Bounded-degree minimum-radius spanning trees in wireless sensor networks

Authors:
Min Kyung An;Nhat X. Lam;Dung T. Huynh;Trac N. Nguyen
Affiliations:
-;-;-;-
Venue:
Theoretical Computer Science
Year:
2013

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Abstract

In this paper, we study the problem of computing a spanning tree of a given undirected disk graph such that the radius of the tree is minimized subject to a given degree constraint @D^@?. We first introduce an (8,4)-bicriteria approximation algorithm for unit disk graphs (which is a special case of disk graphs) that computes a spanning tree such that the degree of any nodes in the tree is at most @D^@?+8 and its radius is at most 4@?OPT, where OPT is the minimum possible radius of any spanning tree with degree bound @D^@?. We also introduce an (@a,2)-bicriteria approximation algorithm for disk graphs that computes a spanning tree whose maximum node degree is at most @D^@?+@a and whose radius is bounded by 2@?OPT, where @a is a non-constant value that depends on M and k with M being the number of distinct disk radii and k being the ratio of the largest and the smallest disk radius.