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<html>
<head>
<title>
LAUPACK - Graph routines by Hang Tong Lau
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
LAUPACK <br> Graph routines by Hang Tong Lau
</h1>
<hr>
<p>
<b>LAUPACK</b>
is a FORTRAN90 library which
carries out a variety of operations on mathematical graphs.
</p>
<p>
Routines are included to:
<ul>
<li>
find an Euler circuit (use every edge once);
</li>
<li>
find a Hamilton circuit (visit every node once);
</li>
<li>
find cliques (nodes that are all connected to each other);
</li>
<li>
find the strongly connected components of a directed graph;
</li>
<li>
find a minimum spanning tree (the shortest collection of edges
that leave the graph connected);
</li>
<li>
find the chromatic number (the number of colors necessary to
paint each node, with no adjacent nodes the same color);
</li>
<li>
find the K shortest paths in a graph whose edge lengths are given;
</li>
<li>
find the maximal flow in a graph with source and sink nodes,
and edge capacities;
</li>
<li>
determine if a graph is planar;
</li>
</ul>
</p>
<h3 align = "center">
Related Data and Programs
</h3>
<p>
<a href = "../../f_src/codepack/codepack.html">
CODEPACK</a>,
a FORTRAN90 library which
computes "codes" that can determine if two graphs are isomorphic.
<p>
<p>
<a href = "../../f_src/dijkstra/dijkstra.html">
DIJKSTRA</a>,
a FORTRAN90 program which
runs a simple example of Dijkstra's minimum distance algorithm for graphs.
</p>
<p>
<a href = "../../f_src/floyd/floyd.html">
FLOYD</a>,
a FORTRAN90 library which
implements Floyd's algorithm for finding the shortest distance between pairs of
nodes on a directed graph.
</p>
<p>
<a href = "../../f_src/grafpack/grafpack.html">
GRAFPACK</a>,
a FORTRAN90 library which
carries out operations on abstract graphs.
</p>
<p>
<a href = "../../data/graph_representation/graph_representation.html">
GRAPH_REPRESENTATION</a>,
a data directory which
contains examples of ways of representing abstract
mathematical graphs
</p>
<p>
<a href = "../../data/grf/grf.html">
GRF</a>,
a data directory which
contains a description and examples of the GRF file format for storing graphs.
<p>
<p>
<a href = "../../f_src/subset/subset.html">
SUBSET</a>,
a FORTRAN90 library which
enumerates combinations, partitions, subsets, index sets,
and other combinatorial objects.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Hang Tong Lau
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Hang Tong Lau,<br>
Algorithms on Graphs,<br>
Tab Books, 1989,<br>
LC: QA166 L38.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "laupack.f90">laupack.f90</a>, the source code.
</li>
<li>
<a href = "laupack.sh">laupack.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "laupack_prb.f90">laupack_prb.f90</a>, a sample problem.
</li>
<li>
<a href = "laupack_prb.sh">laupack_prb.sh</a>,
commands to compile, link and run the sample problem.
</li>
<li>
<a href = "laupack_prb_output.txt">laupack_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>COLOR2</b> carries out a two-coloring for a planarity test.
</li>
<li>
<b>R8_SWAP</b> swaps two R8's.
</li>
<li>
<b>DECOMP</b> does path decomposition for a planarity test.
</li>
<li>
<b>DFS1</b> carries out the first depth first search for a planarity test.
</li>
<li>
<b>DFS2</b> carries out the second depth-first search for a planarity test.
</li>
<li>
<b>DIGRAPH_ARC_EULER</b> returns an Euler circuit in a digraph.
</li>
<li>
<b>DIGRAPH_ARC_FIND_PATH</b> determines if a path exists from 11 to J1.
</li>
<li>
<b>DIGRAPH_ARC_GET_PATH</b> retrieves the edges of the K-th shortest path.
</li>
<li>
<b>DIGRAPH_ARC_HAMCYC</b> finds a Hamiltonian circuit in a digraph.
</li>
<li>
<b>DIGRAPH_ARC_KSHORT1</b> finds the K shortest paths in a digraph.
</li>
<li>
<b>DIGRAPH_ARC_KSHORT2</b> finds the KPATHS shortest distinct path lengths without repeat nodes.
</li>
<li>
<b>DIGRAPH_ARC_MINEQV</b> finds a minimal equivalent of a strongly connected digraph.
</li>
<li>
<b>DIGRAPH_ARC_NFLOW</b> implements Karzanov's network flow algorithm.
</li>
<li>
<b>DIGRAPH_ARC_PRINT</b> prints out a digraph from an edge list.
</li>
<li>
<b>DIGRAPH_ARC_PRT_PATH</b> outputs at most MAXPTH number of K shortest paths between two nodes.
</li>
<li>
<b>DIGRAPH_ARC_SHTREE</b> finds the shortest paths from IROOT to all other nodes.
</li>
<li>
<b>DIGRAPH_ARC_STCOMP</b> finds the strongly connected components of a digraph.
</li>
<li>
<b>DIGRAPH_ARC_TO_STAR</b> sets up the forward star representation of a digraph.
</li>
<li>
<b>DIGRAPH_ARC_WEIGHT_PRINT</b> prints out a weighted digraph from an edge list.
</li>
<li>
<b>DIGRAPH_DIST_ALLPATH</b> finds the shortest paths for all pairs of nodes in a digraph.
</li>
<li>
<b>DIGRAPH_DIST_FMIN</b> stores values of K such that DISTAB(K) = LITTLE and DISTAB(J) = KEY.
</li>
<li>
<b>DIGRAPH_DIST_PRINT</b> prints a distance matrix.
</li>
<li>
<b>DIGRAPH_DIST_SHORT_LN</b> finds the shortest paths from one node to all others.
</li>
<li>
<b>DIGRAPH_DIST_SHORTP</b> finds the shortest path from ISORCE to ISINK in a digraph.
</li>
<li>
<b>GRAPH_ARC_CLIQUE</b> finds all the cliques of a graph.
</li>
<li>
<b>GRAPH_ARC_COLOR_NUMBER</b> finds the chromatic number of a graph.
</li>
<li>
<b>GRAPH_ARC_COLOR_POLY</b> computes the chromatic polynomial of a graph.
</li>
<li>
<b>GRAPH_ARC_CONECT</b> finds the bridges, blocks and cut nodes of an undirected graph.
</li>
<li>
<b>GRAPH_ARC_DEGREE</b> finds the degree of the nodes of an undirected graph.
</li>
<li>
<b>GRAPH_ARC_EDGE_CON</b> finds the edge-connectivity of a connected graph.
</li>
<li>
<b>GRAPH_ARC_EULER</b> returns an Euler circuit in an undirected graph.
</li>
<li>
<b>GRAPH_ARC_FCYCLE</b> finds a fundamental set of cycles in an undirected graph.
</li>
<li>
<b>GRAPH_ARC_HAMCYC</b> finds a Hamiltonian circuit in a graph.
</li>
<li>
<b>GRAPH_ARC_MAKEG</b> constructs a graph with NNODE nodes and K-connectivity.
</li>
<li>
<b>GRAPH_ARC_MATCH</b> finds a maximum cardinality matching in a graph.
</li>
<li>
<b>GRAPH_ARC_MINTR2</b> finds the minimum spanning tree of a graph, using an edge array.
</li>
<li>
<b>GRAPH_ARC_NCOLOR_PRINT</b> prints out a node-colored graph from an edge list.
</li>
<li>
<b>GRAPH_ARC_PLANAR</b> determines if a graph is planar.
</li>
<li>
<b>GRAPH_ARC_PRINT</b> prints out a graph from an edge list.
</li>
<li>
<b>GRAPH_ARC_TO_STAR</b> sets up the forward star representation of an undirected graph.
</li>
<li>
<b>GRAPH_ARC_WEIGHT_PRINT</b> prints out a weighted graph from an edge list.
</li>
<li>
<b>GRAPH_DIST_MINTR1</b> finds a minimum spanning tree for a graph using a distance matrix.
</li>
<li>
<b>GRAPH_DIST_PRINT</b> prints a distance matrix.
</li>
<li>
<b>I4_SWAP</b> swaps two I4's.
</li>
<li>
<b>I4VEC_INDICATOR</b> sets an I4VEC to the indicator vector.
</li>
<li>
<b>I4VEC_PRINT</b> prints an I4VEC.
</li>
<li>
<b>I4VEC_REVERSE</b> reverses the elements of an I4VEC.
</li>
<li>
<b>R8MAT_PRINT</b> prints out a portion of an R8MAT.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 27 November 2006.
</i>
<!-- John Burkardt -->
</body>
</html>