Klein, Nathan and Olver, Neil ORCID: 0000-0001-8897-5459 (2023) Thin trees for laminar families. In: 2023 IEEE 64th Annual Symposium on Foundations of Computer Science: FOCS 2023, Proceedings. Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS. IEEE Computer Society Press. ISBN 9798350318951
Text (Thin trees for laminar families)
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Abstract
In the laminar-constrained spanning tree problem, the goal is to find a minimum-cost spanning tree which respects upper bounds on the number of times each cut in a given laminar family is crossed. This generalizes the well-studied degree-bounded spanning tree problem, as well as a previously studied setting where a chain of cuts is given. We give the first constant-factor approximation algorithm; in particular we show how to obtain a multiplicative violation of the crossing bounds of less than 22 while losing less than a factor of 5 in terms of cost. Our result compares to the natural LP relaxation. As a consequence, our results show that given a k-edge-connected graph and a laminar family L⊆2V of cuts, there exists a spanning tree which contains only an O(1/k) fraction of the edges across every cut in L. This can be viewed as progress towards the Thin Tree Conjecture, which (in a strong form) states that this guarantee can be obtained for all cuts simultaneously.
Item Type: | Book Section |
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Official URL: | https://ieeexplore.ieee.org/xpl/conhome/10353068/p... |
Additional Information: | © 2023 IEEE |
Divisions: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Date Deposited: | 21 Nov 2023 12:24 |
Last Modified: | 11 Dec 2024 18:11 |
URI: | http://eprints.lse.ac.uk/id/eprint/120817 |
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