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Multiway Cuts in Directed and Node Weighted Graphs
 in Proc. 21st ICALP, Lecture Notes in Computer Science 820
, 1994
"... this paper we consider node multiway cuts; the problem of computing a minimum weight node multiway cut is known to be NPhard and max SNPhard [1]. It turns out that the approximation algorithm in [2] for edge multiway cuts does not extend to the node multiway cut problem. Let us give a reason for t ..."
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Cited by 46 (4 self)
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this paper we consider node multiway cuts; the problem of computing a minimum weight node multiway cut is known to be NPhard and max SNPhard [1]. It turns out that the approximation algorithm in [2] for edge multiway cuts does not extend to the node multiway cut problem. Let us give a reason
A distributed algorithm for minimumweight spanning trees
, 1983
"... A distributed algorithm is presented that constructs he minimumweight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm and exchange ..."
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Cited by 435 (3 self)
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A distributed algorithm is presented that constructs he minimumweight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm
Theoretical improvements in algorithmic efficiency for network flow problems

, 1972
"... This paper presents new algorithms for the maximum flow problem, the Hitchcock transportation problem, and the general minimumcost flow problem. Upper bounds on ... the numbers of steps in these algorithms are derived, and are shown to compale favorably with upper bounds on the numbers of steps req ..."
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Cited by 560 (0 self)
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are given. We show that, if each flow augmentation is made along an augmenting path having a minimum number of arcs, then a maximum flow in an nnode network will be obtained after no more than ~(n a n) augmentations; and then we show that if each flow change is chosen to produce a maximum increase
Multiway cuts in node weighted graphs
 JOURNAL OF ALGORITHMS
, 2004
"... A (2 — 2/k) approximation algorithm is presented for the node multiway cut problem, thus matching the result of Dahlhaus et al. (SIAM J. Comput. 23 (4) (1994) 864894) for the edge version of this problem. This is done by showing that the associated LPrelaxation always has a halfintegral optimal s ..."
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Cited by 20 (0 self)
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A (2 — 2/k) approximation algorithm is presented for the node multiway cut problem, thus matching the result of Dahlhaus et al. (SIAM J. Comput. 23 (4) (1994) 864894) for the edge version of this problem. This is done by showing that the associated LPrelaxation always has a halfintegral optimal
Simple fast algorithms for the editing distance between trees and related problems
 SIAM J. COMPUT
, 1989
"... Ordered labeled trees are trees in which the lefttoright order among siblings is. significant. The distance between two ordered trees is considered to be the weighted number of edit operations (insert, delete, and modify) to transform one tree to another. The problem of approximate tree matching i ..."
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Cited by 405 (12 self)
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is also considered. Specifically, algorithms are designed to answer the following kinds of questions: 1. What is the distance between two trees? 2. What is the minimum distance between T and T when zero or more subtrees can be removed from T2 3. Let the pruning of a tree at node n mean removing all
Multicommodity maxflow mincut theorems and their use in designing approximation algorithms
 J. ACM
, 1999
"... In this paper, we establish maxflow mincut theorems for several important classes of multicommodity flow problems. In particular, we show that for any nnode multicommodity flow problem with uniform demands, the maxflow for the problem is within an O(log n) factor of the upper bound implied by ..."
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Cited by 357 (6 self)
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In this paper, we establish maxflow mincut theorems for several important classes of multicommodity flow problems. In particular, we show that for any nnode multicommodity flow problem with uniform demands, the maxflow for the problem is within an O(log n) factor of the upper bound implied
Approximation Algorithms for Connected Dominating Sets
 Algorithmica
, 1996
"... The dominating set problem in graphs asks for a minimum size subset of vertices with the following property: each vertex is required to either be in the dominating set, or adjacent to some node in the dominating set. We focus on the question of finding a connected dominating set of minimum size, whe ..."
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Cited by 366 (9 self)
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The dominating set problem in graphs asks for a minimum size subset of vertices with the following property: each vertex is required to either be in the dominating set, or adjacent to some node in the dominating set. We focus on the question of finding a connected dominating set of minimum size
An improved approximation algorithm for multiway cut
 Journal of Computer and System Sciences
, 1998
"... Given an undirected graph with edge costs and a subset of k nodes called terminals, a multiway cut is a subset of edges whose removal disconnects each terminal from the rest. Multiway Cut is the problem of finding a multiway cut of minimum cost. Previously, a very simple combinatorial algorithm due ..."
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Cited by 71 (5 self)
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Given an undirected graph with edge costs and a subset of k nodes called terminals, a multiway cut is a subset of edges whose removal disconnects each terminal from the rest. Multiway Cut is the problem of finding a multiway cut of minimum cost. Previously, a very simple combinatorial algorithm due
Rounding algorithms for a geometric embedding of minimum multiway cut
 In STOC ’99: Proceedings of the 31st Annual ACM Symposium on Theory of Computing
, 1999
"... Given an undirected graph with edge costs and a subset of k ≥ 3 nodes called terminals, a multiway, or kway, cut is a subset of the edges whose removal disconnects each terminal from the others. The multiway cut problem is to find a minimumcost multiway cut. This problem is MaxSNP hard. Recently ..."
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Cited by 50 (2 self)
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Given an undirected graph with edge costs and a subset of k ≥ 3 nodes called terminals, a multiway, or kway, cut is a subset of the edges whose removal disconnects each terminal from the others. The multiway cut problem is to find a minimumcost multiway cut. This problem is MaxSNP hard. Recently
Computing geodesics and minimal surfaces via graph cuts
 in International Conference on Computer Vision
, 2003
"... Geodesic active contours and graph cuts are two standard image segmentation techniques. We introduce a new segmentation method combining some of their benefits. Our main intuition is that any cut on a graph embedded in some continuous space can be interpreted as a contour (in 2D) or a surface (in 3D ..."
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Cited by 251 (26 self)
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D). We show how to build a grid graph and set its edge weights so that the cost of cuts is arbitrarily close to the length (area) of the corresponding contours (surfaces) for any anisotropic Riemannian metric. There are two interesting consequences of this technical result. First, graph cut
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