On an extremal hypergraph problem related to combinatorial batch codes
نویسندگان
چکیده
منابع مشابه
On an Extremal Hypergraph Problem Related to Combinatorial Batch Codes
Let n, r, k be positive integers such that 3 k < n and 2 r k 1. Let m(n, r, k) denote the maximum number of edges an r-uniform hypergraph on n vertices can have under the condition that any collection of i edges, span at least i vertices for all 1 i k. We are interested in the asymptotic nature of m(n, r, k) for fixed r and k as n!1. This problem is related to the forbidden hypergraph...
متن کاملNote on an Extremal Hypergraph Problem Related to Combinatorial Batch Codes
Let n, r, k be positive integers such that 3 ≤ k < n and 2 ≤ r ≤ k − 1. Let m(n, r, k) denote the maximum number of edges an r-uniform hypergraph on n vertices can have under the condition that any collection of i edges spans at least i vertices for all 1 ≤ i ≤ k. We are interested in the asymptotic nature of m(n, r, k) for fixed r and k as n → ∞. This problem is related to the forbidden hyperg...
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Paterson, Stinson and Wei [2] introduced Combinatorial batch codes, which are combinatorial description of Batch code. Batch codes were first presented by Ishai, Kushilevita, Ostrovsky and Sahai [1] in STOC’04. In this paper we answer some of the questions put forward by Paterson, Stinson and Wei and give some results for the general case t > 1 which were not studied by the authors.
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Let fr(n, v, e) denote the maximum number of edges in an r-uniform hypergraph on n vertices, which does not contain e edges spanned by v vertices. Extending previous results of Ruzsa and Szemerédi and of Erdős, Frankl and Rödl, we partially resolve a problem raised by Brown, Erdős and Sós in 1973, by showing that for any fixed 2 ≤ k < r, we have nk−o(1) < fr(n, 3(r − k) + k + 1, 3) = o(n).
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In this paper, we study batch codes, which were introduced by Ishai, Kushilevitz, Ostrovsky and Sahai in [4]. A batch code specifies a method to distribute a database of n items among m devices (servers) in such a way that any k items can be retrieved by reading at most t items from each of the servers. It is of interest to devise batch codes that minimize the total storage, denoted by N , over...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2014
ISSN: 0166-218X
DOI: 10.1016/j.dam.2013.08.046