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Chain-constrained spanning trees

Olver, Neil and Zenklusen, Rico (2014) Chain-constrained spanning trees. In: The 16th Conference on Integer Programming and Combinatorial Optimization, 2013-03-18 - 2013-03-20, Universidad Técnica Federico Santa María.

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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 became 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 a super-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: Conference or Workshop Item (Paper)
Official URL: https://www.cec.uchile.cl/~ipco2013/
Additional Information: © 2013 Springer-Verlag Berlin Heidelberg
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 24 Jan 2020 14:33
Last Modified: 11 Jul 2020 23:17
URI: http://eprints.lse.ac.uk/id/eprint/103175

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