
Vertex Sparsification for Edge Connectivity in Polynomial Time
An important open question in the area of vertex sparsification is wheth...
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Mimicking Networks Parameterized by Connectivity
Given a graph G=(V,E), capacities w(e) on edges, and a subset of termina...
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A Faster Local Algorithm for Detecting BoundedSize Cuts with Applications to HigherConnectivity Problems
Consider the following "local" cutdetection problem in a directed graph...
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Good rdivisions Imply Optimal Amortised Decremental Biconnectivity
We present a data structure that given a graph G of n vertices and m edg...
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Vertex Sparsifiers for cEdge Connectivity
We show the existence of O(f(c)k) sized vertex sparsifiers that preserve...
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Hedge Connectivity without Hedge Overlaps
Connectivity is a central notion of graph theory and plays an important ...
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Faster Spectral Sparsification in Dynamic Streams
Graph sketching has emerged as a powerful technique for processing massi...
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Vertex Sparsification for Edge Connectivity
Graph compression or sparsification is a basic informationtheoretic and computational question. A major open problem in this research area is whether (1+ϵ)approximate cutpreserving vertex sparsifiers with size close to the number of terminals exist. As a step towards this goal, we study a thresholded version of the problem: for a given parameter c, find a smaller graph, which we call connectivityc mimicking network, which preserves connectivity among k terminals exactly up to the value of c. We show that connectivityc mimicking networks with O(kc^4) edges exist and can be found in time m(clog n)^O(c). We also give a separate algorithm that constructs such graphs with k · O(c)^2c edges in time mc^O(c)log^O(1)n. These results lead to the first data structures for answering fully dynamic offline cedgeconnectivity queries for c ≥ 4 in polylogarithmic time per query, as well as more efficient algorithms for survivable network design on bounded treewidth graphs.
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