 
Summary: On the Computational Complexity of Sensor Network
Localization
James Aspnes , David Goldenberg , and Yang Richard Yang
Yale University
Department of Computer Science
New Haven, CT 065208285, USA
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 polynomialtime 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.
1 Introduction
Localization is the process by which the positions of the nodes in an adhoc network are determined. Knowing
the positions of the network nodes is essential because many other network functionalities such as location
dependent computing (e.g., [11, 29]), geographic routing (e.g., [17]), coverage and tracking (e.g., [18]), and
event detection depend on location. Although localization can be achieved through manual configuration or by
exploiting the Global Positioning System (GPS) [15], neither methodology scales well and both have physical
