Research Article
How to Fit In Another Meeting
@INPROCEEDINGS{10.1109/COLCOM.2006.361843, author={Rolf Klein and Doron Nussbaum and J\o{}rg-R\'{y}diger Sack and Jiehua Yi}, title={How to Fit In Another Meeting}, proceedings={2nd International ICST Conference on Collaborative Computing: Networking, Applications and Worksharing}, publisher={IEEE}, proceedings_a={COLLABORATECOM}, year={2007}, month={5}, keywords={commerce computational complexity computational geometry graph theory scheduling Euclidean plane geometric model geometric network graph-based model inverse Ackermann function meeting locations meeting times}, doi={10.1109/COLCOM.2006.361843} }- Rolf Klein
Doron Nussbaum
Jörg-Rüdiger Sack
Jiehua Yi
Year: 2007
How to Fit In Another Meeting
COLLABORATECOM
IEEE
DOI: 10.1109/COLCOM.2006.361843
Abstract
We are studying 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. For a geometric model, where n participants can travel along straight paths in the Euclidean plane, we present an O(n log n) algorithm to determine the longest meeting duration and a location suitable to all participants. In a graph-based model, transportation is provided by a geometric network over m nodes and e edges in the plane. Participants can have individual weights. Moreover, there can be k groups of participants, such that only one member of each group must attend the meeting. In this model, a location for a meeting of longest possible duration can be determined in time O(enalpha(k) log k + n log n + mn log m), where alpha(k) denotes the extremely slowly growing inverse Ackermann function.