Efficient Linear Systolic Array for the Knapsack Problem

  title={Efficient Linear Systolic Array for the Knapsack Problem},
  author={Rumen Andonov and Patrice Quinton},
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… 

The Derivation of Uniform Recurrence Equations for the Knapsack Problem

  • G. Megson
  • Computer Science
    Parallel 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

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

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

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 optimal algo-tech-cuit for the knapsack problem

  • R. AndonovS. Rajopadhye
  • Computer Science
    Proceedings 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

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

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

  • G. Megson
  • 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.



Adaptive Parallel Algorithms for Integral Knapsack Problems

  • S. Teng
  • Computer Science
    J. Parallel Distributed Comput.
  • 1990

A modular systolic 2-D torus for the general knapsack problem

  • R. AndonovF. Gruau
  • Computer Science
    Proceedings of the International Conference on Application Specific Array Processors
  • 1991
The authors propose a modular 2-D torus pipelined processing elements for solving the general knapsack problem of arbitrary size and show that the minimum and maximum weights w/sub min/ and w/ sub max/ define an upper bound for the possible vertical speed up.

Pipeline architectures for dynamic programming algorithms

Systolic processing for dynamic programming problems

The asymptotically optimal architecture for divide- and-conquer algorithms and efficient methods of mapping a regular AND/OR-graph into systolic arrays are developed.

Knapsack Problems: Algorithms and Computer Implementations

This paper focuses on the part of the knapsack problem where the problem of bin packing is concerned and investigates the role of computer codes in the solution of this problem.

Why systolic architectures?

The basic principle of systolic architectures is reviewed and it is explained why they should result in cost-effective, highperformance special-purpose systems for a wide range of problems.

Integer Programming

The principles of integer programming are directed toward finding solutions to problems from the fields of economic planning, engineering design, and combinatorial optimization. This highly respected

Computers and Intractability: A Guide to the Theory of NP-Completeness

It is proved here that the number ofrules in any irredundant Horn knowledge base involving n propositional variables is at most n 0 1 times the minimum possible number of rules.

Dynamic programming.

The more the authors study the information processing aspects of the mind, the more perplexed and impressed they become, and it will be a very long time before they understand these processes sufficiently to reproduce them.