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MaxCut Parameterized Above the EdwardsErdős Bound. arXiv:1112.3506v2. A preliminary version published
 in ICALP 2012, Part I, Lect. Notes Comput. Sci. 7391
, 2012
"... ar ..."
A Construction Method for Optimally Universal Hash Families and its Consequences for the Existence of RBIBDs (Extended Abstract)
"... We introduce a method for constructing optimally universal hash families and equivalently RBIBDs. As a consequence of our construction we obtain minimal optimally universal hash families, if the cardinalities of the universe and the range are powers of the same prime. A corollary of this result is t ..."
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We introduce a method for constructing optimally universal hash families and equivalently RBIBDs. As a consequence of our construction we obtain minimal optimally universal hash families, if the cardinalities of the universe and the range are powers of the same prime. A corollary of this result is that the necessary condition for the existence of an RBIBD with parameters (v, k, λ), namely v mod k = λ(v − 1) mod (k − 1) = 0, is sufficient, if v and k are powers of the same prime. As an application of our construction, we show that the kMAXCUT algorithm of Hofmeister and Lefmann [9] can be implemented such that it has a polynomial running time, in the case that the number of vertices and k are powers of the same prime.
An Investigation of the MaxCut Problem
, 2004
"... The MaxCut problem seeks to partition the vertices of a graph into two sets such that the weight of the edges joining those sets is maximized. The MaxCut problem has been of continued research interest and has developed an extensive literature. After reviewing of a small portion of that literature, ..."
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The MaxCut problem seeks to partition the vertices of a graph into two sets such that the weight of the edges joining those sets is maximized. The MaxCut problem has been of continued research interest and has developed an extensive literature. After reviewing of a small portion of that literature, this article discusses an approach to the solution of this problem based on a branch and bound algorithm composed with a divide and conquer preprocessing phase. Preliminary results are given and several directions for further research are outlined.
A Construction Method for Optimally Universal Hash Families and its Consequences for the Existence of
"... We introduce a method for constructing optimally universal hash families and equivalently RBIBDs. As a consequence of our construction we obtain minimal optimally universal hash families, if the cardinalities of the universe and the range are powers of the same prime. A corollary of this result is t ..."
Abstract
 Add to MetaCart
(Show Context)
We introduce a method for constructing optimally universal hash families and equivalently RBIBDs. As a consequence of our construction we obtain minimal optimally universal hash families, if the cardinalities of the universe and the range are powers of the same prime. A corollary of this result is that the necessary conditions for the existence of an RBIBD with parameters v, k, λ, namely v ≡ 0 (mod k) and λ(v − 1) ≡ 0 (mod k − 1), are sufficient, if v and k are powers of the same prime. As an application of our construction, we show that the kMAXCUT algorithm of Hofmeister and Lefmann [9] can be implemented such that it has a polynomial running time, in the case that the number of vertices and k are powers of the same prime. 1