# Efficient Linear Systolic Array for the Knapsack Problem

@inproceedings{Andonov1992EfficientLS, title={Efficient Linear Systolic Array for the Knapsack Problem}, author={Rumen Andonov and Patrice Quinton}, booktitle={CONPAR}, year={1992} }

A processor-efficient systolic algorithm for the dynamic programming approach to the knapsack problem is presented in this paper. The algorithm is implemented on a linear systolic array where the number of the cells q, the cell memory storage α and the input/output requirements are design parameters. These are independent of the problem size given by the number of the objects m and the knapsack capacity c. The time complexity of the algorithm is Θ(mc/q + m) and both the time speedup and the…

## 20 Citations

### The Derivation of Uniform Recurrence Equations for the Knapsack Problem

- Computer ScienceParallel Algorithms Appl.
- 1993

A mapping procedure for synthesizing uniform recurrence equations from the dynamic programming formulation of the knapsack problem is proposed and one of these arrays is optimal with respect to both speedup and efficiency.

### Dynamic programming parallel implementations for the knapsack problem

- Computer Science
- 1993

A systolic algorithm for the dynamic programming approach to the knapsack problem that can run on any number of processors and has optimal time speedup and processor efficiency is presented.

### An efficient parallel algorithm for solving the knapsack problem on the hypercube

- Computer ScienceProceedings 11th International Parallel Processing Symposium
- 1997

The main idea is to use the fact that the precedence graph of the dynamic programming function of the knapsack problem is an irregular mesh to use a scheduling algorithm for irregular meshes on the hypercube.

### Dynamic Programming Parallel Implementations for theKnapsack

- 1993

A systolic algorithm for the dynamic programming approach to the knapsack problem is presented. The algorithm can run on any number of processors and has optimal time speedup and processor eeciency.…

### An efficient parallel algorithm for solving the Knapsack problem on hypercubes

- Computer ScienceJ. Parallel Distributed Comput.
- 2004

### Load balancing methods and parallel dynamic programming algorithm using dominance technique applied to the 0-1 knapsack problem

- Computer ScienceJ. Parallel Distributed Comput.
- 2005

### An optimal algo-tech-cuit for the knapsack problem

- Computer ScienceProceedings of International Conference on Application Specific Array Processors (ASAP '93)
- 1993

The authors present a formal derivation and proof of correctness of a systolic array for the knapsack problem, an NP-complete problem whose dependency graph is not completely known statically, and analytically how /spl alpha/ may be chosen to optimize the total computation time, yielding an area time optimal circuit.

### Load balancingmethods and parallel dynamic programming algorithm using dominance technique applied to the 0 – 1 knapsack problem

- Computer Science
- 2004

The parallelization on a supercomputer of a one list dynamic programming algorithm using dominance technique and processor cooperation for the 0–1 knapsack problem is presented and original and efficient load balancing strategies are proposed.

### Knapsack on VLSI: from Algorithm to Optimal Circuit

- Computer ScienceIEEE Trans. Parallel Distributed Syst.
- 1997

This work addresses a number of pragmatic considerations: implementing the array on only a fixed number of PEs, simplifying the control to just two counters and a few latches, and loading the coefficients so that successive problems can be pipelined without any loss of throughput.

### Mapping a class of run-time dependencies onto regular arrays

- Computer Science[1993] Proceedings Seventh International Parallel Processing Symposium
- 1993

The author widens the class of algorithms that can be formally synthesized by introducing a mapping theorem by deriving uniform recurrences for the so-called knapsack problem and the resulting systolic array is known to be optimal.

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