TR-2006-15

Uniquely localizable networks with few anchors

Zsolt Fekete, Tibor Jordán

Published in:
(S. Nikoletseas and J.D.P. Rolim, eds) Springer Lecture Notes in Computer Science 4240, pp. 176-183, 2006.

In the network localization problem the locations of some nodes (called anchors) as well as the distances between some pairs of nodes are known, and the goal is to determine the location of all nodes. The localization problem is said to be solvable (or uniquely localizable) if there is a unique set of locations consistent with the given data. Recent results from graph rigidity theory made it possible to characterize the solvability of the localization problem in two dimensions.
 
In this paper we address the following related optimization problem: given the set of known distances in the network, make the localization problem solvable by computing the locations of as few nodes as possible, that is, by minimizing the number of anchor nodes. We develop a polynomial-time 3-approximation algorithm for this problem by proving new structural results in graph rigidity and by using tools from matroid theory.

Bibtex entry:

@techreport{egres-06-15,

AUTHOR	=	{Fekete, Zsolt and Jord{\'a}n, Tibor},
TITLE	=	{Uniquely localizable networks with few anchors},
NOTE	=	{{\tt egres.elte.hu}},
INSTITUTION	=	{Egerv{\'a}ry Research Group, Budapest},
YEAR	=	{2006},
NUMBER	=	{TR-2006-15}

}