Abstract
Given a graph and degree upper bounds on vertices, the BDMST problem requires us to find the minimum cost spanning tree respecting the given degree bounds.Könemann and Ravi [10,11] give bicriteria approximation algorithms for the problem using local search techniques of Fischer [5]. For a graph with a cost C, degree B spanning tree, and parameters b, w> 1, their algorithm produces a tree whose cost is at most wC and whose degree is at most \(\frac{w}{w-1}bB + \log_b n.\) We give a polynomial-time algorithm that finds a tree of optimal cost and with maximum degree at most bB + 2(b+1)log b n. We also give a quasi-polynomial algorithm which produces a tree of optimal cost C and maximum degree bounded by B + O(log n/loglog n). Our algorithms work when there are upper as well as lower bounds on the degrees of the vertices.
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Chaudhuri, K., Rao, S., Riesenfeld, S., Talwar, K. (2005). What Would Edmonds Do? Augmenting Paths and Witnesses for Degree-Bounded MSTs. In: Chekuri, C., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds) Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2005 2005. Lecture Notes in Computer Science, vol 3624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538462_3
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DOI: https://doi.org/10.1007/11538462_3
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