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A Linear Algorithm for BendOptimal . . .
 J. GRAPH ALGORITHMS APPL
, 1999
"... An orthogonal drawing of a plane graph G is a drawing of G in which each edge is drawn as a sequence of alternate horizontal and vertical line segments. In this paper we give a lineartime algorithm to find an orthogonal drawing of a given 3connected cubic plane graph with the minimum number of ..."
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of bends. The best previously known algorithm takes time O(n 7/4 # log n) for any plane graph with n vertices. Communicated by Giuseppe Di Battista and Petra Mutzel.
Optimal Compaction of Orthogonal Grid Drawings (Extended Abstract)
"... ) Gunnar W. Klau and Petra Mutzel MaxPlanckInstitut fur Informatik Im Stadtwald, D66123 Saarbrucken, Germany fguwek, mutzelg@mpisb.mpg.de Abstract. We consider the twodimensional compaction problem for orthogonal grid drawings in which the task is to alter the coordinates of the vert ..."
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) Gunnar W. Klau and Petra Mutzel MaxPlanckInstitut fur Informatik Im Stadtwald, D66123 Saarbrucken, Germany fguwek, mutzelg@mpisb.mpg.de Abstract. We consider the twodimensional compaction problem for orthogonal grid drawings in which the task is to alter the coordinates
Optimal Labelling of Point Features in the Slider Model (Extended Abstract)
 In Proc. 6th Annual International Computing and Combinatorics Conference (COCOON 2000), LNCS
, 2000
"... ) Gunnar W. Klau 1 and Petra Mutzel 2 1 MPI fur Informatik, Saarbrucken, Germany. Currently TU Wien, Austria. guwek@mpisb.mpg.de 2 TU Wien, Austria. mutzel@apm.tuwien.ac.at Abstract. We investigate the label number maximisation problem (lnm): Given a set of labels , each of which belon ..."
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Cited by 12 (2 self)
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) Gunnar W. Klau 1 and Petra Mutzel 2 1 MPI fur Informatik, Saarbrucken, Germany. Currently TU Wien, Austria. guwek@mpisb.mpg.de 2 TU Wien, Austria. mutzel@apm.tuwien.ac.at Abstract. We investigate the label number maximisation problem (lnm): Given a set of labels , each of which
A Linear Algorithm for BendOptimal Orthogonal Drawings of Triconnected Cubic Plane Graphs
 J. Graph Algorithms Appl
, 1999
"... An orthogonal drawing of a plane graph G is a drawing of G in which each edge is drawn as a sequence of alternate horizontal and vertical line segments. In this paper we give a lineartime algorithm to find an orthogonal drawing of a given 3connected cubic plane graph with the minimum number of ben ..."
Abstract

Cited by 5 (3 self)
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of bends. The best previously known algorithm takes time O(n 7/4 # log n) for any plane graph with n vertices. Communicated by Giuseppe Di Battista and Petra Mutzel. Submitted: March 1998. Revised: November 1998 and March 1999. M. S. Rahman et al., Orthogonal Drawings, JGAA, 3(4) 3162 (1999) 32 1
2Layer Straightline Crossing Minimization: Performance of Exact and Heuristic Algorithms
, 1997
"... We present algorithms for the two layer straightline crossing minimization problem that are able to compute exact optima. Our computational results lead us to the conclusion that there is no need for heuristics if one layer is fixed, even though the problem is NPhard, and that for the general probl ..."
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Cited by 76 (6 self)
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We present algorithms for the two layer straightline crossing minimization problem that are able to compute exact optima. Our computational results lead us to the conclusion that there is no need for heuristics if one layer is fixed, even though the problem is NPhard, and that for the general problem with two variable layers, true optima can be computed for sparse instances in which the smaller layer contains up to 15 nodes. For bigger instances, the iterated barycenter method turns out to be the method of choice among several popular heuristics whose performance we could assess by comparing their results to optimum solutions.
GraphML Progress Report  Structural Layer Proposal
, 2002
"... Following a workshop on graph data formats held with the 8th Symposium on Graph Drawing (GD 2000), a task group was formed to propose a format for graphs and graph drawings that meets current and projected requirements. ..."
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Cited by 52 (2 self)
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Following a workshop on graph data formats held with the 8th Symposium on Graph Drawing (GD 2000), a task group was formed to propose a format for graphs and graph drawings that meets current and projected requirements.
New Facets for the Planar Subgraph Polytope
"... This paper describes certain facet classes for the planar subgraph polytope. These facets are extensions of Kuratowski facets and are of the form 2x(U)+x(E(G)\U) ≤ 2U+E(G)\U  −2 where the edge set U varies and can be empty. Two of the new types of facets complete the class of extended subdivisi ..."
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subdivision facets, explored by Jünger and Mutzel. In addition, the other types of facets consist of a new class of facets for the polytope called 3star subdivisions. It is also shown that the extended and 3star subdivision facets are also equivalent to members of the class of facets with coefficients in {0
An algorithmic framework for the exact solution of the prizecollecting Steiner tree problem
 MATHEMATICAL PROGAMMING, SERIES B
, 2006
"... The PrizeCollecting Steiner Tree Problem (PCST) on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. PCST appears frequently in the design of utility ne ..."
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Cited by 45 (14 self)
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The PrizeCollecting Steiner Tree Problem (PCST) on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. PCST appears frequently in the design of utility networks where profit generating customers and the network connecting them have to be chosen in the most profitable way. Our main contribution is the formulation and implementation of a branchandcut algorithm based on a directed graph model where we combine several stateoftheart methods previously used for the Steiner tree problem. Our method outperforms the previously published results on the standard benchmark set of problems. We can solve all benchmark instances from the literature to optimality, including some of them for which the optimum was not known. Compared to a recent algorithm by Lucena and Resende, our new method is faster by more than two orders of magnitude. We also introduce a new class of more challenging instances and present computational results for them. Finally, for a set of largescale realworld instances arising in the design of fiber optic networks, we also obtain optimal solution values.
Results 1  10
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223