TY - GEN
T1 - Dynamic low-stretch spanning trees in subpolynomial time
AU - Chechik, Shiri
AU - Zhang, Tianyi
N1 - Publisher Copyright:
Copyright © 2020 by SIAM
PY - 2020
Y1 - 2020
N2 - Low-stretch spanning tree has been an important graph-theoretic object, as it is one of the building blocks for fast algorithms that solve symmetrically diagonally dominant linear systems, and a significant line of research has been devoted to finding constructions with optimal average stretch. In a very recent work by Goranci and Forster [STOC 2019], the authors initiated the study of low-stretch spanning trees in the dynamic setting, and they proposed a dynamic algorithm that maintains a spanning tree in n12 +o(1) amortized update time with subpolynomial stretch in an unweighted graph on n vertices undergoing edge insertions and deletions demanded by an oblivious adversary. Our main results are twofold. First, we substantially improve the update time of Goranci and Forster [STOC 2019] from n12 +o(1) to a subpolynomial of no(1). Second, we generalize our result to weighted graphs under the decremental setting. As far as we know, this is the first non trivial dynamic algorithm for maintaining low-stretch spanning tree for weighted graphs.
AB - Low-stretch spanning tree has been an important graph-theoretic object, as it is one of the building blocks for fast algorithms that solve symmetrically diagonally dominant linear systems, and a significant line of research has been devoted to finding constructions with optimal average stretch. In a very recent work by Goranci and Forster [STOC 2019], the authors initiated the study of low-stretch spanning trees in the dynamic setting, and they proposed a dynamic algorithm that maintains a spanning tree in n12 +o(1) amortized update time with subpolynomial stretch in an unweighted graph on n vertices undergoing edge insertions and deletions demanded by an oblivious adversary. Our main results are twofold. First, we substantially improve the update time of Goranci and Forster [STOC 2019] from n12 +o(1) to a subpolynomial of no(1). Second, we generalize our result to weighted graphs under the decremental setting. As far as we know, this is the first non trivial dynamic algorithm for maintaining low-stretch spanning tree for weighted graphs.
UR - http://www.scopus.com/inward/record.url?scp=85084045758&partnerID=8YFLogxK
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AN - SCOPUS:85084045758
T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
SP - 463
EP - 475
BT - 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
A2 - Chawla, Shuchi
PB - Association for Computing Machinery
T2 - 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
Y2 - 5 January 2020 through 8 January 2020
ER -