Book Chapter10.1007/978-3-540-27820-7_5
On the Computational Complexity of Sensor Network Localization
James Aspnes,David K. Goldenberg,Yang Richard Yang +2 more
- 16 Jul 2004
- pp 32-44
TL;DR: It is shown that no polynomial-time algorithm can solve the localization problem for sensor networks in the worst case, even for sets of distance pairs for which a unique solution exists, unless RP = NP.
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Abstract: Determining the positions of the sensor nodes in a network is essential to many network functionalities such as routing, coverage and tracking, and event detection. The localization problem for sensor networks is to reconstruct the positions of all of the sensors in a network, given the distances between all pairs of sensors that are within some radius r of each other. In the past few years, many algorithms for solving the localization problem were proposed, without knowing the computational complexity of the problem. In this paper, we show that no polynomial-time algorithm can solve this problem in the worst case, even for sets of distance pairs for which a unique solution exists, unless RP = NP. We also discuss the consequences of our result and present open problems.
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Citations
•Book
Convex Optimization & Euclidean Distance Geometry
Jon Dattorro
- 01 Jan 2004
TL;DR: This book is about convex optimization, convex geometry (with particular attention to distance geometry), geometric problems, and problems that can be transformed into geometrical problems.
818
A Theory of Network Localization
James Aspnes,Tolga Eren,David K. Goldenberg,A.S. Morse,Walter Whiteley,Yang Yang,Brian D. O. Anderson,Peter N. Belhumeur +7 more
TL;DR: This paper constructs grounded graphs to model network localization and applies graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks, and further study the computational complexity of network localization.
•Posted Content
Euclidean distance geometry and applications
TL;DR: The theory of Euclidean distance geometry and its most important applications are surveyed, with special emphasis on molecular conformation problems.
482
Theory of semidefinite programming for sensor network localization
Anthony Man-Cho So,Yinyu Ye +1 more
- 23 Jan 2005
TL;DR: It is shown, for the first time, that these networks can be localized in polynomial time and a notion called strong localizability is introduced and shown that the SDP model will identify all strongly localizable sub-networks in the input network.
Euclidean Distance Geometry and Applications
TL;DR: Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance as mentioned in this paper, which is useful in several applications where the input data consist of an incomplete set of distances and the output is a set of points in Euclidian space realizing those given distances.
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