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Pitfalls of using PQTrees in Automatic Graph Drawing
, 1997
"... A number of erroneous attempts involving PQtrees in the context of automatic graph drawing algorithms have been presented in the literature in recent years. In order to prevent future research from constructing algorithms with similar errors we point out some of the major mistakes. In particula ..."
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Cited by 10 (0 self)
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A number of erroneous attempts involving PQtrees in the context of automatic graph drawing algorithms have been presented in the literature in recent years. In order to prevent future research from constructing algorithms with similar errors we point out some of the major mistakes. In particular, we examine erroneous usage of the PQtree data structure in algorithms for computing maximal planar subgraphs and an algorithm for testing leveled planarity of leveled directed acyclic graphs with several sources and sinks.
A New Approximation Algorithm for Finding Heavy Planar Subgraphs
 ALGORITHMICA
, 1997
"... We provide the first nontrivial approximation algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH, the NPHard problem of finding a heaviest planar subgraph in an edgeweighted graph G. This problem has applications in circuit layout, facility layout, and graph drawing. No previous algorithm for MAXIMUM ..."
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Cited by 8 (2 self)
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We provide the first nontrivial approximation algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH, the NPHard problem of finding a heaviest planar subgraph in an edgeweighted graph G. This problem has applications in circuit layout, facility layout, and graph drawing. No previous algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH had performance ratio exceeding 1=3, which is obtained by any algorithm that produces a maximum weight spanning tree in G. Based on the BermanRamaiyer Steiner tree algorithm, the new algorithm has performance ratio at least 1/3 + 1/72. We also show that if G is complete and its edge weights satisfy the triangle inequality, then the performance ratio is at least 3/8. Furthermore, we derive the first nontrivial performance ratio (7/12 instead of 1/2) for the NPHard MAXIMUM WEIGHT OUTERPLANAR SUBGRAPH problem.
On Computing a Maximal Planar Subgraph using PQTrees
, 1996
"... The problem of computing a maximal planar subgraph of a nonplanar graph has been deeply investigated over the last 20 years. Several attempts have been tried to solve the problem with the help of PQtrees. The latest attempt has been reported by Jayakumar et al. (1989). In this paper we show that t ..."
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Cited by 4 (3 self)
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The problem of computing a maximal planar subgraph of a nonplanar graph has been deeply investigated over the last 20 years. Several attempts have been tried to solve the problem with the help of PQtrees. The latest attempt has been reported by Jayakumar et al. (1989). In this paper we show that the algorithm presented by Jayakumar et al. is not correct. We show that it does not necessarily compute a maximal planar subgraph and that the same holds for a modified version of the algorithm presented by Kant (1992). Our conclusions most likely suggest not to use PQtrees at all for this specific problem.
A Note on Computing a Maximal Planar Subgraph using PQTrees
, 1998
"... The problem of computing a maximal planar subgraph of a non planar graph has been deeply investigated over the last 20 years. Several attempts have been tried to solve the problem with the help of PQtrees. The latest attempt has been reported by Jayakumar et al. [10]. In this paper we show that ..."
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Cited by 4 (3 self)
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The problem of computing a maximal planar subgraph of a non planar graph has been deeply investigated over the last 20 years. Several attempts have been tried to solve the problem with the help of PQtrees. The latest attempt has been reported by Jayakumar et al. [10]. In this paper we show that the algorithm presented by Jayakumar et al. is not correct. We show that it does not necessarily compute a maximal planar subgraph and we note that the same holds for a modified version of the algorithm presented by Kant [12]. Our conclusions most likely suggest not to use PQtrees at all for this specific problem.
BendMinimal Orthogonal Drawing of NonPlanar Graphs
, 2004
"... This thesis belongs to the field of graph drawing research. It present s a new procedure for calculatp tl bend minimal shape of nonplanar graphswit givent opology. This met9 d is anextP,,9 oft he SimplePodevsnef drawing stKBRK9 SimplePodevsnef is a simplificatPD of t9 more complex Podevsnef  ..."
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Cited by 1 (1 self)
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This thesis belongs to the field of graph drawing research. It present s a new procedure for calculatp tl bend minimal shape of nonplanar graphswit givent opology. This met9 d is anextP,,9 oft he SimplePodevsnef drawing stKBRK9 SimplePodevsnef is a simplificatPD of t9 more complex Podevsnef  also known as Kandinsky  st andard. Bot models guarant ee bendminimalit y for planar graphswit givent opology. Theygenerat ortatK9 drawings wit equal vertF size where mult,PD edges can be at hed t a single side of a node. In cont9F t t Kandinsky, SimplePodevsnef has cert, rests9BD,D on t9 split up of such bundles. The algorit9 present9 int hist hesis expandstd drawing st andard for nonplanar graphs. It tKpK crossing point of edges in a special way, and enablestbl t share identen9 grid points where appropriatK Hence it allows crossings of whole bundles of edges inst9 of single edges only. Furt,PB9EKp we show a sharp upper bound of t9 bend count fort he heuristu use of SimplePodevsnef for nonplanar graphs; we also present an ext9F ion oft he new metP d tB is ablet draw nonplanar clustus9,RDB . Clust ergraphs are an ext ension of graphs, wheret here exis t a hierarchical st,pKBp9 of clusters, in whicht he nodes oft he graph are organized.
A Polynomial Time Randomized Parallel Approximation Algorithm for Finding Heavy Planar Subgraphs
, 2006
"... We provide an approximation algorithm for the Maximum Weight Planar Subgraph problem, the NPhard problem of finding a heaviest planar subgraph in an edgeweighted graph G. In the general case our algorithm has performance ratio at least 1/3 + 1/72 matching the best algorithm known so far, though in ..."
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We provide an approximation algorithm for the Maximum Weight Planar Subgraph problem, the NPhard problem of finding a heaviest planar subgraph in an edgeweighted graph G. In the general case our algorithm has performance ratio at least 1/3 + 1/72 matching the best algorithm known so far, though in several special cases we prove stronger results. In particular, we obtain performance ratio 2/3 (instead of 7/12) for the NPhard Maximum Weight Outerplanar Subgraph problem meeting the performance ratio of the best algorithm for the unweighted case. When the maximum weight planar subgraph is one of several special types of Hamiltonian graphs, we show performance ratios at least 2/5 and 4/9 (instead of 1/3 + 1/72), and 1/2 (instead of 4/9) for the unweighted case.