On (ɛ,k)-min-wise independent permutations
نویسندگان
چکیده
منابع مشابه
Min-Wise Independent Permutations
We define and study the notion of min-wise independent families of permutations. We say that F ⊆ Sn is min-wise independent if for any set X ⊆ [n] and any x ∈ X, when π is chosen at random in F we have Pr(min{π(X)} = π(x)) = 1 |X| . In other words we require that all the elements of any fixed set X have an equal chance to become the minimum element of the image of X under π. Our research was mo...
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A set of permutations F ⊆ Sn is min-wise independent if for any set X ⊆ [n] and any x ∈ X, when π is chosen at random in F we have P (min{π(X)} = π(x)) = 1 |X| . 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 a...
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A family of permutations F of [n] = {1, 2, . . . , n} is (ε, k)-min-wise independent if for every nonempty subset X of at most k elements of [n], and for any x ∈ X, the probability that in a random element π of F , π(x) is the minimum element of π(X), deviates from 1/|X| by at most ε/|X|. This notion can be defined for the uniform case, when the elements of F are picked according to a uniform d...
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Min-wise independence is a recently introduced notion of limited independence, similar in spirit to pairwise independence. The later has proven essential for the derandomization of many algorithms. Here we show that approximate min-wise independence allows similar uses, by presenting a derandomization of the RNC algorithm for approximate set cover due to S. Rajagopalan and V. Vazirani. We also ...
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A family of permutations F ⊆ Sn with a probability distribution on it is called k-restricted min-wise independent if we have Pr[minπ(X) = π(x)] = 1 |X| for every subset X ⊆ [n] with |X | ≤ k, every x ∈ X , and π ∈ F chosen at random. We present a simple proof of a result of Norin: every such family has size at least ( n−1 ⌊ k−1 2 ⌋ ) . Some features of our method might be of independent interes...
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ژورنال
عنوان ژورنال: Random Structures and Algorithms
سال: 2007
ISSN: 1042-9832,1098-2418
DOI: 10.1002/rsa.20184