NDLI: Primal-Dual Meets Local Search: Approximating MSTs With Nonuniform Degree Bounds

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Primal-Dual Meets Local Search: Approximating MSTs With Nonuniform Degree Bounds

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Ravi, R. Knemann, J.
Copyright Year	2005
Abstract	We present a new bicriteria approximation algorithm for the degree-bounded minimum-cost spanning tree (MST) problem: Given an undirected graph with nonnegative edge weights and a degree bound B, find a spanning tree of maximum node-degree B and minimum total edge-cost. Our algorithm outputs a tree of maximum degree at most a constant times B and total edge-cost at most a constant times that of a minimum-cost degree-B-bounded spanning tree.While our new algorithm is based on ideas from Lagrangian relaxation, as is our previous work [SIAM J. Comput., 31 (2002), pp. 1783--1793], it does not rely on computing a solution to a linear program. Instead, it uses a repeated application of Kruskal's MST algorithm interleaved with a combinatorial update of approximate Lagrangian node-multipliers maintained by the algorithm. These updates cause subsequent repetitions of the spanning tree algorithm to run for longer and longer times, leading to overall progress and a proof of the performance guarantee. A second useful feature of our algorithm is that it can handle nonuniform degree bounds on the nodes: Given distinct bounds Bv for every node $v \in V$, the output tree has degree at most O(Bv + log\|V\|) for every $v \in V$. As before, the cost of the tree is at most a constant times that of a minimum-cost tree obeying all degree bounds.
Starting Page	763
Ending Page	773
Page Count	11
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539702418048
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	3
Volume Number	34
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-27
Access Restriction	Subscribed
Subject Keyword	Trees Lagrangian relaxation degree-bounded spanning trees Approximation algorithms Graph theory approximation algorithms Graph algorithms network algorithms spanning trees Multi-objective and goal programming bicriteria approximation
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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