We consider the problem of determining suitable meeting times and locations for a group of participants wishing to schedule a new meeting subject to already scheduled meetings possibly held at a number of different locations. Each participant must be able to reach the new meeting location, attend for the entire duration, and reach the next meeting location on time. In particular, we give a solution to the problem instance where each participant has two scheduled meetings separated by a free time interval. In [2], we presented an O(n log n) algorithm for n participants obtained by purely geometrical arguments. Our new approach uses the concept of LP-type problems and leads to a randomized algorithm with expected running time O(n).
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