Results 1 - 10 of 328

Cooperative Cuts: Graph Cuts with Submodular Edge Weights

by Stefanie Jegelka, Jeff Bilmes , 2010
"... We introduce a problem we call Cooperative cut, where the goal is to find a minimum-cost graph cut but where a submodular function is used to define the cost of a subsets of edges. That means, the cost of an edge that is added to the current cut set C depends on the edges in C. This generalization o ..."
Abstract - Cited by 11 (8 self) - Add to MetaCart
and compare four approximation algorithms with an overall approximation factor of min { |V |/2, |C ∗ |, O ( √ |E | log |V |), |Pmax | } , where C ∗ is the optimal solution, and Pmax is the longest s, t path across the cut between given s, t. We also introduce additional heuristics for the problem which have

An Approximate Max-Flow Min-Cut Theorem for Uniform Multicommodity Flow Problems with Applications to Approximation Algorithms

by Tom Leighton, Satish Rao , 1989
"... In this paper, we consider a multicommodity flow problem where for each pair of vertices, (u,v), we are required to sendf half-units of commodity (uv) from u to v and f half-units of commodity (vu) from v to u without violating capacity constraints. Our main result is an algorithm for performing th9 ..."
Abstract - Cited by 246 (12 self) - Add to MetaCart
the first poly-log times optimal approximation algorithms for a wide variety of problems, including minimum quotient separators, 1/3-2/3 separators, bifurcators, crossing number and VLSI layout area. The result can also be used to efficiently route packets in arbitrary distributed networks. For example, we

The Complexity of Multiterminal Cuts

by E. Dahlhaus, D. S. Johnson, C. H. Papadimitriou, P. D. Seymour, M. Yannakakis - SIAM Journal on Computing , 1994
"... In the Multiterminal Cut problem we are given an edge-weighted graph and a subset of the vertices called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the mincut, max-flow problem, and ..."
Abstract - Cited by 194 (0 self) - Add to MetaCart
In the Multiterminal Cut problem we are given an edge-weighted graph and a subset of the vertices called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the mincut, max-flow problem

Graph sparsification by effective resistances

by Daniel A. Spielman, Nikhil Srivastava - SIAM J. Comput
"... We present a nearly-linear time algorithm that produces high-quality sparsifiers of weighted graphs. Given as input a weighted graph G = (V, E, w) and a parameter ǫ> 0, we produce a weighted subgraph H = (V, ˜ E, ˜w) of G such that | ˜ E | = O(n log n/ǫ 2) and for all vectors x ∈ R V (1 − ǫ) ∑ ..."
Abstract - Cited by 143 (9 self) - Add to MetaCart
We present a nearly-linear time algorithm that produces high-quality sparsifiers of weighted graphs. Given as input a weighted graph G = (V, E, w) and a parameter ǫ> 0, we produce a weighted subgraph H = (V, ˜ E, ˜w) of G such that | ˜ E | = O(n log n/ǫ 2) and for all vectors x ∈ R V (1 − ǫ

Multiway cuts in node weighted graphs

by Naveen Garg, Vijay V. Vazirani, Mihalis Yannakakis - 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) 864-894) for the edge version of this problem. This is done by showing that the associated LP-relaxation always has a half-integral optimal s ..."
Abstract - Cited by 20 (0 self) - Add to MetaCart
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) 864-894) for the edge version of this problem. This is done by showing that the associated LP-relaxation always has a half-integral optimal

Multiway Cuts in Directed and Node Weighted Graphs

by Naveen Garg, Vijay V. Vazirani, Mihalis Yannakakais - 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 NP-hard and max SNP-hard [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 ..."
Abstract - Cited by 46 (4 self) - Add to MetaCart
this paper we consider node multiway cuts; the problem of computing a minimum weight node multiway cut is known to be NP-hard and max SNP-hard [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

RANDOM SAMPLING IN CUT, FLOW, AND NETWORK DESIGN PROBLEMS

by David R. Karger , 1999
"... We use random sampling as a tool for solving undirected graph problems. We show that the sparse graph, or skeleton, that arises when we randomly sample a graph’s edges will accurately approximate the value of all cuts in the original graph with high probability. This makes sampling effective for pro ..."
Abstract - Cited by 101 (12 self) - Add to MetaCart
for problems involving cuts in graphs. We present fast randomized (Monte Carlo and Las Vegas) algorithms for approximating and exactly finding minimum cuts and maximum flows in unweighted, undirected graphs. Our cut-approximation algorithms extend unchanged to weighted graphs while our weighted-graph flow

An optimal SDP algorithm for Max-Cut, . . .

by Ryan O'Donnell, Yi Wu , 2007
"... Let G be an undirected graph for which the standard Max-Cut SDP relaxation achieves at least a c fraction of the total edge weight, 1 2 ≤ c ≤ 1. If the actual optimal cut for G is at most an s fraction of the total edge weight, we say that (c, s) is an SDP gap. We define the SDP gap curve GapSDP: [ ..."
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Let G be an undirected graph for which the standard Max-Cut SDP relaxation achieves at least a c fraction of the total edge weight, 1 2 ≤ c ≤ 1. If the actual optimal cut for G is at most an s fraction of the total edge weight, we say that (c, s) is an SDP gap. We define the SDP gap curve Gap

Global Min-cuts in RNC, and Other Ramifications of a Simple Min-Cut Algorithm

by David R. Karger , 1992
"... This paper presents a new algorithm for nding global min-cuts in weighted, undirected graphs. One of the strengths of the algorithm is its extreme simplicity. This randomized algorithm can be implemented as a strongly polynomial sequential algorithm with running time ~ O(mn 2), even if space is res ..."
Abstract - Cited by 70 (4 self) - Add to MetaCart
is restricted to O(n), or can be parallelized as an RN C algorithm which runs in time O(log 2 n) on a CRCW PRAM with mn 2 log n processors. In addition to yielding the best known processor bounds on unweighted graphs, this algorithm provides the first proof that the min-cut problem for weighted undirected

Sketching cuts in graphs and hypergraphs

by Dmitry Kogan, Robert Krauthgamer , 2014
"... Sketching and streaming algorithms are in the forefront of current research directions for cut problems in graphs. In the streaming model, we show that (1 − ε)-approximation for Max-Cut must use n1−O(ε) space; moreover, beating 4/5-approximation requires polynomial space. For the sketching model, we ..."
Abstract - Cited by 3 (1 self) - Add to MetaCart
, we show that r-uniform hypergraphs admit a (1 + ε)-cut-sparsifier (i.e., a weighted subhypergraph that approximately preserves all the cuts) with O(ε−2n(r + log n)) edges. We also make first steps towards sketching general CSPs (Constraint Satisfaction Problems). 1
Results 1 - 10 of 328