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  5. <title>GTL - Graph Template Library: maxflow_sap Class Reference</title>
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  35. <h1>maxflow_sap Class Reference</h1><!-- doxytag: class="maxflow_sap" --><!-- doxytag: inherits="algorithm" -->Maximum flow <a class="el" href="a00001.html" title="Abstract baseclass for all algoritm-classes.">algorithm</a> with shortest augmenting paths.
  36. <a href="#_details">More...</a>
  37. <p>
  38. <div class="dynheader">
  39. Inheritance diagram for maxflow_sap:</div>
  40. <div class="dynsection">
  41. <p><center><img src="a00164.gif" border="0" usemap="#a00165" alt="Inheritance graph"></center>
  42. <map name="a00165">
  43. <area shape="rect" href="a00001.html" title="Abstract baseclass for all algoritm&#45;classes." alt="" coords="16,7,93,31"></map>
  44. <center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
  45. <div class="dynheader">
  46. Collaboration diagram for maxflow_sap:</div>
  47. <div class="dynsection">
  48. <p><center><img src="a00166.gif" border="0" usemap="#a00167" alt="Collaboration graph"></center>
  49. <map name="a00167">
  50. <area shape="rect" href="a00001.html" title="Abstract baseclass for all algoritm&#45;classes." alt="" coords="428,5,505,29"><area shape="rect" href="a00020.html" title="A node in a graph." alt="" coords="441,92,492,116"><area shape="rect" title="net_source\nnet_target" alt="" coords="489,103,497,111"><area shape="rect" title="net_source\nnet_target" alt="" coords="725,164,733,172"><area shape="rect" title="int_node" alt="" coords="437,91,445,99"><area shape="rect" title="int_node" alt="" coords="489,89,497,97"><area shape="rect" href="a00021.html" title="node_map\&lt; int \&gt;" alt="" coords="405,140,528,164"><area shape="rect" title="dist_label" alt="" coords="524,155,532,163"><area shape="rect" title="dist_label" alt="" coords="696,171,704,179"><area shape="rect" href="a00019.html" title="ne_map\&lt; node, int, graph, allocator\&lt; int \&gt; \&gt;" alt="" coords="32,140,315,164"><area shape="rect" href="a00011.html" title="edge_map\&lt; double \&gt;" alt="" coords="392,196,541,220"><area shape="rect" title="edge_max_flow\nedge_capacity" alt="" coords="537,211,545,219"><area shape="rect" title="edge_max_flow\nedge_capacity" alt="" coords="719,189,727,197"><area shape="rect" href="a00019.html" title="ne_map\&lt; edge, double, graph, allocator\&lt; double \&gt; \&gt;" alt="" coords="7,196,340,220"><area shape="rect" href="a00011.html" title="edge_map\&lt; edge \&gt;" alt="" coords="397,244,536,268"><area shape="rect" title="back_edge" alt="" coords="532,256,540,264"><area shape="rect" title="back_edge" alt="" coords="733,189,741,197"><area shape="rect" href="a00019.html" title="ne_map\&lt; edge, edge, graph, allocator\&lt; edge \&gt; \&gt;" alt="" coords="16,244,331,268"><area shape="rect" href="a00011.html" title="edge_map\&lt; bool \&gt;" alt="" coords="400,303,533,327"><area shape="rect" title="edge_org\nback_edge_exists" alt="" coords="531,319,539,327"><area shape="rect" title="edge_org\nback_edge_exists" alt="" coords="741,189,749,197"><area shape="rect" href="a00019.html" title="ne_map\&lt; edge, bool, graph, allocator\&lt; bool \&gt; \&gt;" alt="" coords="21,303,325,327"></map>
  51. <center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
  52. <p>
  53. <a href="a00168.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
  54. <tr><td></td></tr>
  55. <tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
  56. <tr><td class="memItemLeft" nowrap align="right" valign="top">&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00017.html#d10178be6ae1050c713e192937bbdc8b">maxflow_sap</a> ()</td></tr>
  57. <tr><td class="memItemLeft" nowrap align="right" valign="top">virtual&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00017.html#66e9c3b70dee37a7c8d8d728b4331be0">~maxflow_sap</a> ()</td></tr>
  58. <tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00017.html#c50ba0330c169c7ce697947a76702e13">set_vars</a> (const <a class="el" href="a00011.html">edge_map</a>&lt; double &gt; &amp;edge_capacity)</td></tr>
  59. <tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00017.html#936f6afa25de80046c7bd69dc47fdfa9">set_vars</a> (const <a class="el" href="a00011.html">edge_map</a>&lt; double &gt; &amp;edge_capacity, const <a class="el" href="a00020.html">node</a> &amp;net_source, const <a class="el" href="a00020.html">node</a> &amp;net_target)</td></tr>
  60. <tr><td class="memItemLeft" nowrap align="right" valign="top">virtual int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00017.html#f94644633a5cfb386de082cc02febef3">check</a> (<a class="el" href="a00014.html">graph</a> &amp;G)</td></tr>
  61. <tr><td class="memItemLeft" nowrap align="right" valign="top">int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00017.html#b4305a2bb370ad9c43cc68d339b2dda0">run</a> (<a class="el" href="a00014.html">graph</a> &amp;G)</td></tr>
  62. <tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00017.html#590b1f80b82f09d555ca297b210b1f26">get_max_flow</a> (const <a class="el" href="a00010.html">edge</a> &amp;e) const </td></tr>
  63. <tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00017.html#e2cfd282ab946ea39c5b36c59683f6cd">get_max_flow</a> () const </td></tr>
  64. <tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00017.html#396e9ebda36d04f00f646ae02cabded3">get_rem_cap</a> (const <a class="el" href="a00010.html">edge</a> &amp;e) const </td></tr>
  65. <tr><td class="memItemLeft" nowrap align="right" valign="top">virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00017.html#6c35136743e38cee6c31e18cf8ca20be">reset</a> ()</td></tr>
  66. </table>
  67. <hr><a name="_details"></a><h2>Detailed Description</h2>
  68. Maximum flow <a class="el" href="a00001.html" title="Abstract baseclass for all algoritm-classes.">algorithm</a> with shortest augmenting paths.
  69. <p>
  70. This class implements a maximum flow <a class="el" href="a00001.html" title="Abstract baseclass for all algoritm-classes.">algorithm</a> with shortest augmenting paths due to Ahuja and Orlin.<p>
  71. In the case V is the set of vertices and E is the set of edges of the <a class="el" href="a00014.html" title="A directed or undirected graph.">graph</a>, the <a class="el" href="a00001.html" title="Abstract baseclass for all algoritm-classes.">algorithm</a> needs O(|V| * |V| * |E|) time to proceed.<p>
  72. <dl class="see" compact><dt><b>See also:</b></dt><dd><a class="el" href="a00015.html" title="Maximum flow algorithm (Edmonds-Karp).">maxflow_ff</a> <p>
  73. <a class="el" href="a00016.html" title="Maximum flow algorithm (Malhotra, Kumar, Maheshwari).">maxflow_pp</a> </dd></dl>
  74. <hr><h2>Constructor &amp; Destructor Documentation</h2>
  75. <a class="anchor" name="d10178be6ae1050c713e192937bbdc8b"></a><!-- doxytag: member="maxflow_sap::maxflow_sap" ref="d10178be6ae1050c713e192937bbdc8b" args="()" -->
  76. <div class="memitem">
  77. <div class="memproto">
  78. <table class="memname">
  79. <tr>
  80. <td class="memname">maxflow_sap::maxflow_sap </td>
  81. <td>(</td>
  82. <td class="paramname"> </td>
  83. <td>&nbsp;)&nbsp;</td>
  84. <td width="100%"></td>
  85. </tr>
  86. </table>
  87. </div>
  88. <div class="memdoc">
  89. <p>
  90. Default constructor. Enables only the calculation of maximum flow.<p>
  91. <dl class="see" compact><dt><b>See also:</b></dt><dd><a class="el" href="a00001.html#b79e1ddec2f2afdf4b36b10724db8b15" title="Creates an algorithm object.">algorithm::algorithm</a> </dd></dl>
  92. </div>
  93. </div><p>
  94. <a class="anchor" name="66e9c3b70dee37a7c8d8d728b4331be0"></a><!-- doxytag: member="maxflow_sap::~maxflow_sap" ref="66e9c3b70dee37a7c8d8d728b4331be0" args="()" -->
  95. <div class="memitem">
  96. <div class="memproto">
  97. <table class="memname">
  98. <tr>
  99. <td class="memname">virtual maxflow_sap::~maxflow_sap </td>
  100. <td>(</td>
  101. <td class="paramname"> </td>
  102. <td>&nbsp;)&nbsp;</td>
  103. <td width="100%"><code> [virtual]</code></td>
  104. </tr>
  105. </table>
  106. </div>
  107. <div class="memdoc">
  108. <p>
  109. Destructor.<p>
  110. <dl class="see" compact><dt><b>See also:</b></dt><dd><a class="el" href="a00001.html#dca9b1e7fa3afd914519a9dbb44e9fd5" title="Destroys the algorithm object.">algorithm::~algorithm</a> </dd></dl>
  111. </div>
  112. </div><p>
  113. <hr><h2>Member Function Documentation</h2>
  114. <a class="anchor" name="c50ba0330c169c7ce697947a76702e13"></a><!-- doxytag: member="maxflow_sap::set_vars" ref="c50ba0330c169c7ce697947a76702e13" args="(const edge_map&lt; double &gt; &amp;edge_capacity)" -->
  115. <div class="memitem">
  116. <div class="memproto">
  117. <table class="memname">
  118. <tr>
  119. <td class="memname">void maxflow_sap::set_vars </td>
  120. <td>(</td>
  121. <td class="paramtype">const <a class="el" href="a00011.html">edge_map</a>&lt; double &gt; &amp;&nbsp;</td>
  122. <td class="paramname"> <em>edge_capacity</em> </td>
  123. <td>&nbsp;)&nbsp;</td>
  124. <td width="100%"></td>
  125. </tr>
  126. </table>
  127. </div>
  128. <div class="memdoc">
  129. <p>
  130. Sets capacity of every <a class="el" href="a00010.html" title="An edge in a graph.">edge</a> for maximum flow calculation where artificial start-node and end_node will be computed automatically.<p>
  131. <dl compact><dt><b>Parameters:</b></dt><dd>
  132. <table border="0" cellspacing="2" cellpadding="0">
  133. <tr><td valign="top"></td><td valign="top"><em>edge_capacity</em>&nbsp;</td><td>capacity of every <a class="el" href="a00010.html" title="An edge in a graph.">edge</a> </td></tr>
  134. </table>
  135. </dl>
  136. </div>
  137. </div><p>
  138. <a class="anchor" name="936f6afa25de80046c7bd69dc47fdfa9"></a><!-- doxytag: member="maxflow_sap::set_vars" ref="936f6afa25de80046c7bd69dc47fdfa9" args="(const edge_map&lt; double &gt; &amp;edge_capacity, const node &amp;net_source, const node &amp;net_target)" -->
  139. <div class="memitem">
  140. <div class="memproto">
  141. <table class="memname">
  142. <tr>
  143. <td class="memname">void maxflow_sap::set_vars </td>
  144. <td>(</td>
  145. <td class="paramtype">const <a class="el" href="a00011.html">edge_map</a>&lt; double &gt; &amp;&nbsp;</td>
  146. <td class="paramname"> <em>edge_capacity</em>, </td>
  147. </tr>
  148. <tr>
  149. <td class="paramkey"></td>
  150. <td></td>
  151. <td class="paramtype">const <a class="el" href="a00020.html">node</a> &amp;&nbsp;</td>
  152. <td class="paramname"> <em>net_source</em>, </td>
  153. </tr>
  154. <tr>
  155. <td class="paramkey"></td>
  156. <td></td>
  157. <td class="paramtype">const <a class="el" href="a00020.html">node</a> &amp;&nbsp;</td>
  158. <td class="paramname"> <em>net_target</em></td><td>&nbsp;</td>
  159. </tr>
  160. <tr>
  161. <td></td>
  162. <td>)</td>
  163. <td></td><td></td><td width="100%"></td>
  164. </tr>
  165. </table>
  166. </div>
  167. <div class="memdoc">
  168. <p>
  169. Sets capacity of every <a class="el" href="a00010.html" title="An edge in a graph.">edge</a> for maximum flow calculation<p>
  170. <dl compact><dt><b>Parameters:</b></dt><dd>
  171. <table border="0" cellspacing="2" cellpadding="0">
  172. <tr><td valign="top"></td><td valign="top"><em>edge_capacity</em>&nbsp;</td><td>capacity of every <a class="el" href="a00010.html" title="An edge in a graph.">edge</a> </td></tr>
  173. <tr><td valign="top"></td><td valign="top"><em>net_source</em>&nbsp;</td><td>start-node </td></tr>
  174. <tr><td valign="top"></td><td valign="top"><em>net_target</em>&nbsp;</td><td>end-node </td></tr>
  175. </table>
  176. </dl>
  177. </div>
  178. </div><p>
  179. <a class="anchor" name="f94644633a5cfb386de082cc02febef3"></a><!-- doxytag: member="maxflow_sap::check" ref="f94644633a5cfb386de082cc02febef3" args="(graph &amp;G)" -->
  180. <div class="memitem">
  181. <div class="memproto">
  182. <table class="memname">
  183. <tr>
  184. <td class="memname">virtual int maxflow_sap::check </td>
  185. <td>(</td>
  186. <td class="paramtype"><a class="el" href="a00014.html">graph</a> &amp;&nbsp;</td>
  187. <td class="paramname"> <em>G</em> </td>
  188. <td>&nbsp;)&nbsp;</td>
  189. <td width="100%"><code> [virtual]</code></td>
  190. </tr>
  191. </table>
  192. </div>
  193. <div class="memdoc">
  194. <p>
  195. Checks whether following preconditions are satisfied: <ul>
  196. <li>
  197. <a class="el" href="a00017.html#c50ba0330c169c7ce697947a76702e13">maxflow_sap::set_vars</a> has been executed before. </li>
  198. <li>
  199. only edge_capacities &gt;= 0 are applied. </li>
  200. <li>
  201. <code>G</code> is directed. </li>
  202. <li>
  203. <code>G</code> is connected. </li>
  204. <li>
  205. <code>G</code> has at least one <a class="el" href="a00010.html" title="An edge in a graph.">edge</a> and two nodes. </li>
  206. <li>
  207. if not applied, start-nodes and end-nodes exists. </li>
  208. <li>
  209. if applied, start-node is not the same <a class="el" href="a00020.html" title="A node in a graph.">node</a> as end-node. </li>
  210. </ul>
  211. <p>
  212. <dl compact><dt><b>Parameters:</b></dt><dd>
  213. <table border="0" cellspacing="2" cellpadding="0">
  214. <tr><td valign="top"></td><td valign="top"><em>G</em>&nbsp;</td><td><a class="el" href="a00014.html" title="A directed or undirected graph.">graph</a> </td></tr>
  215. </table>
  216. </dl>
  217. <dl class="return" compact><dt><b>Returns:</b></dt><dd><code><a class="el" href="a00001.html#f1a0078e153aa99c24f9bdf0d97f67105114c20e4a96a76b5de9f28bf15e282b">algorithm::GTL_OK</a></code> on success <code><a class="el" href="a00001.html#f1a0078e153aa99c24f9bdf0d97f67106fcf574690bbd6cf710837a169510dd7">algorithm::GTL_ERROR</a></code> otherwise </dd></dl>
  218. <dl class="see" compact><dt><b>See also:</b></dt><dd><a class="el" href="a00001.html#76361fb03ad1cf643affc51821e43bed" title="Checks whether all preconditions are satisfied.">algorithm::check</a> </dd></dl>
  219. <p>Implements <a class="el" href="a00001.html#76361fb03ad1cf643affc51821e43bed">algorithm</a>.</p>
  220. </div>
  221. </div><p>
  222. <a class="anchor" name="b4305a2bb370ad9c43cc68d339b2dda0"></a><!-- doxytag: member="maxflow_sap::run" ref="b4305a2bb370ad9c43cc68d339b2dda0" args="(graph &amp;G)" -->
  223. <div class="memitem">
  224. <div class="memproto">
  225. <table class="memname">
  226. <tr>
  227. <td class="memname">int maxflow_sap::run </td>
  228. <td>(</td>
  229. <td class="paramtype"><a class="el" href="a00014.html">graph</a> &amp;&nbsp;</td>
  230. <td class="paramname"> <em>G</em> </td>
  231. <td>&nbsp;)&nbsp;</td>
  232. <td width="100%"><code> [virtual]</code></td>
  233. </tr>
  234. </table>
  235. </div>
  236. <div class="memdoc">
  237. <p>
  238. Computes maximum flow of <a class="el" href="a00014.html" title="A directed or undirected graph.">graph</a> <code>G</code>.<p>
  239. <dl compact><dt><b>Parameters:</b></dt><dd>
  240. <table border="0" cellspacing="2" cellpadding="0">
  241. <tr><td valign="top"></td><td valign="top"><em>G</em>&nbsp;</td><td><a class="el" href="a00014.html" title="A directed or undirected graph.">graph</a> </td></tr>
  242. </table>
  243. </dl>
  244. <dl class="return" compact><dt><b>Returns:</b></dt><dd><code><a class="el" href="a00001.html#f1a0078e153aa99c24f9bdf0d97f67105114c20e4a96a76b5de9f28bf15e282b">algorithm::GTL_OK</a></code> on success <code><a class="el" href="a00001.html#f1a0078e153aa99c24f9bdf0d97f67106fcf574690bbd6cf710837a169510dd7">algorithm::GTL_ERROR</a></code> otherwise </dd></dl>
  245. <dl class="see" compact><dt><b>See also:</b></dt><dd><a class="el" href="a00001.html#734b189509a8d6b56b65f8ff772d43ca" title="Applies algorithm to graph g.">algorithm::run</a> </dd></dl>
  246. <p>Implements <a class="el" href="a00001.html#734b189509a8d6b56b65f8ff772d43ca">algorithm</a>.</p>
  247. </div>
  248. </div><p>
  249. <a class="anchor" name="590b1f80b82f09d555ca297b210b1f26"></a><!-- doxytag: member="maxflow_sap::get_max_flow" ref="590b1f80b82f09d555ca297b210b1f26" args="(const edge &amp;e) const " -->
  250. <div class="memitem">
  251. <div class="memproto">
  252. <table class="memname">
  253. <tr>
  254. <td class="memname">double maxflow_sap::get_max_flow </td>
  255. <td>(</td>
  256. <td class="paramtype">const <a class="el" href="a00010.html">edge</a> &amp;&nbsp;</td>
  257. <td class="paramname"> <em>e</em> </td>
  258. <td>&nbsp;)&nbsp;</td>
  259. <td width="100%"> const</td>
  260. </tr>
  261. </table>
  262. </div>
  263. <div class="memdoc">
  264. <p>
  265. Returns the maximum flow of an <a class="el" href="a00010.html" title="An edge in a graph.">edge</a>.<p>
  266. <dl compact><dt><b>Parameters:</b></dt><dd>
  267. <table border="0" cellspacing="2" cellpadding="0">
  268. <tr><td valign="top"></td><td valign="top"><em>e</em>&nbsp;</td><td><a class="el" href="a00010.html" title="An edge in a graph.">edge</a> of a <a class="el" href="a00014.html" title="A directed or undirected graph.">graph</a> <code>G</code> </td></tr>
  269. </table>
  270. </dl>
  271. <dl class="return" compact><dt><b>Returns:</b></dt><dd>maximum flow value </dd></dl>
  272. </div>
  273. </div><p>
  274. <a class="anchor" name="e2cfd282ab946ea39c5b36c59683f6cd"></a><!-- doxytag: member="maxflow_sap::get_max_flow" ref="e2cfd282ab946ea39c5b36c59683f6cd" args="() const " -->
  275. <div class="memitem">
  276. <div class="memproto">
  277. <table class="memname">
  278. <tr>
  279. <td class="memname">double maxflow_sap::get_max_flow </td>
  280. <td>(</td>
  281. <td class="paramname"> </td>
  282. <td>&nbsp;)&nbsp;</td>
  283. <td width="100%"> const</td>
  284. </tr>
  285. </table>
  286. </div>
  287. <div class="memdoc">
  288. <p>
  289. Returns the maximum flow of the whole <a class="el" href="a00014.html" title="A directed or undirected graph.">graph</a> G.<p>
  290. <dl class="return" compact><dt><b>Returns:</b></dt><dd>maximum flow value </dd></dl>
  291. </div>
  292. </div><p>
  293. <a class="anchor" name="396e9ebda36d04f00f646ae02cabded3"></a><!-- doxytag: member="maxflow_sap::get_rem_cap" ref="396e9ebda36d04f00f646ae02cabded3" args="(const edge &amp;e) const " -->
  294. <div class="memitem">
  295. <div class="memproto">
  296. <table class="memname">
  297. <tr>
  298. <td class="memname">double maxflow_sap::get_rem_cap </td>
  299. <td>(</td>
  300. <td class="paramtype">const <a class="el" href="a00010.html">edge</a> &amp;&nbsp;</td>
  301. <td class="paramname"> <em>e</em> </td>
  302. <td>&nbsp;)&nbsp;</td>
  303. <td width="100%"> const</td>
  304. </tr>
  305. </table>
  306. </div>
  307. <div class="memdoc">
  308. <p>
  309. Returns the remaining free capacity of an <a class="el" href="a00010.html" title="An edge in a graph.">edge</a>.<p>
  310. <dl compact><dt><b>Parameters:</b></dt><dd>
  311. <table border="0" cellspacing="2" cellpadding="0">
  312. <tr><td valign="top"></td><td valign="top"><em>e</em>&nbsp;</td><td><a class="el" href="a00010.html" title="An edge in a graph.">edge</a> of a <a class="el" href="a00014.html" title="A directed or undirected graph.">graph</a> <code>G</code> </td></tr>
  313. </table>
  314. </dl>
  315. <dl class="return" compact><dt><b>Returns:</b></dt><dd>remaining capacity </dd></dl>
  316. </div>
  317. </div><p>
  318. <a class="anchor" name="6c35136743e38cee6c31e18cf8ca20be"></a><!-- doxytag: member="maxflow_sap::reset" ref="6c35136743e38cee6c31e18cf8ca20be" args="()" -->
  319. <div class="memitem">
  320. <div class="memproto">
  321. <table class="memname">
  322. <tr>
  323. <td class="memname">virtual void maxflow_sap::reset </td>
  324. <td>(</td>
  325. <td class="paramname"> </td>
  326. <td>&nbsp;)&nbsp;</td>
  327. <td width="100%"><code> [virtual]</code></td>
  328. </tr>
  329. </table>
  330. </div>
  331. <div class="memdoc">
  332. <p>
  333. Resets maximum flow <a class="el" href="a00001.html" title="Abstract baseclass for all algoritm-classes.">algorithm</a>, i.e. prepares the <a class="el" href="a00001.html" title="Abstract baseclass for all algoritm-classes.">algorithm</a> to be applied to another <a class="el" href="a00014.html" title="A directed or undirected graph.">graph</a>.<p>
  334. <dl class="see" compact><dt><b>See also:</b></dt><dd><a class="el" href="a00001.html#21aba63d066ae7897de6ca7d8425c408" title="Resets algorithm.">algorithm::reset</a> </dd></dl>
  335. <p>Implements <a class="el" href="a00001.html#21aba63d066ae7897de6ca7d8425c408">algorithm</a>.</p>
  336. </div>
  337. </div><p>
  338. <p class="links">
  339. <a href="http://www.uni-passau.de/">University of Passau</a>
  340. &nbsp;-&nbsp;
  341. <a href="http://www.fmi.uni-passau.de/">FMI</a>
  342. &nbsp;-&nbsp;
  343. <a href="http://www.fmi.uni-passau.de/fmi/lehrstuehle/brandenburg/">Theoretical
  344. Computer Science</a>
  345. </p>
  346. <div class="copyright">
  347. Design &copy; 2002, 2003 <a href="mailto:raitner@fmi.uni-passau.de">Marcus Raitner</a>, University of Passau
  348. </div>
  349. </body>
  350. </html>