 
Summary: Power Consumption in Packet Radio Networks \Lambda
Lefteris M. Kirousis x
(kirousis@cti.gr)
Evangelos Kranakis \Lambday
(kranakis@scs.carleton.ca)
Danny Krizanc \Lambday
(krizanc@scs.carleton.ca)
Andrzej Pelc zy
(pelc@uqah.uquebec.ca)
Abstract
In this paper we study the problem of assigning transmission ranges to the nodes of a multi
hop packet radio network so as to minimize the total power consumed under the constraint
that adequate power is provided to the nodes to ensure that the network is strongly connected
(i.e., each node can communicate along some path in the network to every other node). Such
assignment of transmission ranges is called complete. We also consider the problem of achieving
strongly connected bounded diameter networks.
For the case of n + 1 colinear points at unit distance apart (the unit chain) we give a tight
asymptotic bound for the minimum cost of a range assignment of diameter h when h is a fixed
constant and when h – (1 + ffl) log n, for some constant ffl ? 0. When the distances between
the colinear points are arbitrary, we give an O(n 4 ) time dynamic programming algorithm for
