@article{35f5ee63632c43199e7ed85d2602b42b,
title = "Discrete Kakeya-type problems and small bases",
abstract = "A subset U of a group G is called k-universal if U contains a translate of every k-element subset of G. We give several nearly optimal constructions of small k-universal sets, and use them to resolve an old question of Erd{\'o}s and Newman on bases for sets of integers, and to obtain several extensions for other groups.",
author = "Noga Alon and Boris Bukh and Benny Sudakov",
note = "Funding Information: ∗Research supported in part by a USA Israeli BSF grant, by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University, by an ERC ad-vanced grant, by NSF grant CCF 0832797 and by the Ambrose Monell Foundation. ∗∗Research supported in part by NSF CAREER award DMS-0812005, NSF grant DMS-0635607, by a USA-Israeli BSF grant, and by the State of New Jersey. Received November 10, 2007 and in revised form March 31, 2008",
year = "2009",
month = nov,
doi = "10.1007/s11856-009-0115-9",
language = "English (US)",
volume = "174",
pages = "285--301",
journal = "Israel Journal of Mathematics",
issn = "0021-2172",
publisher = "Springer New York",
number = "1",
}