scholarly journals Trivial geometric heuristic for subset sum problem

2017 ◽  
Author(s):  
R U

All exact algorithms for solving subset sum problem (SUBSET\_SUM) are exponential (brute force, branch and bound search, dynamic programming which is pseudo-polynomial). To find the approximate solutions both a classical greedy algorithm and its improved variety, and different approximation schemes are used.This paper is an attempt to build another greedy algorithm by transferring representation of analytic geometry to such an object of discrete structure as a set. Set of size $n$ is identified with $n$-dimensional space with Euclidean metric, the subset-sum is identified with (hyper)plane.

Author(s):  
Rajesh K. Pandey ◽  
Om P. Agrawal

This paper presents a numerical scheme for a class of Isoperimetric Constraint Variational Problems (ICVPs) defined in terms of an A-operator introduced recently. In this scheme, Bernstein’s polynomials are used to approximate the desired function and to reduce the problem from a functional space to an eigenvalue problem in a finite dimensional space. Properties of the eigenvalues and eigenvectors of this problem are used to obtain approximate solutions to the problem. Results for two examples are presented to demonstrate the effectiveness of the proposed scheme. In special cases the A-operator reduce to Riemann-Liouville, Caputo, Riesz-Riemann-Liouville and Riesz-Caputo, and several other fractional derivatives defined in the literature. Thus, the approach presented here provides a general scheme for ICVPs defined using different types of fractional derivatives. Although, only Bernstein’s polynomials are used here to approximate the solutions, many other approximation schemes are possible. Effectiveness of these approximation schemes will be presented in the future.


1990 ◽  
Vol 21 (2) ◽  
pp. 1-10
Author(s):  
Toshiro Tachibana ◽  
Hideo Nakano ◽  
Yoshiro Nakanishi ◽  
Mitsuru Nakao

1987 ◽  
Vol 24 (4) ◽  
pp. 417-432 ◽  
Author(s):  
Joseph G. Peters ◽  
Larry Rudolph

Sign in / Sign up

Export Citation Format

Share Document