We present a new technique to prove lower bounds for geometric on-line sear
ching problems. We assume that a target of unknown location is hidden somew
here in a known environment and a searcher is trying to find it. We are int
erested in lower bounds on the competitive ratio of the search strategy, th
at is, the ratio of the distance traveled by the searcher to the distance o
f the target.
The technique we present is applicable to a number of problems, such as bia
sed searching on m rays and on-line construction of on-line algorithms. For
each problem we prove tight lower bounds. (C) 2001 Elsevier Science B.V. A
ll rights reserved.