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» On Equations over Sets of Integers
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TIME
2008
IEEE
14 years 1 months ago
Decomposition of Decidable First-Order Logics over Integers and Reals
We tackle the issue of representing infinite sets of realvalued vectors. This paper introduces an operator for combining integer and real sets. Using this operator, we decompose ...
Florent Bouchy, Alain Finkel, Jérôme ...
IEICET
2008
84views more  IEICET 2008»
13 years 7 months ago
Factorization of Square-Free Integers with High Bits Known
Abstract. In this paper we propose an algorithm of factoring any integer N which has k different prime factors with the same bit-length, when ( 1 k+2 + k(k-1) ) log N high-order bi...
Bagus Santoso, Noboru Kunihiro, Naoki Kanayama, Ka...
ORL
2008
111views more  ORL 2008»
13 years 7 months ago
Certificates of linear mixed integer infeasibility
A central result in the theory of integer optimization states that a system of linear diophantine equations Ax = b has no integral solution if and only if there exists a vector in...
Kent Andersen, Quentin Louveaux, Robert Weismantel
CORR
2006
Springer
95views Education» more  CORR 2006»
13 years 7 months ago
Solving Sparse Integer Linear Systems
We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a p-adic lifting technique combined with the use of block matr...
Wayne Eberly, Mark Giesbrecht, Pascal Giorgi, Arne...
CORR
2010
Springer
173views Education» more  CORR 2010»
13 years 7 months ago
CONCISE: Compressed 'n' Composable Integer Set
Bit arrays, or bitmaps, are used to significantly speed up set operations in several areas, such as data warehousing, information retrieval, and data mining, to cite a few. Howeve...
Alessandro Colantonio, Roberto Di Pietro