A Parallel Time/Hardware Tradeoff T.H=O(2/sup n/2/) for the Knapsack Problem
IEEE Transactions on Computers
Computing Partitions with Applications to the Knapsack Problem
Journal of the ACM (JACM)
On the security of multiple encryption
Communications of the ACM
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Fundamentals of Computer Alori
Fundamentals of Computer Alori
A Parallel Algorithm for the Knapsack Problem
IEEE Transactions on Computers
Hiding information and signatures in trapdoor knapsacks
IEEE Transactions on Information Theory
A critical analysis of the security of knapsack public-key algorithms
IEEE Transactions on Information Theory
A polynomial-time algorithm for breaking the basic Merkle - Hellman cryptosystem
IEEE Transactions on Information Theory
Linearly shift knapsack public-key cryptosystem
IEEE Journal on Selected Areas in Communications
Comments on parallel algorithms for the knapsack problem
Parallel Computing
Journal of Parallel and Distributed Computing
Optimal parallel algorithm for the knapsack problem without memory conflicts
Journal of Computer Science and Technology
An optimal parallelization of the two-list algorithm of cost O(2n/2)
Parallel Computing
Solving knapsack problems on GPU
Computers and Operations Research
A parallel O(n27n/8) time-memory-processor tradeoff for Knapsack-like problems
NPC'05 Proceedings of the 2005 IFIP international conference on Network and Parallel Computing
A note on developing optimal and scalable parallel two-list algorithms
ICA3PP'12 Proceedings of the 12th international conference on Algorithms and Architectures for Parallel Processing - Volume Part II
Proceedings of Programming Models and Applications on Multicores and Manycores
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An n-element knapsack problem has 2^n possible solutions to search over, so a task which can be accomplished in 2'' trials if an exhaustive search is used. Due to the exponential time in solving the knapsack problem, the problem is considered to be very hard. In the past decade, much effort has been done in order to find techniques which could lead to practical algorithms with reasonable running time. In 1994, Chang et al. proposed a brilliant parallel algorithm, which needs O(2^n^/^8) processors to solve the knapsack problem in O(2^n^/^2) time; that is, the cost of Chang et al.'s parallel algorithm is O(2^5^n^/^8). In this paper, we propose a parallel algorithm to improve Chang et al.'s parallel algorithm by reducing the time complexity to be O(2^3^n^/^8) under the same O(2^n^/^8) processors available. Thus, the proposed parallel algorithm has a cost of O(2^n^/^2). It is an improvement over previous literature. We believe that the proposed parallel algorithm is pragmatically feasible at the moment when multiprocessor systems become more and more popular.