A meeting scheduling problem respecting time and space

• Published in: GeoInformatica Vol. 13; no. 4; pp. 453 - 481
• Main Authors: Berger, Florian, Klein, Rolf, Nussbaum, Doron, Sack, Jörg-Rüdiger, Yi, Jiehua
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.12.2009; Springer; Springer Nature B.V
• Subjects: Algorithms; Computer Science; Data Structures and Information Theory; Earth and Environmental Science; Earth sciences; Earth, ocean, space; Exact sciences and technology; Geographic information systems; Geographical Information Systems/Cartography; Geography; Information Storage and Retrieval; Meetings; Multimedia Information Systems; Scheduling algorithms; Computational geometry; Algorithms; Geographic information system; Meeting schedule; algorithms; models; color; data processing; geographic information systems; lead; duration; solution; geometry; computers
• ISSN: 1384-6175; 1573-7624
• DOI: 10.1007/s10707-008-0053-4

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 two solutions to the problem instance where each participant has two scheduled meetings separated by a free time interval. We present an O ( n log n ) algorithm for n participants obtained by purely geometrical arguments. Our second approach uses the concept of LP-type problems and leads to a randomized algorithm with expected running time O ( n ). We also consider a graph-based model where participants belong to different groups and can travel along the edges of a graph. For the meeting, only one member out of each group is required. The resulting problem can be solved using furthest color Voronoi diagrams on graphs.