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

  • Michael A. Bender
  • Ritwik Bose
  • Rezaul Chowdhury
  • Samuel McCauley
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7288)


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.


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Michael A. Bender
    • 1
    • 2
  • Ritwik Bose
    • 1
  • Rezaul Chowdhury
    • 1
  • Samuel McCauley
    • 1
  1. 1.Department of Computer ScienceStony Brook UniversityUSA
  2. 2.Tokutek, Inc.USA

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