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<h1 title="Package" class="title">Package org.jgrapht.alg.cycle</h1>
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<div class="docSummary">
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<div class="block">Algorithms for enumeration of simple cycles in graphs.</div>
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</div>
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<p>See: <a href="#package_description">Description</a></p>
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<th class="colFirst" scope="col">Interface</th>
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</tr>
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<tbody>
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<tr class="altColor">
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<td class="colFirst"><a href="../../../../org/jgrapht/alg/cycle/DirectedSimpleCycles.html" title="interface in org.jgrapht.alg.cycle">DirectedSimpleCycles</a><V,E></td>
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<td class="colLast">
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<div class="block">A common interface for classes implementing algorithms for enumeration of the
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simple cycles of a directed graph.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><a href="../../../../org/jgrapht/alg/cycle/UndirectedCycleBase.html" title="interface in org.jgrapht.alg.cycle">UndirectedCycleBase</a><V,E></td>
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<td class="colLast">
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<div class="block">A common interface for classes implementing algorithms for finding a cycle
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base of an undirected graph.</div>
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</td>
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<th class="colFirst" scope="col">Class</th>
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<tr class="altColor">
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<td class="colFirst"><a href="../../../../org/jgrapht/alg/cycle/HawickJamesSimpleCycles.html" title="class in org.jgrapht.alg.cycle">HawickJamesSimpleCycles</a><V,E></td>
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<td class="colLast">
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<div class="block">Find all simple cycles of a directed graph using the algorithm described by
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Hawick and James.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><a href="../../../../org/jgrapht/alg/cycle/JohnsonSimpleCycles.html" title="class in org.jgrapht.alg.cycle">JohnsonSimpleCycles</a><V,E></td>
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<td class="colLast">
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<div class="block">Find all simple cycles of a directed graph using the Johnson's algorithm.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><a href="../../../../org/jgrapht/alg/cycle/PatonCycleBase.html" title="class in org.jgrapht.alg.cycle">PatonCycleBase</a><V,E></td>
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<td class="colLast">
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<div class="block">Find a cycle base of an undirected graph using the Paton's algorithm.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><a href="../../../../org/jgrapht/alg/cycle/SzwarcfiterLauerSimpleCycles.html" title="class in org.jgrapht.alg.cycle">SzwarcfiterLauerSimpleCycles</a><V,E></td>
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<td class="colLast">
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<div class="block">Find all simple cycles of a directed graph using the Schwarcfiter and Lauer's
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algorithm.</div>
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</td>
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<td class="colFirst"><a href="../../../../org/jgrapht/alg/cycle/TarjanSimpleCycles.html" title="class in org.jgrapht.alg.cycle">TarjanSimpleCycles</a><V,E></td>
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<td class="colLast">
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<div class="block">Find all simple cycles of a directed graph using the Tarjan's algorithm.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><a href="../../../../org/jgrapht/alg/cycle/TiernanSimpleCycles.html" title="class in org.jgrapht.alg.cycle">TiernanSimpleCycles</a><V,E></td>
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<td class="colLast">
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<div class="block">Find all simple cycles of a directed graph using the Tiernan's algorithm.</div>
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</td>
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</tr>
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</tbody>
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</table>
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</li>
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</ul>
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<a name="package_description">
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<!-- -->
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</a>
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<h2 title="Package org.jgrapht.alg.cycle Description">Package org.jgrapht.alg.cycle Description</h2>
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<div class="block"><p>Algorithms for enumeration of simple cycles in graphs.</p>
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<b>Implementation Note:</b><p> All the implementations work correctly
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with loops but not with multiple duplicate edges.
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</p>
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<b>Performance Notes:</b>
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<p> The worst case time complexity of
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the algorithms for finding cycles in directed graphs is:
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<ol>
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<li>Tiernan - O(V.const^V)</li>
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<li>Tarjan - O(VEC)</li>
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<li>Johnson - O(((V+E)C)</li>
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<li>Szwarcfiter and Lauer - O(V+EC)</li>
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</ol>
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where V is the number of vertices, E is the number of edges and C is
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the number of the simple cycles in the graph.
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</p>
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<p> The worst case performance is
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achieved for graphs with special structure, so on practical
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workloads an algorithm with higher worst case complexity may
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outperform an algorithm with lower worst case complexity. Note
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also that "administrative costs" of algorithms with better worst
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case performance are higher. Also higher is their memory cost
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(which is in all cases O(V+E)).</p>
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<p> The package author's workloads
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contain typically several hundred nodes and from tens to several
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thousand simple cycles. On these workloads the algorithms score
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by performance (best to worst ) so :
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<ol>
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<li>Szwarcfiter and Lauer</li>
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<li>Tarjan</li>
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<li>Johnson</li>
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<li>Tiernan</li>
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</ol>
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The worst case time complexity of the
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Paton's algorithm for finding a cycle base in undirected graphs
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is O(V^3)
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</p>
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<b>Literature:</b>
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<br>
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<ol>
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<li>J.C.Tiernan An Efficient Search Algorithm Find the
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Elementary Circuits of a Graph., Communications of the ACM,
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V13, 12, (1970), pp. 722 - 726.</li>
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<li>R.Tarjan, Depth-first search and linear graph
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algorithms., SIAM J. Comput. 1 (1972), pp. 146-160.</li>
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<li>R. Tarjan, Enumeration of the elementary circuits of a
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directed graph, SIAM J. Comput., 2 (1973), pp. 211-216.</li>
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<li>D.B.Johnson, Finding all the elementary circuits of a
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directed graph, SIAM J. Comput., 4 (1975), pp. 77-84.</li>
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<li>J.L.Szwarcfiter and P.E.Lauer, Finding the elementary
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cycles of a directed graph in O(n + m) per cycle, Technical
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Report Series, #60, May 1974, Univ. of Newcastle upon Tyne,
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Newcastle upon Tyne, England.</li>
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<li>P.Mateti and N.Deo, On algorithms for enumerating all
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circuits of a graph., SIAM J. Comput., 5 (1978), pp. 90-99.</li>
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<li>L.G.Bezem and J.van Leeuwen, Enumeration in graphs.,
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Technical report RUU-CS-87-7, University of Utrecht, The
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Netherlands, 1987.</li>
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<li>K. Paton, An algorithm for finding a fundamental set of
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cycles for an undirected linear graph, Comm. ACM 12 (1969),
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pp. 514-518.</li>
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