Results 1  10
of
16
A Polylogarithmic Approximation of the Minimum Bisection
, 2001
"... A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n=2. The bisection cost is the number of edges connecting the two sets. ..."
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Cited by 89 (7 self)
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A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n=2. The bisection cost is the number of edges connecting the two sets.
A New Rounding Procedure for the Assignment Problem with Applications to Dense Graph Arrangement Problems
, 2001
"... We present a randomized procedure for rounding fractional perfect matchings to (integral) matchings. If the original fractional matching satis es any linear inequality, then with high probability, the new matching satis es that linear inequality in an approximate sense. This extends the wellkn ..."
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Cited by 78 (3 self)
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We present a randomized procedure for rounding fractional perfect matchings to (integral) matchings. If the original fractional matching satis es any linear inequality, then with high probability, the new matching satis es that linear inequality in an approximate sense. This extends the wellknown LP rounding procedure of Raghavan and Thompson, which is usually used to round fractional solutions of linear programs.
Improved Bounds for the Unsplittable Flow Problem
 In Proceedings of the 13th ACMSIAM Symposium on Discrete Algorithms
, 2002
"... In this paper we consider the unsplittable ow problem (UFP): given a directed or undirected network G = (V, E) with edge capacities and a set of terminal pairs (or requests) with associated demands, find a subset of the pairs of maximum total demand for which a single flow path can be chosen for eac ..."
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Cited by 56 (6 self)
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In this paper we consider the unsplittable ow problem (UFP): given a directed or undirected network G = (V, E) with edge capacities and a set of terminal pairs (or requests) with associated demands, find a subset of the pairs of maximum total demand for which a single flow path can be chosen for each pair so that for every edge, the sum of the demands of the paths crossing the edge does not exceed its capacity.
Network Lifetime and Power Assignment in AdHoc Wireless Networks
 IN ESA
, 2003
"... Used for topology control in adhoc wireless networks, Power Assignment is a family of problems, each defined by a certain connectivity constraint (such as strong connectivity) The input consists of a directed complete weighted graph G = (V; c). The power of a vertex u in a directed spanning subgra ..."
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Cited by 53 (4 self)
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Used for topology control in adhoc wireless networks, Power Assignment is a family of problems, each defined by a certain connectivity constraint (such as strong connectivity) The input consists of a directed complete weighted graph G = (V; c). The power of a vertex u in a directed spanning subgraph H is given by pH(u) = maxuv2E(H) c(uv). The power of H is given by p(H) = P u2V pH(u), Power Assignment seeks to minimize p(H) while H satisfies the given connectivity constraint. We
Cuts, trees and l1embeddings of graphs
, 2002
"... Motivated by many recent algorithmic applications, this paper aims to promote a systematic study of the relationship between the topology of a graph and the metric distortion incurred when the graph is embedded into ` 1 space. The main results are: 1. Explicit constantdistortion embeddings of all s ..."
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Cited by 31 (3 self)
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Motivated by many recent algorithmic applications, this paper aims to promote a systematic study of the relationship between the topology of a graph and the metric distortion incurred when the graph is embedded into ` 1 space. The main results are: 1. Explicit constantdistortion embeddings of all seriesparallel graphs, and all graphs with bounded Euler number. These are the rst natural families known to have constant distortion (strictly greater than 1). Using the above embeddings, algorithms are obtained which approximate the sparsest cut in such graphs to within a constant factor. 2. A constantdistortion embedding of outerplanar graphs into the restricted class of ` 1 metrics known as \dominating tree metrics". A lower bound of (logn) on the distortion for embeddings of seriesparallel graphs into (distributions over) dominating tree metrics
Approximate Classification via Earthmover Metrics
 In SODA ’04: Proceedings of the fifteenth annual ACMSIAM symposium on Discrete algorithms
, 2004
"... Given a metric space (X, d), a natural distance measure on probability distributions over X is the earthmover metric. We use randomized rounding of earthmover metrics to devise new approximation algorithms for two wellknown classification problems, namely, metric labeling and 0extension. ..."
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Cited by 21 (4 self)
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Given a metric space (X, d), a natural distance measure on probability distributions over X is the earthmover metric. We use randomized rounding of earthmover metrics to devise new approximation algorithms for two wellknown classification problems, namely, metric labeling and 0extension.
Computing an Optimal Orientation of a Balanced Decomposition Tree for Linear Arrangement Problems
, 2001
"... Divideandconquer approximation algorithms for vertex ordering problems partition the vertex set of graphs, compute recursively an ordering of each part, and "glue" the orderings of the parts together. The computed ordering is specified by a decomposition tree that describes the recursive ..."
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Cited by 21 (0 self)
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Divideandconquer approximation algorithms for vertex ordering problems partition the vertex set of graphs, compute recursively an ordering of each part, and "glue" the orderings of the parts together. The computed ordering is specified by a decomposition tree that describes the recursive partitioning of the subproblems. At each internal node of the decomposition tree, there is a degree of freedom regarding the order in which the parts are glued together. Approximation algorithms that use this technique ignore these degrees of freedom, and prove that the cost of every ordering that agrees with the computed decomposition tree is within the range specified by the approximation factor. We address the question of whether an optimal ordering can be e#ciently computed among the exponentially many orderings induced by a binary decomposition tree. We present a polynomial time algorithm for computing an optimal ordering induced by a binary balanced decomposition tree with respect to two problems: Minimum Linear Arrangement (minla) and Minimum Cutwidth (mincw). For 1/3balanced decomposition trees of bounded degree graphs, the time complexity of our algorithm is O(n 2.2 ), where n denotes the number of vertices. Additionally, we present experimental evidence that computing an optimal orientation of a decomposition tree is useful in practice. It is shown, through an implementation for minla, that optimal orientations of decomposition trees can produce arrangements of roughly the same quality as those produced by the best known heuristic, at a fraction of the running time.
On Average Distortion of Embedding Metrics into the Line
 L1, in 35th Annual ACM Symposium on Theory of Computing, 2003
, 2003
"... We introduce and study the notion of the average distortion of a nonexpanding embedding of one metric space into another. Less sensitive than the multiplicative metric distortion, the average distortion captures well the global picture, and, overall, is a quite interesting new measure of metric p ..."
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Cited by 11 (0 self)
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We introduce and study the notion of the average distortion of a nonexpanding embedding of one metric space into another. Less sensitive than the multiplicative metric distortion, the average distortion captures well the global picture, and, overall, is a quite interesting new measure of metric proximity, related to the concentration of measure phenomenon. The paper mostly deals with embeddings into the real line with a low (as much as it is possible) average distortion. Our main technical contribution is that the shortestpath metrics of special (e.g., planar, bounded treewidth, etc.) undirected graphs can be embedded into the line with constant average distortion. This has implications, e.g., on the value of the MinCutMaxFlow gap in uniformdemand multicommodity ows on such graphs.
Improved Approximations of Crossings in Graph Drawings and VLSI Layout Areas
, 2000
"... We give improved approximations for two classical embedding problems: (i) minimizing the number of crossings in a drawing of a bounded degree graph on the plane; and (ii) minimizing the VLSI layout area of a degree four graph. These improved algorithms can be applied to improve a variety of VLSI lay ..."
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Cited by 10 (0 self)
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We give improved approximations for two classical embedding problems: (i) minimizing the number of crossings in a drawing of a bounded degree graph on the plane; and (ii) minimizing the VLSI layout area of a degree four graph. These improved algorithms can be applied to improve a variety of VLSI layout problems. Our results are as follows. (i) We compute a drawing on the plane of a bounded degree graph in which the sum of the numbers of vertices and crossings is O(log 3 n) times the optimal minimum sum. This is a logarithmic factor improvement relative to the best known result. (ii) We compute a VLSI layout of a degree four graph in a grid with constant aspect ratio the area of which is O(log 4 n) times the optimal minimum layout area. This is an O(log 2 n) improvement over the best known long standing result. 1 Introduction In this paper we study two related problems: (1) drawing a bounded degree graph on the plane with the fewest number of crossings of edges and (2) minimizat...