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
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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 -