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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.
Vertex sparsifiers: New results from old techniques
 IN 13TH INTERNATIONAL WORKSHOP ON APPROXIMATION, RANDOMIZATION, AND COMBINATORIAL OPTIMIZATION, VOLUME 6302 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2010
"... Given a capacitated graph G = (V, E) and a set of terminals K ⊆ V, how should we produce a graph H only on the terminals K so that every (multicommodity) flow between the terminals in G could be supported in H with low congestion, and vice versa? (Such a graph H is called a flowsparsifier for G.) ..."
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Cited by 15 (6 self)
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Given a capacitated graph G = (V, E) and a set of terminals K ⊆ V, how should we produce a graph H only on the terminals K so that every (multicommodity) flow between the terminals in G could be supported in H with low congestion, and vice versa? (Such a graph H is called a flowsparsifier for G.) What if we want H to be a “simple ” graph? What if we allow H to be a convex combination of simple graphs? Improving on results of Moitra [FOCS 2009] and Leighton and Moitra [STOC 2010], we give efficient algorithms for constructing: (a) a flowsparsifier H that log k log log k maintains congestion up to a factor of O (), where k = K. (b) a convex combination of trees over the terminals K that maintains congestion up to a factor of O(log k). (c) for a planar graph G, a convex combination of planar graphs that maintains congestion up to a constant factor. This requires us to give a new algorithm for the 0extension problem, the first one in which the preimages of each terminal are connected in G. Moreover, this result extends to minorclosed families of graphs. Our bounds immediately imply improved approximation guarantees for several terminalbased cut and ordering problems.
Minmax graph partitioning and small set expansion
, 2011
"... We study graph partitioning problems from a minmax perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main versions we consider are: (i) the k parts need to be of equal s ..."
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Cited by 14 (2 self)
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We study graph partitioning problems from a minmax perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main versions we consider are: (i) the k parts need to be of equal size, and (ii) the parts must separate a set of k given terminals. We consider a common generalization of these two problems, and design for it an O ( √ log n log k)approximation algorithm. This improves over an O(log 2 n) approximation for the second version due to Svitkina and Tardos [22], and roughly O(k log n) approximation for the first version that follows from other previous work. We also give an improved O(1)approximation algorithm for graphs that exclude any fixed minor. Our algorithm uses a new procedure for solving the SmallSet Expansion problem. In this problem, we are given a graph G and the goal is to find a nonempty set S ⊆ V of size S  ≤ ρn with minimum edgeexpansion. We give an O ( √ log n log (1/ρ)) bicriteria approximation algorithm for the general case of SmallSet Expansion, and O(1) approximation algorithm for graphs that exclude any fixed minor.
Approximating Sparsest Cut in Graphs of Bounded Treewidth
"... We give the first constantfactor approximation algorithm for SparsestCut with general demands in bounded treewidth graphs. In contrast to previous algorithms, which rely on the flowcut gap and/or metric embeddings, our approach exploits the SheraliAdams hierarchy of linear programming relaxation ..."
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We give the first constantfactor approximation algorithm for SparsestCut with general demands in bounded treewidth graphs. In contrast to previous algorithms, which rely on the flowcut gap and/or metric embeddings, our approach exploits the SheraliAdams hierarchy of linear programming relaxations.
MINMAX GRAPH PARTITIONING AND SMALL SET EXPANSION∗
"... Abstract. We study graph partitioning problems from a minmax perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main versions we consider are where the k parts need to be ..."
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Abstract. We study graph partitioning problems from a minmax perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main versions we consider are where the k parts need to be of equal size, and where they must separate a set of k given terminals. We consider a common generalization of these two problems, and design for it an O( logn log k) approximation algorithm. This improves over an O(log2 n) approximation for the second version due to Svitkina and Tardos [Minmax multiway cut, in APPROXRANDOM, 2004, Springer, Berlin, 2004], and roughly O(k logn) approximation for the first version that follows from other previous work. We also give an O(1) approximation algorithm for graphs that exclude any fixed minor. Our algorithm uses a new procedure for solving the smallset expansion problem. In this problem, we are given a graph G and the goal is to find a nonempty set S ⊆ V of size S  ≤ ρn with minimum edge expansion. We give an O( logn log (1/ρ)) bicriteria approximation algorithm for smallset expansion in general graphs, and an improved factor of O(1) for graphs that exclude any fixed minor.