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247
Computing maximum cplanar subgraphs
 Graph Drawing, volume 5417 of Lecture Notes Comput. Sci
, 2008
"... Abstract. Deciding cplanarity for a given clustered graph C = (G, T) is one of the most challenging problems in current graph drawing research. Though it is yet unknown if this problem is solvable in polynomial time, latest research focused on algorithmic approaches for special classes of clustered ..."
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Cited by 3 (3 self)
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of clustered graphs. In this paper, we introduce an approach to solve the general problem using integer linear programming (ILP) techniques. We give an ILP formulation that also includes the natural generalization of cplanarity testing—the maximum cplanar subgraph problem—and solve this ILP with a branch
CPlanarity of cconnected clustered graphs
, 2008
"... We present the first characterization of cplanarity for cconnected clustered graphs. The characterization is based on the interplay between the hierarchy of the clusters and the hierarchies of the triconnected and biconnected components of the underlying graph. Based on such a characterization, we ..."
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Cited by 6 (5 self)
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, we provide a lineartime cplanarity testing and embedding algorithm for cconnected clustered graphs. The algorithm is reasonably easy to implement, since it exploits as building blocks simple algorithmic tools like the computation of lowest common ancestors, minimum and maximum spanning trees
The Dense kSubgraph Problem
 Algorithmica
, 1999
"... This paper considers the problem of computing the dense kvertex subgraph of a given graph, namely, the subgraph with the most edges. An approximation algorithm is developed for the problem, with approximation ratio O(n ffi ), for some ffi ! 1=3. 1 Introduction We study the dense ksubgraph (D ..."
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Cited by 199 (11 self)
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(DkS) maximization problem, of computing the dense k vertex subgraph of a given graph. That is, on input a graph G and a parameter k, we are interested in finding a set of k vertices with maximum average degree in the subgraph induced by this set. As this problem is NPhard (say, by reduction from
Approximation Algorithms for Projective Clustering
 Proceedings of the ACM SIGMOD International Conference on Management of data, Philadelphia
, 2000
"... We consider the following two instances of the projective clustering problem: Given a set S of n points in R d and an integer k ? 0; cover S by k hyperstrips (resp. hypercylinders) so that the maximum width of a hyperstrip (resp., the maximum diameter of a hypercylinder) is minimized. Let w ..."
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Cited by 302 (22 self)
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be the smallest value so that S can be covered by k hyperstrips (resp. hypercylinders), each of width (resp. diameter) at most w : In the plane, the two problems are equivalent. It is NPHard to compute k planar strips of width even at most Cw ; for any constant C ? 0 [50]. This paper contains four main
BranchandBound Techniques for the Maximum Planar Subgraph Problem
, 1994
"... We present branchandbound algorithms for finding a maximum planar subgraph of a nonplanar graph. The problem has important applications in circuit layout, automated graph drawing, and facility layout. The algorithms described utilize heuristics to obtain an initial lower bound for the size of a ..."
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Cited by 2 (0 self)
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of a maximum planar subgraph, then apply a sequence of fast preliminary tests for planarity to eliminate infeasible partial solutions. Computational experience is reported from testing the algorithms on a set of random nonplanar graphs and is encouraging. A bestfirst search technique is shown
On Maximum Symmetric Subgraphs
 Proc. of Graph Drawing 2000, Lecture Notes in Computer Science
, 2001
"... Let G be an nnode graph. We address the problem of computing a maximum symmetric graph H from G by deleting nodes, deleting edges, and contracting edges. This NPcomplete problem arises naturally from the objective of drawing G as symmetrically as possible. We show that its tractability for the spe ..."
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Cited by 8 (1 self)
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Let G be an nnode graph. We address the problem of computing a maximum symmetric graph H from G by deleting nodes, deleting edges, and contracting edges. This NPcomplete problem arises naturally from the objective of drawing G as symmetrically as possible. We show that its tractability
Maximum planar subgraphs in dense graphs
"... Kühn, Osthus and Taraz showed that for each γ> 0 there exists C such that any nvertex graph with minimum degree γn contains a planar subgraph with at least 2n − C edges. We find the optimum value of C for all γ < 1/2 and sufficiently large n. 1 ..."
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Cited by 2 (2 self)
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Kühn, Osthus and Taraz showed that for each γ> 0 there exists C such that any nvertex graph with minimum degree γn contains a planar subgraph with at least 2n − C edges. We find the optimum value of C for all γ < 1/2 and sufficiently large n. 1
Improved Approximations of Maximum Planar Subgraph
, 1996
"... The maximum planar subgraph problem (MPSP) asks for a planar subgraph of a given graph with the maximum total cost. We suggest a new approximation algorithm for the weighted MPSP. We show that it has performance ratio of 5/12 in the case of graphs where the maxumum cost of an edge is at most twice t ..."
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nonnegative cost function on edges c : E ! R + . The maximum planar subgraph problem (MPSP) asks for a planar subgraph of G with the maximum total cost. This problem has applications in circuit layout, facility layout, and graph drawings [8, 11]. So many approximation algorithms appear in the last decade [7
Approximations For The Maximum Acyclic Subgraph Problem
 Information Processing Letters
, 1994
"... : Given a directed graph G = (V; A), the maximum acyclic subgraph problem is to compute a subset, A 0 , of arcs of maximum size or total weight so that G 0 = (V; A 0 ) is acyclic. We discuss several approximation algorithms for this problem. Our main result is an O(jAj + d 3 max ) algorithm ..."
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Cited by 18 (1 self)
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: Given a directed graph G = (V; A), the maximum acyclic subgraph problem is to compute a subset, A 0 , of arcs of maximum size or total weight so that G 0 = (V; A 0 ) is acyclic. We discuss several approximation algorithms for this problem. Our main result is an O(jAj + d 3 max ) algorithm
The Maximum Weight Connected Subgraph Problem
, 2013
"... The Maximum (Node) Weight Connected Subgraph Problem (MWCS) searches for a connected subgraph with maximum total weight in a nodeweighted (di)graph. In this work we introduce a new integer linear programming formulation built on node variables only, which uses new constraints based on nodeseparat ..."
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Cited by 3 (1 self)
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The Maximum (Node) Weight Connected Subgraph Problem (MWCS) searches for a connected subgraph with maximum total weight in a nodeweighted (di)graph. In this work we introduce a new integer linear programming formulation built on node variables only, which uses new constraints based on node
Results 1  10
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