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...

• Type: Conference
• Year: 2003
• Where: STOC
• Authors: Jochen Könemann, R. Ravi
• Keywords: Algorithms, Bicriteria Approximation Algorithm, Spanning Tree, STOC 2003, Tree Algorithm