TY - JOUR
T1 - Feasible schedules for rotating transmissions
AU - Alon, Noga
PY - 2006/9
Y1 - 2006/9
N2 - Motivated by a scheduling problem that arises in the study of optical networks, we prove the following result, which is a variation of a conjecture of Haxell, Wilfong and Winkler. et k, n be two positive integers, let w sj, 1 ≤ s ≤ n, 1 ≤ j ≤ k be nonnegative reals satisfying Σj=1k wsj < 1/n every 1 ≤ s ≤ n and let dsj be arbitrary nonnegative reals. Then there are real numbers x1, x2,...,xn such that for every j, 1 ≤j ≤ k, the n cyclic closed intervals Is(j) = [xs + dsj, xs + ddj + w sj], (1 ≤ s ≤ n), where the endpoints are reduced modulo 1, are pairwise disjoint on the unit circle. The proof is based on some properties of multivariate polynomials and on the validity of the Dyson conjecture.
AB - Motivated by a scheduling problem that arises in the study of optical networks, we prove the following result, which is a variation of a conjecture of Haxell, Wilfong and Winkler. et k, n be two positive integers, let w sj, 1 ≤ s ≤ n, 1 ≤ j ≤ k be nonnegative reals satisfying Σj=1k wsj < 1/n every 1 ≤ s ≤ n and let dsj be arbitrary nonnegative reals. Then there are real numbers x1, x2,...,xn such that for every j, 1 ≤j ≤ k, the n cyclic closed intervals Is(j) = [xs + dsj, xs + ddj + w sj], (1 ≤ s ≤ n), where the endpoints are reduced modulo 1, are pairwise disjoint on the unit circle. The proof is based on some properties of multivariate polynomials and on the validity of the Dyson conjecture.
UR - http://www.scopus.com/inward/record.url?scp=33746608571&partnerID=8YFLogxK
U2 - 10.1017/S0963548306007632
DO - 10.1017/S0963548306007632
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AN - SCOPUS:33746608571
SN - 0963-5483
VL - 15
SP - 783
EP - 787
JO - Combinatorics Probability and Computing
JF - Combinatorics Probability and Computing
IS - 5
ER -