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97
Drawing Graphs on Two and Three Lines
 GRAPH DRAWING, 10TH INTERNATIONAL SYMPOSIUM (GD 2002), VOLUME TO APPEAR OF LECTURE NOTES IN COMPUTER SCIENCE
, 2002
"... We give a lineartime algorithm to decide whether a graph has a planar LLdrawing, i.e. a planar drawingo two parallel lines. This has previo)L/ beenkno wnoLq fo trees. We utilize this resultto oult planar drawings on three lines for a generalization of bipartite graphs, also in linear time. ..."
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Cited by 9 (1 self)
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We give a lineartime algorithm to decide whether a graph has a planar LLdrawing, i.e. a planar drawingo two parallel lines. This has previo)L/ beenkno wnoLq fo trees. We utilize this resultto oult planar drawings on three lines for a generalization of bipartite graphs, also in linear time.
Visual Ranking of Link Structures
 Journal of Graph Algorithms and Applications
, 2003
"... Methods for ranking World Wide Web resources according to their position in the link structure of the Web are receiving considerable attention, because they provide the first e#ective means for search engines to cope with the explosive growth and diversification of the Web. Closely related metho ..."
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Cited by 21 (4 self)
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Methods for ranking World Wide Web resources according to their position in the link structure of the Web are receiving considerable attention, because they provide the first e#ective means for search engines to cope with the explosive growth and diversification of the Web. Closely related methods have been used in other disciplines for quite some time.
Drawing Clusters and Hierarchies
, 2001
"... with respect to edges can be of interest as well. A method to do this can be found in Paulish (1993, Chapter 5). Clustering of graphs means grouping of vertices into components called clusters. Thus, clustering is related to partitioning the vertex set. Denition 8.1 (Partition). A (kway) partitio ..."
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Cited by 15 (0 self)
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with respect to edges can be of interest as well. A method to do this can be found in Paulish (1993, Chapter 5). Clustering of graphs means grouping of vertices into components called clusters. Thus, clustering is related to partitioning the vertex set. Denition 8.1 (Partition). A (kway) partition of a set C is a family of subsets (C 1 ; : : : ; C k ) with { S k i=1 C i = C and { C i \ C j = ; for i 6= j. The C i are called parts. We refer to a 2way partition as a bipartition. Now, we can dene one of the most basic denitions of clustered graphs. 8. Drawing Clusters and Hierarchies 195<F14.
Completely connected clustered graphs
 IN PROC. 29TH INTL. WORKSHOP ON GRAPHTHEORETIC CONCEPTS IN COMPUTER SCIENCE (WG 2003), VOLUME 2880 OF LNCS
, 2003
"... Planar drawings of clustered graphs are considered. We introduce the notion of completely connected clustered graphs, i.e. hierarchically clustered graphs that have the property that not only every cluster but also each complement of a cluster induces a connected subgraph. As a main result, we prove ..."
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Cited by 17 (1 self)
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Planar drawings of clustered graphs are considered. We introduce the notion of completely connected clustered graphs, i.e. hierarchically clustered graphs that have the property that not only every cluster but also each complement of a cluster induces a connected subgraph. As a main result, we prove that a completely connected clustered graph is cplanar if and only if the underlying graph is planar. Further, we investigate the influence of the root of the inclusion tree to the choice of the outer face of the underlying graph and vice versa.
Accelerated bend minimization
, 2012
"... We present an O(n 3/2) algorithm for minimizing the number of bends in an orthogonal drawing of a plane graph. It has been posed as a long standing open problem at Graph Drawing 2003, whether the bound of O(n 7/4 √ log n) shown by Garg and Tamassia in 1996 could be improved. To answer this question, ..."
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Cited by 7 (1 self)
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We present an O(n 3/2) algorithm for minimizing the number of bends in an orthogonal drawing of a plane graph. It has been posed as a long standing open problem at Graph Drawing 2003, whether the bound of O(n 7/4 √ log n) shown by Garg and Tamassia in 1996 could be improved. To answer this question, we show how to solve the uncapacitated mincost flow problem on a planar bidirected graph with bounded costs and face sizes in O(n 3/2) time.
Finding Short Integral Cycle Bases for Cyclic Timetabling
 IN PROC. OF ESA, LNCS 2832
, 2003
"... Cyclic timetabling for public transportation companies is usually modeled by the periodic event scheduling problem. To deduce a mixedinteger programming formulation, artificial integer variables have to be introduced. There are many ways to define these integer variables. We show that the minimal n ..."
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Cited by 16 (3 self)
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Cyclic timetabling for public transportation companies is usually modeled by the periodic event scheduling problem. To deduce a mixedinteger programming formulation, artificial integer variables have to be introduced. There are many ways to define these integer variables. We show that the minimal number of integer variables required to encode an instance is achieved by introducing an integer variable for each element of some integral cycle basis. An integral cycle basis consists of A  − V  + 1 oriented cycles of a directed graph D = (V, A) that enable any oriented cycle of the directed graph to be expressed as an integer linear combination. The solution times for the originating application vary extremely with different integral cycle bases. However, our computational studies show that the width of integral cycle bases is a good empirical measure for the solution time of the MIP. Clearly, integral cycle bases permit a much wider choice than the former standard approach, in which integer variables are associated with the cotree arcs of some spanning tree. Hence, to formulate better solvable integer programs, we present algorithms that construct integral cycle bases of small width. To that end, we investigate classes of directed cycle bases that are closely related to integral cycle bases, namely (generalized) fundamental and undirected cycle bases. This gives rise to both, a compact classification of directed cycle bases and notable reductions of running times for cyclic timetabling.
Blocks of Hypergraphs  applied to Hypergraphs and Outerplanarity
, 2010
"... A support of a hypergraph H is a graph with the same vertex set as H in which each hyperedge induces a connected subgraph. We show how to test in polynomial time whether a given hypergraph has a cactus support, i.e. a support that is a tree of edges and cycles. While it is N Pcomplete to decide w ..."
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Cited by 4 (2 self)
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A support of a hypergraph H is a graph with the same vertex set as H in which each hyperedge induces a connected subgraph. We show how to test in polynomial time whether a given hypergraph has a cactus support, i.e. a support that is a tree of edges and cycles. While it is N Pcomplete to decide whether a hypergraph has a 2outerplanar support, we show how to test in polynomial time whether a hypergraph that is closed under intersections and differences has an outerplanar or a planar support. In all cases our algorithms yield a construction of the required support if it exists. The algorithms are based on a new definition of biconnected components in hypergraphs.
Results 1  10
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