منابع مشابه
Triangle Sparsifiers
In this work, we introduce the notion of triangle sparsifiers, i.e., sparse graphs which are approximately the same to the original graph with respect to the triangle count. This results in a practical triangle counting method with strong theoretical guarantees. For instance, for unweighted graphs we show a randomized algorithm for approximately counting the number of triangles in a graph G, wh...
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We study resistance sparsification of graphs, in which the goal is to find a sparse subgraph (with reweighted edges) that approximately preserves the effective resistances between every pair of nodes. We show that every dense regular expander admits a (1 + ε)-resistance sparsifier of size Õ(n/ε), and conjecture this bound holds for all graphs on n nodes. In comparison, spectral sparsification i...
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We study treewidth sparsifiers. Informally, given a graph G of treewidth k, a treewidth sparsifier H is a minor of G, whose treewidth is close to k, |V (H)| is small, and the maximum vertex degree in H is bounded. Treewidth sparsifiers of degree 3 are of particular interest, as routing on node-disjoint paths, and computing minors seems easier in sub-cubic graphs than in general graphs. In this ...
متن کاملTowards (1 + ∊)-Approximate Flow Sparsifiers
A useful approach to “compress” a large network G is to represent it with a flow-sparsifier, i.e., a small network H that supports the same flows as G, up to a factor q ≥ 1 called the quality of sparsifier. Specifically, we assume the network G contains a set of k terminals T , shared with the network H, i.e., T ⊆ V (G) ∩ V (H), and we want H to preserve all multicommodity flows that can be rou...
متن کاملTowards (1+\epsilon)-Approximate Flow Sparsifiers
A useful approach to “compress” a large network G is to represent it with a flow-sparsifier, i.e., a small network H that supports the same flows as G, up to a factor q ≥ 1 called the quality of sparsifier. Specifically, we assume the network G contains a set of k terminals T , shared with the network H, i.e., T ⊆ V (G) ∩ V (H), and we want H to preserve all multicommodity flows that can be rou...
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ژورنال
عنوان ژورنال: Journal of Graph Algorithms and Applications
سال: 2011
ISSN: 1526-1719
DOI: 10.7155/jgaa.00245