Approximating the minimum-degree Steiner tree to within one of optimal
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
A Matter of Degree: Improved Approximation Algorithms for Degree-Bounded Minimum Spanning Trees
SIAM Journal on Computing
Primal-dual meets local search: approximating MST's with nonuniform degree bounds
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Degree-constrained multicasting in point-to-point networks
INFOCOM '95 Proceedings of the Fourteenth Annual Joint Conference of the IEEE Computer and Communication Societies (Vol. 1)-Volume - Volume 1
Minimum Bounded Degree Spanning Trees
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Approximating minimum bounded degree spanning trees to within one of optimal
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
An O(log n/ log log n)-approximation algorithm for the asymmetric traveling salesman problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Additive Guarantees for Degree-Bounded Directed Network Design
SIAM Journal on Computing
Dependent Randomized Rounding via Exchange Properties of Combinatorial Structures
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Matroidal degree-bounded minimum spanning trees
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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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.