منابع مشابه
Solving Low - density Subset Sum
Definition 1. Subset sum (SSUM) is the following problem: given a1, . . . , an ∈ [0, X] and s = ∑ aixi where each xi ∈ {0, 1}, find ~x = (x1, . . . , xn). Definition 2. The density of a subset sum problem is defined as n logX ; the ratio between the number of elements in your sum to the number of bits in the range of ais. Low density means n logX is very small, for example 1 n2 where X = 2 n . ...
متن کاملImproved Low - Density Subset
The general subset sum problem is NP-complete. However, there are two algorithms, one due to Brickell and the other to Lagarias and Odlyzko, which in polynomial time solve almost all subset sum problems of suuciently low density. Both methods rely on basis reduction algorithms to nd short non-zero vectors in special lattices. The Lagarias-Odlyzko algorithm would solve almost all subset sum prob...
متن کاملIMPROVED LOW - DENSITY SUBSET SUMALGORITHMSMatthijs
The general subset sum problem is NP-complete. However, there are two algorithms, one due to Brickell and the other to Lagarias and Odlyzko, which in polynomial time solve almost all subset sum problems of suuciently low density. Both methods rely on basis reduction algorithms to nd short non-zero vectors in special lattices. The Lagarias-Odlyzko algorithm would solve almost all subset sum prob...
متن کاملBranching proofs of infeasibility in low density subset sum problems
We prove that the subset sum problem ax = β x ∈ {0, 1}n (SUB) has a polynomial time computable certificate of infeasibility for all a with density at most 1/(2n), and for almost all β integer right hand sides. The certificate is branching on a hyperplane, i.e. by a methodology dual to the one explored by Lagarias and Odlyzko [6]; Frieze [3]; Furst and Kannan [4]; and Coster et. al. in [1]. We p...
متن کاملQuantum Algorithms for the Subset-Sum Problem
This paper introduces a subset-sum algorithm with heuristic asymptotic cost exponent below 0.25. The new algorithm combines the 2010 Howgrave-Graham–Joux subset-sum algorithm with a new streamlined data structure for quantum walks on Johnson graphs.
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ژورنال
عنوان ژورنال: Computational Complexity
سال: 1992
ISSN: 1016-3328,1420-8954
DOI: 10.1007/bf01201999