Walking in circles

Noga Alon, Michal Feldman, Ariel D. Procaccia, Moshe Tennenholtz

Research output: Contribution to journalArticle

6 Scopus citations


Consider the unit circle S1 with distance function d measured along the circle. We show that for every selection of 2n points x1,⋯,xn,y1, ⋯,yn∈S1 there exists i∈1,⋯,n such that ∑k=1nd(xi,xk)≤∑k=1nd(xi,yk). We also discuss a game theoretic interpretation of this result.

Original languageEnglish (US)
Pages (from-to)3432-3435
Number of pages4
JournalDiscrete Mathematics
Issue number23
StatePublished - Dec 6 2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


  • Game theory
  • Geometry

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    Alon, N., Feldman, M., Procaccia, A. D., & Tennenholtz, M. (2010). Walking in circles. Discrete Mathematics, 310(23), 3432-3435. https://doi.org/10.1016/j.disc.2010.08.007