Tuyển tập các báo cáo nghiên cứu khoa học trên tạp chí toán học quốc tế đề tài: Min-Wise independent linear permutations. | Min-Wise independent linear permutations Tom Bohman Department of Mathematical Sciences Carnegie Mellon University Pittsburgh PA15213 . E-mail tbohman@ Colin Cooped School of Mathematical Sciences University of North London London N7 8DB UK. E-mail Alan Frieze Department of Mathematical Sciences Carnegie Mellon University Pittsburgh PA15213 . E-mail alan@ Submitted January 12 2000 Accepted April 23 2000 Abstract A set of permutations F c Sn is min-wise independent if for any set X c n and any x 2 X when ft is chosen at random in F we have P min X x p ĩ. This notion was introduced by Broder Charikar Frieze and Mitzenmacher and is motivated by an algorithm for filtering near-duplicate web documents. Linear permutations are an important class of permutations. Let p be a large prime and let Fp a b 1 a p 1 0 b p 1 where for x 2 p 0 1 . p 1 Ka b x ax b mod p. For X c p we let F X Supported in part by NSF Grant DMS-9627408 Research supported by the STORM Research Group Supported in part by NSF grant CCR-9818411 1 THE ELECTRONIC .JOURNAL OF COMBINATORICS 7 2000 R26 2 maxx2X Pa b min X t where Pa b is over chosen uniformly at random from Fp. We show that as k p 1 EX F X k O lkf k2 confirming that a simply chosen random linear permutation will suffice for an average set from the point of view of approximate min-wise independence. 1 Introduction Broder Charikar Frieze and Mitzenmacher 3 introduced the notion of a set of min-wise independent permutations. We say that F c Sn is min-wise independent if for any set X c n and any x 2 X when is chosen at random in F we have P min X x Xj 1 The research was motivated by the fact that such a family under some relaxations is essential to the algorithm used in practice by the AltaVista web index software to detect and filter near-duplicate documents. A set of permutations satisfying 1 needs to be exponentially large 3 . In practice we can allow certain relaxations. First we .
