Web1 Answer. The sparsest cut problem, in which one attempts to minimize the ratio between the number of edges cut to the size of the smaller size of the bipartition, is NP-complete. The "last word" on this problem theoretically speaking is the O ( log n) algorithm by Arora, Rao and Vazirani (affectionately knows as ARV), which has found many uses ... WebA na˜‡ve reduction from Sparsest Cut to Minimum Multicut would only give an approximation ratio of O(p n logD), where D is the sum of the demands. We obtain the improvement using a novel LP-rounding method for fractional Sparsest Cut, the dual of Maximum Concurrent Flow. Keywords: approximation algorithms, directed graphs, …
Multicommodity Max-Flow Min-Cut Theorems and Their Use …
WebJun 1, 2013 · We give a 2-approximation algorithm for the non-uniform Sparsest Cut problem that runs in time n O(k), where k is the treewidth of the graph.This improves on the previous 2 2 k-approximation in time poly(n) 2 O(k) due to Chlamtac et al. [18].. To complement this algorithm, we show the following hardness results: If the non-uniform … WebMar 7, 2024 · Good approximations have been attained for the sparsest cut problem by rounding solutions to convex relaxations via low-distortion metric embeddings. Recently, Bryant and Tupper showed that this approach extends to the hypergraph setting by formulating a linear program whose solutions are so-called diversities which are rounded … fed crim p 33
New Hardness Results for Planar Graph Problems in P and an …
Webthe Generalized Sparsest Cut problem seeks to mini-mize a linear function over all cuts of the graph, which is equivalent to optimizing over all n-point `1 metrics. Since this problem is NP-hard, we can optimize over all n-point metrics instead, and then use an algorithmic version of Bourgain’s embedding to embed into `1 with WebJul 1, 2012 · The sparsest cut of a graph is a measure of its expansion and is closely related to other graph expansion measures including edge expansion, vertex expansion, and … The sparsest cut problem is to bipartition the vertices so as to minimize the ratio of the number of edges across the cut divided by the number of vertices in the smaller half of the partition. This objective function favors solutions that are both sparse (few edges crossing the cut) and balanced (close to a bisection). … See more In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets. Any cut determines a cut-set, the set of edges that have one endpoint in each subset of the partition. These edges are said to cross the … See more A cut is minimum if the size or weight of the cut is not larger than the size of any other cut. The illustration on the right shows a minimum … See more The family of all cut sets of an undirected graph is known as the cut space of the graph. It forms a vector space over the two-element finite field of arithmetic modulo two, with the See more A cut C = (S,T) is a partition of V of a graph G = (V,E) into two subsets S and T. The cut-set of a cut C = (S,T) is the set {(u,v) ∈ E u ∈ S, v ∈ T} of … See more A cut is maximum if the size of the cut is not smaller than the size of any other cut. The illustration on the right shows a maximum cut: the … See more • Connectivity (graph theory) • Graph cuts in computer vision • Split (graph theory) • Vertex separator • Bridge (graph theory) See more declaration of independence history for kids