGraph& g, WeightMap w, VertexIndexMap id,
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TSPVertexVisitor vis)
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template<typename VertexListGraph, typename WeightMap,
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typename TSPVertexVisitor>
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void metric_tsp_approx_from_vertex(VertexListGraph& g,
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typename graph_traits<VertexListGraph>::vertex_descriptor start,
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WeightMap w, TSPVertexVisitor vis)
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</PRE>
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<P>
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This is a traveling salesperson heuristic for generating a tour of vertices
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for a fully connected undirected graph with weighted edges that obey the triangle inequality.
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The current implementation is based off of the algorithm presented in <i>Introduction to Algorithms</i>
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on page 1029. This implementation generates solutions that are twice as long as the optimal tour in the worst case.
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The pseudo-code is listed below.
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</p>
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<table>
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<tr>
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<td valign="top">
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<pre>
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TSP-APPROX(<i>G</i>, <i>w</i>)
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select a vertex <i>r</i> <i>in</i> <i>V[G]</i>
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compute a minimum spanning tree <i>T</i> for <i>G</i> from root <i>r</i>
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using PRIM-MST(<i>G</i>, <i>r</i>, <i>w</i>)
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let <i>L</i> be the list of vertices visited in a preorder traversal of <i>T</i>
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<b>return</b> (the Hamiltonian cycle <i>H</i> that visites the vertices in the order <i>L</i>)
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</pre>
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</td>
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</tr>
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</table>
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<H3>Where Defined</H3>
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<P>
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<a href="../../../boost/graph/metric_tsp_approx.hpp"><TT>boost/graph/metric_tsp_approx.hpp</TT></a>
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<P>
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<h3>Parameters</h3>
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IN: <tt>const Graph& g</tt>
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<blockquote>
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An undirected graph. The type <tt>Graph</tt> must be a
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model of <a href="./VertexListGraph.html">Vertex List Graph</a>
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and <a href="./IncidenceGraph.html">Incidence Graph</a> <a href="#2">[2]</a>.<br>
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</blockquote>
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IN: <tt>vertex_descriptor start</tt>
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<blockquote>
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The vertex that will be the start (and end) of the tour.<br>
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<b>Default:</b> <tt>*vertices(g).first</tt>
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</blockquote>
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IN: <tt>WeightMap weightmap</tt>
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<blockquote>
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The weight of each edge in the graph.
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The type <tt>WeightMap</tt> must be a model of
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<a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map</a>. The edge descriptor type of
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the graph needs to be usable as the key type for the weight
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map.<br>
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<b>Default:</b> <tt>get(edge_weight, g)</tt><br>
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</blockquote>
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IN: <tt>VertexIndexMap indexmap</tt>
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<blockquote>
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This maps each vertex to an integer in the range <tt>[0,
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num_vertices(g))</tt>. This is necessary for efficient updates of the
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heap data structure when an edge is relaxed. The type
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<tt>VertexIndexMap</tt> must be a model of
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<a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map</a>. The value type of the map must be an
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integer type. The vertex descriptor type of the graph needs to be
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usable as the key type of the map.<br>
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<b>Default:</b> <tt>get(vertex_index, g)</tt>
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Note: if you use this default, make sure your graph has
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an internal <tt>vertex_index</tt> property. For example,
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<tt>adjacency_list</tt> with <tt>VertexList=listS</tt> does
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not have an internal <tt>vertex_index</tt> property.
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<br>
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</blockquote>
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OUT: <tt>OutputIterator o</tt>
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<blockquote>
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The OutputIterator holds the vertices of the tour.
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The type <tt>OutputIterator</tt> must be a model of the
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OutputIterator concept.
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</blockquote>
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OUT: <tt>TSPTourVisitor vis</tt>
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<blockquote>
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Use this to specify actions that you would like to happen
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when the algorithm visits a vertex of the tour.
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The type <tt>TSPTourVisitor</tt> must be a model of the <a href="./TSPTourVisitor.html">TSP Tour Visitor</a>
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concept.
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The visitor object is passed by value <a
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href="#1">[1]</a>.<br>
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</blockquote>
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<H3>Complexity</H3>
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<P>
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The time complexity is <i>O(E log V)</i>.
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<P>
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<H3>Example</H3>
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<P>
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The file <a
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href="../test/metric_tsp_approx.cpp"><TT>test/metric_tsp_approx.cpp</TT></a>
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contains an example of using this TSP approximation algorithm.
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<h3>Notes</h3>
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<p><a name="1">[1]</a>
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Since the visitor parameter is passed by value, if your visitor
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contains state then any changes to the state during the algorithm
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will be made to a copy of the visitor object, not the visitor object
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passed in. Therefore you may want the visitor to hold this state by
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pointer or reference.
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</p>
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<p><a name="2">[2]</a>
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Passing an <tt>adjacency_list</tt> with a vertex <em>not</em> set selected by
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<tt>vecS</tt> will result in <i>O(n<sup>2</sup>)</i> performance.
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</p>
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<HR>
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<TABLE>
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<TR valign=top>
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<TD nowrap>Copyright © 2008</TD><TD>
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Matyas Egyhazy
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</TD></TR></TABLE>
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</BODY>
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</HTML>
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