1.1 --- a/lemon/hao_orlin.h Mon Oct 30 15:29:50 2006 +0000
1.2 +++ b/lemon/hao_orlin.h Mon Oct 30 16:12:44 2006 +0000
1.3 @@ -42,11 +42,11 @@
1.4 ///
1.5 /// \brief %Hao-Orlin algorithm to find a minimum cut in directed graphs.
1.6 ///
1.7 - /// Hao-Orlin calculates a minimum cut in a directed graph \f$
1.8 - /// D=(V,A) \f$. It takes a fixed node \f$ source \in V \f$ and consists
1.9 + /// Hao-Orlin calculates a minimum cut in a directed graph
1.10 + /// \f$ D=(V,A) \f$. It takes a fixed node \f$ source \in V \f$ and consists
1.11 /// of two phases: in the first phase it determines a minimum cut
1.12 - /// with \f$ source \f$ on the source-side (i.e. a set \f$ X\subsetneq V
1.13 - /// \f$ with \f$ source \in X \f$ and minimal out-degree) and in the
1.14 + /// with \f$ source \f$ on the source-side (i.e. a set \f$ X\subsetneq V \f$
1.15 + /// with \f$ source \in X \f$ and minimal out-degree) and in the
1.16 /// second phase it determines a minimum cut with \f$ source \f$ on the
1.17 /// sink-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source \notin X \f$
1.18 /// and minimal out-degree). Obviously, the smaller of these two
1.19 @@ -56,8 +56,9 @@
1.20 /// highest-label rule). The purpose of such an algorithm is testing
1.21 /// network reliability. For an undirected graph with \f$ n \f$
1.22 /// nodes and \f$ e \f$ edges you can use the algorithm of Nagamochi
1.23 - /// and Ibaraki which solves the undirected problem in \f$ O(ne +
1.24 - /// n^2 \log(n)) \f$ time: it is implemented in the MinCut algorithm
1.25 + /// and Ibaraki which solves the undirected problem in
1.26 + /// \f$ O(ne + n^2 \log(n)) \f$ time: it is implemented in the MinCut
1.27 + /// algorithm
1.28 /// class.
1.29 ///
1.30 /// \param _Graph is the graph type of the algorithm.
1.31 @@ -535,8 +536,8 @@
1.32 /// source-side.
1.33 ///
1.34 /// \brief Calculates a minimum cut with \f$ source \f$ on the
1.35 - /// source-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source \in X
1.36 - /// \f$ and minimal out-degree).
1.37 + /// source-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source \in X \f$
1.38 + /// and minimal out-degree).
1.39 void calculateOut() {
1.40 for (NodeIt it(*_graph); it != INVALID; ++it) {
1.41 if (it != _source) {
1.42 @@ -550,8 +551,8 @@
1.43 /// source-side.
1.44 ///
1.45 /// \brief Calculates a minimum cut with \f$ source \f$ on the
1.46 - /// source-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source \in X
1.47 - /// \f$ and minimal out-degree). The \c target is the initial target
1.48 + /// source-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source \in X \f$
1.49 + /// and minimal out-degree). The \c target is the initial target
1.50 /// for the push-relabel algorithm.
1.51 void calculateOut(const Node& target) {
1.52 findMinCut(target, true, *_out_res_graph, *_out_current_edge);
1.53 @@ -561,8 +562,9 @@
1.54 /// sink-side.
1.55 ///
1.56 /// \brief Calculates a minimum cut with \f$ source \f$ on the
1.57 - /// sink-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source \notin X
1.58 - /// \f$ and minimal out-degree).
1.59 + /// sink-side (i.e. a set \f$ X\subsetneq V \f$ with
1.60 + /// \f$ source \notin X \f$
1.61 + /// and minimal out-degree).
1.62 void calculateIn() {
1.63 for (NodeIt it(*_graph); it != INVALID; ++it) {
1.64 if (it != _source) {
1.65 @@ -576,8 +578,9 @@
1.66 /// sink-side.
1.67 ///
1.68 /// \brief Calculates a minimum cut with \f$ source \f$ on the
1.69 - /// sink-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source \notin
1.70 - /// X \f$ and minimal out-degree). The \c target is the initial
1.71 + /// sink-side (i.e. a set \f$ X\subsetneq V
1.72 + /// \f$ with \f$ source \notin X \f$ and minimal out-degree).
1.73 + /// The \c target is the initial
1.74 /// target for the push-relabel algorithm.
1.75 void calculateIn(const Node& target) {
1.76 findMinCut(target, false, *_in_res_graph, *_in_current_edge);