/* -*- mode: C++; indent-tabs-mode: nil; -*-
*
* This file is a part of LEMON, a generic C++ optimization library.
*
* Copyright (C) 2003-2010
* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
* (Egervary Research Group on Combinatorial Optimization, EGRES).
*
* Permission to use, modify and distribute this software is granted
* provided that this copyright notice appears in all copies. For
* precise terms see the accompanying LICENSE file.
*
* This software is provided "AS IS" with no warranty of any kind,
* express or implied, and with no claim as to its suitability for any
* purpose.
*
*/
namespace lemon {
/**
[PAGE]sec_graph_adaptors[PAGE] Graph Adaptors
\todo Clarify this section.
Alteration of standard containers need a very limited number of
operations, these together satisfy the everyday requirements.
In the case of graph structures, different operations are needed which do
not alter the physical graph, but gives another view. If some nodes or
arcs have to be hidden or the reverse oriented graph have to be used, then
this is the case. It also may happen that in a flow implementation
the residual graph can be accessed by another algorithm, or a node-set
is to be shrunk for another algorithm.
LEMON also provides a variety of graphs for these requirements called
\ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only
in conjunction with other graph representations.
The main parts of LEMON are the different graph structures, generic
graph algorithms, graph concepts, which couple them, and graph
adaptors. While the previous notions are more or less clear, the
latter one needs further explanation. Graph adaptors are graph classes
which serve for considering graph structures in different ways.
A short example makes this much clearer. Suppose that we have an
instance \c g of a directed graph type, say ListDigraph and an algorithm
\code
template
int algorithm(const Digraph&);
\endcode
is needed to run on the reverse oriented graph. It may be expensive
(in time or in memory usage) to copy \c g with the reversed
arcs. In this case, an adaptor class is used, which (according
to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph.
The adaptor uses the original digraph structure and digraph operations when
methods of the reversed oriented graph are called. This means that the adaptor
have minor memory usage, and do not perform sophisticated algorithmic
actions. The purpose of it is to give a tool for the cases when a
graph have to be used in a specific alteration. If this alteration is
obtained by a usual construction like filtering the node or the arc set or
considering a new orientation, then an adaptor is worthwhile to use.
To come back to the reverse oriented graph, in this situation
\code
template class ReverseDigraph;
\endcode
template class can be used. The code looks as follows
\code
ListDigraph g;
ReverseDigraph rg(g);
int result = algorithm(rg);
\endcode
During running the algorithm, the original digraph \c g is untouched.
This techniques give rise to an elegant code, and based on stable
graph adaptors, complex algorithms can be implemented easily.
In flow, circulation and matching problems, the residual
graph is of particular importance. Combining an adaptor implementing
this with shortest path algorithms or minimum mean cycle algorithms,
a range of weighted and cardinality optimization algorithms can be
obtained. For other examples, the interested user is referred to the
detailed documentation of particular adaptors.
The behavior of graph adaptors can be very different. Some of them keep
capabilities of the original graph while in other cases this would be
meaningless. This means that the concepts that they meet depend
on the graph adaptor, and the wrapped graph.
For example, if an arc of a reversed digraph is deleted, this is carried
out by deleting the corresponding arc of the original digraph, thus the
adaptor modifies the original digraph.
However in case of a residual digraph, this operation has no sense.
Let us stand one more example here to simplify your work.
ReverseDigraph has constructor
\code
ReverseDigraph(Digraph& digraph);
\endcode
This means that in a situation, when a `const %ListDigraph&`
reference to a graph is given, then it have to be instantiated with
`Digraph=const %ListDigraph`.
\code
int algorithm1(const ListDigraph& g) {
ReverseDigraph rg(g);
return algorithm2(rg);
}
\endcode

The LEMON graph adaptor classes serve for considering graphs in
different ways. The adaptors can be used exactly the same as "real"
graphs (i.e., they conform to the graph concepts), thus all generic
algorithms can be performed on them. However, the adaptor classes use
the underlying graph structures and operations when their methods are
called, thus they have only negligible memory usage and do not perform
sophisticated algorithmic actions. This technique yields convenient and
elegant tools for the cases when a graph has to be used in a specific
alteration, but copying it would be too expensive (in time or in memory
usage) compared to the algorithm that should be executed on it. The
following example shows how the \ref ReverseDigraph adaptor can be used
to run Dijksta's algorithm on the reverse oriented graph. Note that the
maps of the original graph can be used in connection with the adaptor,
since the node and arc types of the adaptors convert to the original
item types.
\code
dijkstra(reverseDigraph(g), length).distMap(dist).run(s);
\endcode
Using \ref ReverseDigraph could be as efficient as working with the
original graph, but not all adaptors can be so fast, of course. For
example, the subgraph adaptors have to access filter maps for the nodes
and/or the arcs, thus their iterators are significantly slower than the
original iterators. LEMON also provides some more complex adaptors, for
instance, \ref SplitNodes, which can be used for splitting each node in
a directed graph and \ref ResidualDigraph for modeling the residual
network for flow and matching problems.
Therefore, in cases when rather complex algorithms have to be used
on a subgraph (e.g. when the nodes and arcs have to be traversed several
times), it could worth copying the altered graph into an efficient structure
and run the algorithm on it.
Note that the adaptor classes can also be used for doing this easily,
without having to copy the graph manually, as shown in the following
example.
\code
ListDigraph g;
ListDigraph::NodeMap filter_map(g);
// construct the graph and fill the filter map
{
SmartDigraph temp_graph;
ListDigraph::NodeMap node_ref(g);
digraphCopy(filterNodes(g, filter_map), temp_graph)
.nodeRef(node_ref).run();
// use temp_graph
}
\endcode

Another interesting adaptor in LEMON is \ref SplitNodes.
It can be used for splitting each node into an in-node and an out-node
in a directed graph. Formally, the adaptor replaces each node
u in the graph with two nodes, namely node u_{in} and node
u_{out}. Each arc (u,c) in the original graph will correspond to an
arc (u_{out},v_{in}). The adaptor also adds an
additional bind arc (u_{in},u_{out}) for each node u
of the original digraph.
The aim of this class is to assign costs to the nodes when using
algorithms which would otherwise consider arc costs only.
For example, let us suppose that we have a directed graph with costs
given for both the nodes and the arcs.
Then Dijkstra's algorithm can be used in connection with \ref SplitNodes
as follows.
\code
typedef SplitNodes SplitGraph;
SplitGraph sg(g);
SplitGraph::CombinedArcMap
combined_cost(node_cost, arc_cost);
SplitGraph::NodeMap dist(sg);
dijkstra(sg, combined_cost).distMap(dist).run(sg.outNode(u));
\endcode
Note that this problem can be solved more efficiently with
map adaptors.
These techniques help writing compact and elegant code, and makes it possible
to easily implement complex algorithms based on well tested standard components.
For instance, in flow and matching problems the residual graph is of
particular importance.
Combining \ref ResidualDigraph adaptor with various algorithms, a
range of weighted and cardinality optimization methods can be obtained
directly.
[TRAILER]
*/
}