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The Banquet Seating Problem

MSRI-UP 2015: Geometric Combinatorics Motivated by the Social Sciences June 13, 2015 - July 26, 2015

July 24, 2015 (02:00 PM PDT - 02:45 PM PDT)
Speaker(s): Michelle Rosado (University of Puerto Rico), Ashley Scruse (Clark Atlanta University), Alexis Jane Torre (University of Arizona)
Location: SLMath: Baker Board Room

Perez, Scruse, Torre


Suppose you want to seat n = mk people around k tables with m people at each table. Each person gives you a list of j people next to whom they would enjoy sitting. What is the smallest j for which you can always make a seating arrangement that would seat each person next to one of the people on their list? In this paper we show that j must be strictly more than half of n, the total number of people. Our key tool is a particular ‘blue-green-red’ lemma that helps us construct ‘worst-case scenario’ seating arrangements. We consider cases with two tables and more than two tables and explore seating arrangements with particular kinds of preferences.

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Perez, Scruse, Torre

H.264 Video Team_5.mp4 128 MB video/mp4 rtsp://videos.msri.org/data/000/023/919/original/Team_5.mp4 Download
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