Chain-constrained spanning trees

Olver, Neil ORCID: 0000-0001-8897-5459 and Zenklusen, Rico (2017) Chain-constrained spanning trees. Mathematical Programming, 167 (2). 293 - 314. ISSN 0025-5610

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Abstract

We consider the problem of finding a spanning tree satisfying a family of additional constraints. Several settings have been considered previously, the most famous being the problem of finding a spanning tree with degree constraints. Since the problem is hard, the goal is typically to find a spanning tree that violates the constraints as little as possible. Iterative rounding has become the tool of choice for constrained spanning tree problems. However, iterative rounding approaches are very hard to adapt to settings where an edge can be part of more than a constant number of constraints. We consider a natural constrained spanning tree problem of this type, namely where upper bounds are imposed on a family of cuts forming a chain. Our approach reduces the problem to a family of independent matroid intersection problems, leading to a spanning tree that violates each constraint by a factor of at most 9. We also present strong hardness results: among other implications, these are the first to show, in the setting of a basic constrained spanning tree problem, a qualitative difference between what can be achieved when allowing multiplicative as opposed to additive constraint violations.

Item Type:	Article
Official URL:	https://link.springer.com/journal/10107
Additional Information:	© 2017 The Author(s)
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	20 Jan 2020 09:45
Last Modified:	01 Nov 2024 19:33
URI:	http://eprints.lse.ac.uk/id/eprint/103085

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