منابع مشابه
A quadratic lower bound for subset sums
Let A be a finite nonempty subset of an additive abelian group G, and let Σ(A) denote the set of all group elements representable as a sum of some subset of A. We prove that |Σ(A)| ≥ |H|+ 1 64 |A \H|2 where H is the stabilizer of Σ(A). Our result implies that Σ(A) = Z/nZ for every set A of units of Z/nZ with |A| ≥ 8√n. This consequence was first proved by Erdős and Heilbronn for n prime, and by...
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It is a well-known problem to give an estimate for the largest clique of the Paley-graph, i.e. , to give an estimate for |A| if A ⊂ Fp (p ≡ 1 (mod 4)) is such that A−A = {a−a′ |a, a′ ∈ A} avoids the set of quadratic nonresidues. In this paper we will study a much simpler problem namely when A− A is substituted by the set FS(A) = { ∑ εaa | εa = 0 or 1 and ∑ εa > 0}. In other words we will estima...
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1 The MinRep problem The challenge of making k << |T | is highly non trivial. The difficulty is among other things the need for reduction for subset k-connectivity. The construction is essentially new and has only minor intersection with the one from [KKL]. Generally speaking, we must make the reduction local. For example in the sense that we mainly connect vertices at distance 2. We describe t...
متن کاملA Lower Bound for the Optimization of Finite Sums
This paper presents a lower bound for optimizing a finite sum of n functions, where each function is L-smooth and the sum is μ-strongly convex. We show that no algorithm can reach an error ε in minimizing all functions from this class in fewer than Ω(n+ √ n(κ−1) log(1/ε)) iterations, where κ = L/μ is a surrogate condition number. We then compare this lower bound to upper bounds for recently dev...
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An algebraic branching program (ABP) is a directed acyclic graph, with a start vertex s, and end vertex t and each edge having a weight which is an affine form in F[x1, x2, . . . , xn]. An ABP computes a polynomial in a natural way, as the sum of weights of all paths from s to t, where the weight of a path is the product of the weights of the edges in the path. An ABP is said to be homogeneous ...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2007
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa129-2-4