Unit disk graph approximation

Fabian Kuhn, Thomas Moscibroda, Roger Wattenhofer
2004 Proceedings of the 2004 joint workshop on Foundations of mobile computing - DIALM-POMC '04  
Finding a good embedding of a unit disk graph given by its connectivity information is a problem of practical importance in a variety of fields. In wireless ad hoc and sensor networks, such an embedding can be used to obtain virtual coordinates. In this paper, we prove a non-approximability result for the problem of embedding a given unit disk graph. Particularly, we show that if non-neighboring nodes are not allowed to be closer to each other than distance 1, then two neighbors can be as far
more » ... ors can be as far apart as 3/2 − , where goes to 0 as n goes to infinity, unless P = N P . We further show that finding a realization of a d-quasi unit disk graph with d ≥ 1/ √ 2 is N P -hard.
doi:10.1145/1022630.1022634 dblp:conf/dialm/KuhnMW04 fatcat:uiwek2e52zdhxarb7gdjp2hzli