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Primal-dual meets local search: approximating MST's with nonuniform degree bounds

9 years 5 months ago
Primal-dual meets local search: approximating MST's with nonuniform degree bounds
We present a new bicriteria approximation algorithm for the degree-bounded minimum-cost spanning tree problem: Given an undirected graph with nonnegative edge weights and degree bounds Bv > 1 for all vertices v, find a spanning tree T of minimum total edge-cost such that the maximum degree of each node v in T is at most Bv. Our algorithm finds a tree in which the degree of each node v is O(Bv + log n) and the total edge-cost is at most a constant times the cost of any tree that obeys all degree constraints. Our previous algorithm[9] with similar guarantees worked only in the case of uniform degree bounds (i.e. Bv = B for all vertices v). While the new algorithm is based on ideas from Lagrangean relaxation as is our previous work, 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 Lagrangean node-multipliers maintained by the algorithm. These updat...
Jochen Könemann, R. Ravi
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2003
Where STOC
Authors Jochen Könemann, R. Ravi
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