Results 11  20
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29
New existence proofs for ɛNets
"... We describe a new technique for proving the existence of small ɛnets for hypergraphs satisfying certain simple conditions. The technique is particularly useful for proving o ( 1 1 ɛ log ɛ) upper bounds which is not possible using the standard VC dimension theory. We apply the technique to several g ..."
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We describe a new technique for proving the existence of small ɛnets for hypergraphs satisfying certain simple conditions. The technique is particularly useful for proving o ( 1 1 ɛ log ɛ) upper bounds which is not possible using the standard VC dimension theory. We apply the technique to several geometric hypergraphs and obtain simple proofs for the existence of O ( 1 ɛ) size ɛnets for them. This includes the geometric hypergraph in which the vertex set is a set of points in the plane and the hyperedges are defined by a set of pseudodisks. This result was not known previously. We also get a very short proof for the existence of O ( 1
Balanced VertexOrderings of Graphs
, 2002
"... We consider the problem of determining a balanced ordering of the vertices of a graph; that is, the neighbors of each vertex v are as evenly distributed to the left and right of v as possible. This problem, which has applications in graph drawing for example, is shown to be NPhard, and remains N ..."
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Cited by 4 (3 self)
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We consider the problem of determining a balanced ordering of the vertices of a graph; that is, the neighbors of each vertex v are as evenly distributed to the left and right of v as possible. This problem, which has applications in graph drawing for example, is shown to be NPhard, and remains NPhard for bipartite simple graphs with maximum degree six. We then describe and analyze a number of methods for determining a balanced vertexordering, obtaining optimal orderings for directed acyclic graphs and graphs with maximum degree three. Finally we
Graph Orientation Algorithms to Minimize the Maximum Outdegree
, 2006
"... We study the problem of orienting the edges of a weighted graph such that the maximum weighted outdegree of vertices is minimized. This problem, which has applications in the guard arrangement for example, can be shown to be generally. In this paper we first give optimal orientation algorithms wh ..."
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Cited by 4 (2 self)
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We study the problem of orienting the edges of a weighted graph such that the maximum weighted outdegree of vertices is minimized. This problem, which has applications in the guard arrangement for example, can be shown to be generally. In this paper we first give optimal orientation algorithms which run in polynomial time for the following special cases: (i) the input is an unweighted graph, or more generally, a graph with identically weighted edges, and (ii) the input graph is a tree. Then, by using those algorithms as subprocedures, we provide a simple, combinatorial, min{ , (2#)}approximation algorithm for the general case, where wmax and w min are the maximum and the minimum weights of edges, respectively, and # is some small positive real number that depends on the input.
Oracles for bounded length shortest paths in planar graphs
 ACM Trans. Algorithms
"... We present a new approach for answering short path queries in planar graphs. For any fixed constant k and a given unweighted planar graph G = (V, E) one can build in O(V ) time a data structure, which allows to check in O(1) time whether two given vertices are at distance at most k in G and if so ..."
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We present a new approach for answering short path queries in planar graphs. For any fixed constant k and a given unweighted planar graph G = (V, E) one can build in O(V ) time a data structure, which allows to check in O(1) time whether two given vertices are at distance at most k in G and if so a shortest path between them is returned. Graph G can be undirected as well as directed. Our data structure works in fully dynamic environment. It can be updated in O(1) time after removing an edge or a vertex while updating after an edge insertion takes polylogarithmic amortized time. Besides deleting elements one can also disable ones for some time. It is motivated by a practical situation where nodes or links of a network may be temporarily out of service. Our results can be easily generalized to other wide classes of graphs – for instance we can take any minorclosed family of graphs.
Connectivity, Graph Minors, and Subgraph Multiplicity
, 1993
"... It is well known that any planar graph contains at most O(n) complete subgraphs. We extend this to an exact characterization: G occurs O(n) times as a subgraph of any planar graph, if and only if G is threeconnected. We generalize these results to similarly characterize certain other minorclosed f ..."
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Cited by 4 (3 self)
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It is well known that any planar graph contains at most O(n) complete subgraphs. We extend this to an exact characterization: G occurs O(n) times as a subgraph of any planar graph, if and only if G is threeconnected. We generalize these results to similarly characterize certain other minorclosed families of graphs; in particular, G occurs O(n) times as a subgraph of the Kb,cfree graphs, b ≥ c and c ≤ 4, iff G is cconnected. Our results use a simple Ramseytheoretic lemma that may be of independent interest.
Graph Drawing '93
, 1993
"... not Available. Characterizing Proximity Trees Prosenjit Bose, William Lenhart, y and Giuseppe Liotta z Much attention has been given over the past several years to developing algorithms for embedding abstract graphs in the plane such that the resulting drawing has certain geometric properties ..."
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not Available. Characterizing Proximity Trees Prosenjit Bose, William Lenhart, y and Giuseppe Liotta z Much attention has been given over the past several years to developing algorithms for embedding abstract graphs in the plane such that the resulting drawing has certain geometric properties. For example, those graphs which admit planar drawings have been completely characterized and efficient algorithms for producing planar drawings of these graphs have been designed ([4], [9]). For an overview of graph drawing problems and algorithms, the reader is referred to the excellent bibliography of Di Battista, Eades, Tamassia and Tollis [2]. Moreover, many problems in pattern recognition and classification, geographic variation analysis, geographic information systems, computational geometry, computational morphology, and computer vision use the underlying structure present in a set of data points revealed by means of a proximity graph. A proximity graph attempts to exhibit the rela...
Vertexunfoldings of simplicial polyhedra
 in Firms’ Financing Activities, Bank of Japan
, 2001
"... We present two algorithms for unfolding the surface of any polyhedron, all of whose faces are triangles, to a nonoverlapping, connected planar layout. The surface is cut only along polyhedron edges. The layout is connected, but it may have a disconnected interior: the triangles are connected at vert ..."
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We present two algorithms for unfolding the surface of any polyhedron, all of whose faces are triangles, to a nonoverlapping, connected planar layout. The surface is cut only along polyhedron edges. The layout is connected, but it may have a disconnected interior: the triangles are connected at vertices, but not necessarily joined along edges. 1
Faster Finding of Simple Cycles in Planar Graphs on a randomized EREWPRAM
 Proc. 2 nd Workshop on Randomized Parallel Computing
, 1997
"... We show that if a planar graph has a simple cycle of length k, where k is a fixed integer, such a cycle may be computed in O(log n) time by a randomized EREWPRAM with O(n) processors with high probability. This improves a previous result of [8]. The improvement relies on an efficient parallel algor ..."
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We show that if a planar graph has a simple cycle of length k, where k is a fixed integer, such a cycle may be computed in O(log n) time by a randomized EREWPRAM with O(n) processors with high probability. This improves a previous result of [8]. The improvement relies on an efficient parallel algorithm for computing a large independent set in a constantdegreebounded conflict graph, which is a natural method to avoid memory access conflicts in EREWPRAM graph algorithms. Many EREWPRAM algorithms use results from [6], [11], which can be used to compute such a set in O(log n) parallel time. This paper gives an O(1) time randomized algorithm using O(n) processors for that problem. This method can also be used to improve the randomized running time of many other EREWPRAM algorithms. 1 Introduction It is well known that finding the longest cycle in a graph is a hard problem, since finding a hamiltonian cycle is NPcomplete [10]. Hence finding a simple cycle of lenght k, for an arbi...
A Note on Improving the Running Time of a Class of Parallel Algorithms Using Randomization
, 1996
"... A natural method to avoid memory access conflicts in EREWPRAM graph algorithms is to compute a large independent set in a constantdegreebounded conflict graph. Many EREWPRAM algorithms use results from [CV 86], [GPS 87], which can be used to compute such a set in O(log n) parallel time. This p ..."
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A natural method to avoid memory access conflicts in EREWPRAM graph algorithms is to compute a large independent set in a constantdegreebounded conflict graph. Many EREWPRAM algorithms use results from [CV 86], [GPS 87], which can be used to compute such a set in O(log n) parallel time. This paper gives an O(1) time randomized algorithm using O(n) processors for that problem. Our algorithm improves with high probability the running time of many EREWPRAM algorithms. Institut fur Informatik V, Universitat Bonn, Romerstr. 164, D53117 Bonn, Germany, email: carsten@cs.unibonn.de y Institut fur Informatik V, Universitat Bonn, Romerstr. 164, D53117 Bonn, Germany, email: wirtgen@cs.unibonn.de 1 Introduction We consider the problem of computing an independent set of size\Omega\Gamma n) in a graph where the maximum degree is bounded by a constant on a randomized EREWPRAM. We present an O(1) time algorithm for this task which returns an independent set of size\Omega\Gamma n)...