Walking in circles

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

doi:10.1016/j.disc.2010.08.007

Walking in circles

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

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	3432-3435
Number of pages	4
Journal	Discrete Mathematics
Volume	310
Issue number	23
DOIs	https://doi.org/10.1016/j.disc.2010.08.007
State	Published - Dec 6 2010
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

Keywords

Game theory
Geometry

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10.1016/j.disc.2010.08.007

Cite this

@article{12098ebbc22e4a26994e2c95c1391ead,

title = "Walking in circles",

abstract = "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.",

keywords = "Game theory, Geometry",

author = "Noga Alon and Michal Feldman and Procaccia, \{Ariel D.\} and Moshe Tennenholtz",

note = "Funding Information: The first author{\textquoteright}s research was supported in part by a USA Israeli BSF grant , by an ERC advanced grant and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University . The second author{\textquoteright}s research was supported in part by the Israel Science Foundation (grant number 1219/09 ) and by the Leon Recanati Fund of the Jerusalem school of business administration .",

year = "2010",

month = dec,

day = "6",

doi = "10.1016/j.disc.2010.08.007",

language = "English (US)",

volume = "310",

pages = "3432--3435",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier B.V.",

number = "23",

}

TY - JOUR

T1 - Walking in circles

AU - Alon, Noga

AU - Feldman, Michal

AU - Procaccia, Ariel D.

AU - Tennenholtz, Moshe

N1 - Funding Information: The first author’s research was supported in part by a USA Israeli BSF grant , by an ERC advanced grant and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University . The second author’s research was supported in part by the Israel Science Foundation (grant number 1219/09 ) and by the Leon Recanati Fund of the Jerusalem school of business administration .

PY - 2010/12/6

Y1 - 2010/12/6

N2 - 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.

AB - 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.

KW - Game theory

KW - Geometry

UR - https://www.scopus.com/pages/publications/77957276436

UR - https://www.scopus.com/pages/publications/77957276436#tab=citedBy

U2 - 10.1016/j.disc.2010.08.007

DO - 10.1016/j.disc.2010.08.007

M3 - Article

AN - SCOPUS:77957276436

SN - 0012-365X

VL - 310

SP - 3432

EP - 3435

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 23

ER -

Walking in circles

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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