2nd International ICST Conference on Collaborative Computing: Networking, Applications and Worksharing

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},
        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},
  • Rolf Klein
    Doron Nussbaum
    Jörg-Rüdiger Sack
    Jiehua Yi
    Year: 2007
    How to Fit In Another Meeting
    DOI: 10.1109/COLCOM.2006.361843
Rolf Klein1,*, Doron Nussbaum2,*, Jörg-Rüdiger Sack2,*, Jiehua Yi2,*
  • 1: Institute of Computer Science, University of Bonn, Bonn, Germany 53117
  • 2: School of Computer Science, Carleton University, Ottawa, Canada K1S 5B6
*Contact email: rolf.klein@uni-bonn.de, nussbaum@scs.carleton.ca, sack@scs.carleton.ca, jyi@scs.carleton.ca


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.