Abstract
Given a finite set S of points (i.e. the stations of a radio network) on the plane and a positive integer 1 ≤ h ≤ |S| − 1, the 2d Min h R. Assign. problem consists of assigning transmission ranges to the stations so as to minimize the total power consumption provided that the transmission ranges of the stations ensure the communication between any pair of stations in at most h hops.
We provide a lower bound on the total power consumption opth(S) yielded by an optimal range assignment for any instance (S, h) of 2d Min h R. Assign., for any positive constant h > 0. The lower bound is a function of |S|, h and the minimum distance over all the pairs of stations in S. Then, we derive a constructive upper bound for the same problem as a function of |S|, h and the maximum distance over all the pairs of stations in S (i.e. the diameter of S). Finally, by combining the above bounds, we obtain a polynomial-time approximation algorithm for 2d Min h R. Assign. restricted to well-spread instances, for any positive constant h.
Previous results for this problem were known only in special 1-dimensional configurations (i.e. when points are arranged on a line).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. Arikan, “Some Complexity Results about Packet Radio Networks”, IEEE Transactions on Information Theory, 456–461, IT-30, 1984.
A.E.F. Clementi, P. Penna, and R. Silvestri, “Hardness Results for the Power Range Assignment Problem in Packet Radio Networks”, II International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX’99), LNCS, 1671, 1999.
A. Ephemides and T. Truong, “Scheduling Broadcast in Multihop Radio Networks”, IEEE Transactions on Communications, 456–461, 30, 1990.
L. M. Kirousis and E. Kranakis and D. Krizanc and A. Pelc, “Power Consumption in Packet Radio Networks”, 14th Annual Symposium on Theoretical Aspects of Computer Science (STACS 97), LNCS 1200, 363–374, 1997 (to appear also in TCS).
C.H. Papadimitriou, “Computational Complexity”, Addison-Wesley Publishing Company, Inc., 1995.
K. Pahlavan and A. Levesque, “Wireless Information Networks”, Wiley-Interscience, New York, 1995.
S. Ramanathan and E. Lloyd, “Scheduling Broadcasts in Multi-hop Radio Networks” IEEE/ACM Transactions on Networking, 166–172, 1, 1993.
R. Ramaswami and K. Parhi, “Distributed Scheduling of Broadcasts in Radio Network”, INFOCOM’89, 497–504, 1989.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Clementi, A.E.F., Penna, P., Silvestri, R. (2000). The Power Range Assignment Problem in Radio Networks on the Plane. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_54
Download citation
DOI: https://doi.org/10.1007/3-540-46541-3_54
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67141-1
Online ISBN: 978-3-540-46541-6
eBook Packages: Springer Book Archive