# OpenGraph DrawingFramework

v. 2023.09 (Elderberry)

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ogdf::MinSteinerTreeMehlhorn< T > Class Template Reference

This class implements the Minimum Steiner Tree 2-approximation algorithm by Mehlhorn. More...

#include <ogdf/graphalg/MinSteinerTreeMehlhorn.h>

Inheritance diagram for ogdf::MinSteinerTreeMehlhorn< T >:

## Classes

struct  MehlhornTriple
Represents a triple as specified in the algorithms description (see paper) More...

class  MehlhornTripleBucketMaxFunc
Helper class to sort MehlhornTriples lexicographically. More...

class  MehlhornTripleBucketMinFunc
Helper class to sort MehlhornTriples lexicographically. More...

## Public Member Functions

MinSteinerTreeMehlhorn ()

virtual ~MinSteinerTreeMehlhorn ()

Public Member Functions inherited from ogdf::MinSteinerTreeModule< T >
virtual ~MinSteinerTreeModule ()
Do nothing on destruction.

virtualcall (const EdgeWeightedGraph< T > &G, const List< node > &terminals, const NodeArray< bool > &isTerminal, EdgeWeightedGraphCopy< T > *&finalSteinerTree)
Calls the Steiner tree algorithm for nontrivial cases but handles trivial cases directly.

## Static Public Member Functions

static void calculateCompleteGraph (const EdgeWeightedGraph< T > &wG, const List< node > &terminals, const Voronoi< T > &voronoi, EdgeArray< edge > &bridges, EdgeWeightedGraphCopy< T > &completeTerminalGraph)
Builds a complete terminal graph.

Static Public Member Functions inherited from ogdf::MinSteinerTreeModule< T >
static void getNonterminals (ArrayBuffer< node > &nonterminals, const EdgeWeightedGraph< T > &G, const NodeArray< bool > &isTerminal)
Generates a list (as ArrayBuffer<node>) of all nonterminals.

static void getTerminals (List< node > &terminals, const EdgeWeightedGraph< T > &G, const NodeArray< bool > &isTerminal)
Generates a list (as List<node>) of all terminals.

static bool isQuasiBipartite (const EdgeWeightedGraph< T > &G, const NodeArray< bool > &isTerminal)
Checks in O(n + m) time if a given Steiner tree problem instance is quasi-bipartite.

static bool isSteinerTree (const EdgeWeightedGraph< T > &G, const List< node > &terminals, const NodeArray< bool > &isTerminal, const EdgeWeightedGraphCopy< T > &steinerTree)
Checks in O(n) time if a given tree is acually a Steiner Tree.

static void sortTerminals (List< node > &terminals)
Sort terminals by index.

staticpruneAllDanglingSteinerPaths (EdgeWeightedGraphCopy< T > &steinerTree, const NodeArray< bool > &isTerminal)
Prunes nonterminal leaves and their paths to terminal or branching nodes.

staticpruneDanglingSteinerPathFrom (EdgeWeightedGraphCopy< T > &steinerTree, const NodeArray< bool > &isTerminal, node start)
Prunes the dangling Steiner path beginning at a given nonterminal leaf only.

staticpruneDanglingSteinerPathsFrom (EdgeWeightedGraphCopy< T > &steinerTree, const NodeArray< bool > &isTerminal, const List< node > &start)
Prunes dangling Steiner paths beginning at given nonterminal leaves only.

staticremoveCyclesFrom (EdgeWeightedGraphCopy< T > &steinerTree, const NodeArray< bool > &isTerminal)
Remove remaining cycles from a Steiner "almost" tree.

static void singleSourceShortestPathsPreferringTerminals (const EdgeWeightedGraph< T > &G, node source, const NodeArray< bool > &isTerminal, NodeArray< T > &distance, NodeArray< edge > &pred)
Modified single-source-shortest-paths (Dijkstra) with heuristic to prefer paths over terminals.

static void singleSourceShortestPathsStandard (const EdgeWeightedGraph< T > &G, node source, const NodeArray< bool > &, NodeArray< T > &distance, NodeArray< edge > &pred)
Standard single-source-shortest-paths algoritm (Dijkstra)

static void singleSourceShortestPaths (const EdgeWeightedGraph< T > &G, node source, const NodeArray< bool > &isTerminal, NodeArray< T > &distance, NodeArray< edge > &pred)
The default single-source-shortest-paths algorithm.

static void allTerminalShortestPathsStandard (const EdgeWeightedGraph< T > &G, const List< node > &terminals, const NodeArray< bool > &isTerminal, NodeArray< NodeArray< T > > &distance, NodeArray< NodeArray< edge > > &pred)
Runs singleSourceShortestPathsStandard from all terminals.

static void allTerminalShortestPathsPreferringTerminals (const EdgeWeightedGraph< T > &G, const List< node > &terminals, const NodeArray< bool > &isTerminal, NodeArray< NodeArray< T > > &distance, NodeArray< NodeArray< edge > > &pred)
Runs singleSourceShortestPathsPreferringTerminals from all terminals.

static void allTerminalShortestPaths (const EdgeWeightedGraph< T > &G, const List< node > &terminals, const NodeArray< bool > &isTerminal, NodeArray< NodeArray< T > > &distance, NodeArray< NodeArray< edge > > &pred, std::function< void(const EdgeWeightedGraph< T > &, node, const NodeArray< bool > &, NodeArray< T > &, NodeArray< edge > &)> ssspFunc=singleSourceShortestPaths)
Runs a given (or the default) single-source-shortest-paths function from all terminals.

static void allNodeShortestPathsStandard (const EdgeWeightedGraph< T > &G, const List< node > &terminals, const NodeArray< bool > &isTerminal, NodeArray< NodeArray< T > > &distance, NodeArray< NodeArray< edge > > &pred)
Runs singleSourceShortestPathsStandard from all nodes.

static void allNodeShortestPathsPreferringTerminals (const EdgeWeightedGraph< T > &G, const List< node > &terminals, const NodeArray< bool > &isTerminal, NodeArray< NodeArray< T > > &distance, NodeArray< NodeArray< edge > > &pred)
Runs singleSourceShortestPathsPreferringTerminals from all nodes.

static void allNodeShortestPaths (const EdgeWeightedGraph< T > &G, const List< node > &terminals, const NodeArray< bool > &isTerminal, NodeArray< NodeArray< T > > &distance, NodeArray< NodeArray< edge > > &pred, std::function< void(const EdgeWeightedGraph< T > &, node, const NodeArray< bool > &, NodeArray< T > &, NodeArray< edge > &)> ssspFunc=singleSourceShortestPaths)
Runs a given (or the default) single-source-shortest-paths function from all nodes.

static void allPairShortestPathsPreferringTerminals (const EdgeWeightedGraph< T > &G, const NodeArray< bool > &isTerminal, NodeArray< NodeArray< T > > &distance, NodeArray< NodeArray< edge > > &pred)
Modified all-pair-shortest-paths algorithm (Floyd-Warshall) with heuristic to prefer paths over terminals.

static void allPairShortestPathsStandard (const EdgeWeightedGraph< T > &G, const NodeArray< bool > &, NodeArray< NodeArray< T > > &distance, NodeArray< NodeArray< edge > > &pred)
Standard all-pair-shortest-paths algorithm (Floyd-Warshall)

static void allPairShortestPaths (const EdgeWeightedGraph< T > &G, const NodeArray< bool > &isTerminal, NodeArray< NodeArray< T > > &distance, NodeArray< NodeArray< edge > > &pred)
The default all-pair-shortest-paths algorithm.

static void drawSVG (const EdgeWeightedGraph< T > &G, const NodeArray< bool > &isTerminal, const EdgeWeightedGraphCopy< T > &steinerTree, const char *filename)
Writes an SVG file of a minimum Steiner tree in the original graph.

static void drawSVG (const EdgeWeightedGraph< T > &G, const NodeArray< bool > &isTerminal, const char *filename)
Writes an SVG file of the instance graph.

static void drawSteinerTreeSVG (const EdgeWeightedGraphCopy< T > &steinerTree, const NodeArray< bool > &isTerminal, const char *filename)
Writes a SVG that shows only the given Steiner tree.

## Protected Member Functions

virtualcomputeSteinerTree (const EdgeWeightedGraph< T > &G, const List< node > &terminals, const NodeArray< bool > &isTerminal, EdgeWeightedGraphCopy< T > *&finalSteinerTree) override
Builds a minimum Steiner tree given a weighted graph and a list of terminals.

void insertPath (node u, const Voronoi< T > &voronoi, EdgeWeightedGraphCopy< T > &finalSteinerTree, const EdgeWeightedGraph< T > &wG)
Inserts a shortest path corresponding to an edge in the complete terminal graph.

void reinsertShortestPaths (EdgeWeightedGraphCopy< T > &completeTerminalGraph, const Voronoi< T > &voronoi, const NodeArray< edge > &mstPred, const EdgeArray< edge > &bridges, EdgeWeightedGraphCopy< T > &finalSteinerTree, const EdgeWeightedGraph< T > &wG)
Swaps an edge in the complete terminal graph with the corresponding shortest path in the original graph.

## Detailed Description

template<typename T>
class ogdf::MinSteinerTreeMehlhorn< T >

This class implements the Minimum Steiner Tree 2-approximation algorithm by Mehlhorn.

This implementation is based on:

(K. Mehlhorn, A faster approximation algorithm for the Steiner problem in graphs, Information Processing Letters, volume 27, number 3, pages 125-128, 1998)

Definition at line 53 of file MinSteinerTreeMehlhorn.h.

## ◆ MinSteinerTreeMehlhorn()

template<typename T >
 ogdf::MinSteinerTreeMehlhorn< T >::MinSteinerTreeMehlhorn ( )
inline

Definition at line 55 of file MinSteinerTreeMehlhorn.h.

## ◆ ~MinSteinerTreeMehlhorn()

template<typename T >
 virtual ogdf::MinSteinerTreeMehlhorn< T >::~MinSteinerTreeMehlhorn ( )
inlinevirtual

Definition at line 57 of file MinSteinerTreeMehlhorn.h.

## ◆ calculateCompleteGraph()

template<typename T >
 void ogdf::MinSteinerTreeMehlhorn< T >::calculateCompleteGraph ( const EdgeWeightedGraph< T > & wG, const List< node > & terminals, const Voronoi< T > & voronoi, EdgeArray< edge > & bridges, EdgeWeightedGraphCopy< T > & completeTerminalGraph )
static

Builds a complete terminal graph.

Parameters
 wG the original graph terminals list of terminals voronoi Voronoi regions (providing a mapping from each edge in the complete terminal graph to the shortest path in the original graph) bridges list of edges connecting terminal nodes by voronoi regions completeTerminalGraph the resulting complete terminal graph

Definition at line 182 of file MinSteinerTreeMehlhorn.h.

## ◆ computeSteinerTree()

template<typename T >
 T ogdf::MinSteinerTreeMehlhorn< T >::computeSteinerTree ( const EdgeWeightedGraph< T > & G, const List< node > & terminals, const NodeArray< bool > & isTerminal, EdgeWeightedGraphCopy< T > *& finalSteinerTree )
overrideprotectedvirtual

Builds a minimum Steiner tree given a weighted graph and a list of terminals.

Parameters
 G The weighted input graph terminals The list of terminal nodes isTerminal A bool array of terminals finalSteinerTree The final Steiner tree
Returns
The objective value (sum of edge costs) of the final Steiner tree

Implements ogdf::MinSteinerTreeModule< T >.

Definition at line 158 of file MinSteinerTreeMehlhorn.h.

## ◆ insertPath()

template<typename T >
 void ogdf::MinSteinerTreeMehlhorn< T >::insertPath ( node u, const Voronoi< T > & voronoi, EdgeWeightedGraphCopy< T > & finalSteinerTree, const EdgeWeightedGraph< T > & wG )
protected

Inserts a shortest path corresponding to an edge in the complete terminal graph.

Parameters
 u terminal node needed to access the according predecessor edge in the minimum terminal spanning tree voronoi Voronoi regions (contains shortest paths) finalSteinerTree the resulting Steiner tree wG the original graph

Definition at line 265 of file MinSteinerTreeMehlhorn.h.

## ◆ reinsertShortestPaths()

template<typename T >
 void ogdf::MinSteinerTreeMehlhorn< T >::reinsertShortestPaths ( EdgeWeightedGraphCopy< T > & completeTerminalGraph, const Voronoi< T > & voronoi, const NodeArray< edge > & mstPred, const EdgeArray< edge > & bridges, EdgeWeightedGraphCopy< T > & finalSteinerTree, const EdgeWeightedGraph< T > & wG )
protected

Swaps an edge in the complete terminal graph with the corresponding shortest path in the original graph.

Parameters
 completeTerminalGraph the complete terminal graph voronoi Voronoi regions (providing a mapping from each edge in the complete terminal graph to the shortest path in the original graph) mstPred predecessor data structure of a minimum terminal spanning tree bridges list of edges connecting terminal nodes by voronoi regions finalSteinerTree the resulting Steiner tree wG the original graph

Definition at line 247 of file MinSteinerTreeMehlhorn.h.

The documentation for this class was generated from the following file: