Thin trees for laminar families

Klein, Nathan and Olver, Neil ORCID: 0000-0001-8897-5459 (2023) Thin trees for laminar families. In: Proceedings of the 64th IEEE Symposium on Foundations of Computer Science (FOCS). Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS. IEEE Computer Society Press. ISBN 9798350318944

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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
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:	17 Feb 2024 19:03
URI:	http://eprints.lse.ac.uk/id/eprint/120817

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