منابع مشابه
Subset sum problem in polycyclic groups
We consider a group-theoretic analogue of the classic subset sum problem. It is known that every virtually nilpotent group has polynomial time decidable subset sum problem. In this paper we use subgroup distortion to show that every polycyclic non-virtually-nilpotent group has NP-complete subset sum problem.
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This thesis explores new modifications to the successful LLL approach to solving the Subset Sum problem. This work is an optimization of the matrix representation of an instance. Traditionally, the basis matrix contained only one column with set elements and the sum. In this thesis we suggest having several data columns (thus introducing multidimensionality). This allows us to reduce the size o...
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In their paper [22], Myasnikov, Nikolaev, and Ushakov started the investigation of classical discrete integer optimization problems in general non-commutative groups. Among other problems, they introduced for a finitely generated (f.g.) group G the knapsack problem and the subset sum problem. The input for the knapsack problem is a sequence of group elements g1, . . . , gk, g ∈ G and it is aske...
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In the field of algorithmic analysis, one of the more well-known exercises is the subset sum problem. That is, given a set of integers, determine whether one or more integers in the set can sum to a target value. Aside from the brute-force approach of verifying all combinations of integers, several solutions have been found, ranging from clever uses of various data structures to computationally...
متن کاملApproximability of the Subset Sum Reconfiguration Problem
The subset sum problem is a well-known NP-complete problem in which we wish to find a packing (subset) of items (integers) into a knapsack with capacity so that the sum of the integers in the packing is at most the capacity of the knapsack and at least a given integer threshold. In this paper, we study the problem of reconfiguring one packing into another packing by moving only one item at a ti...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2018
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2017.03.007