Projects per year
Graph compression or sparsification is a basic information-theoretic and computational question. A major open problem in this research area is whether (1 + ε)-approximate cut-preserving 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 connectivity-c mimicking network, which preserves connectivity among k terminals exactly up to the value of c. We show that connectivity-c mimicking networks with O(kc4) edges exist and can be found in time m(c log n)O(c). We also give a separate algorithm that constructs such graphs with k · O(c)2c edges in time mcO(c) logO(1) n. These results lead to the first data structures for answering fully dynamic offline c-edge-connectivity queries for c ≥ 4 in polylogarithmic time per query, as well as more efficient algorithms for survivable network design on bounded treewidth graphs.
|Title of host publication||ACM-SIAM Symposium on Discrete Algorithms, SODA 2021|
|Number of pages||20|
|Publication status||Published - 2021|
|MoE publication type||A4 Article in a conference publication|
|Event||ACM-SIAM Symposium on Discrete Algorithms - Virtual, Online, Alexandria, United States|
Duration: 10 Jan 2021 → 13 Jan 2021
Conference number: 32
|Name||Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms|
|Conference||ACM-SIAM Symposium on Discrete Algorithms|
|Period||10/01/2021 → 13/01/2021|
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01/09/2017 → 31/08/2022
Project: Academy of Finland: Other research funding