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The Kissing Problem: How to End a Gathering When Everyone Kisses Everyone Else Goodbye

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7288)

Abstract

This paper introduces the kissing problem: given a rectangular room with n people in it, what is the most efficient way for each pair of people to kiss each other goodbye? The room is viewed as a set of pixels that form a subset of the integer grid. At most one person can stand on a pixel at once, and people move horizontally or vertically. In order to move into a pixel in time step t, the pixel must be empty in time step t − 1.

The paper gives one algorithm for kissing everyone goodbye.

(1) This algorithm is a 4 + o(1)-approximation algorithm in a crowded room (e.g., only one unoccupied pixel).

(2) It is a 10 + o(1)-approximation algorithm for kissing in a comfortable room (e.g., at most half the pixels are empty).

(3) It is a 25+o(1)-approximation for kissing in a sparse room.

Keywords

  • Approximation Algorithm
  • Mobile Robot
  • Approximation Ratio
  • Travel Salesman Problem
  • Travel Salesman Problem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bender, M.A., Bose, R., Chowdhury, R., McCauley, S. (2012). The Kissing Problem: How to End a Gathering When Everyone Kisses Everyone Else Goodbye. In: Kranakis, E., Krizanc, D., Luccio, F. (eds) Fun with Algorithms. FUN 2012. Lecture Notes in Computer Science, vol 7288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30347-0_6

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  • DOI: https://doi.org/10.1007/978-3-642-30347-0_6

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