New Algorithms for Subset Sum Problem
Data Structures and Algorithms
2018-07-17 v2
Abstract
Given a set (or multiset) S of n numbers and a target number t, the subset sum problem is to decide if there is a subset of S that sums up to t. There are several methods for solving this problem, including exhaustive search, divide-and-conquer method, and Bellman's dynamic programming method. However, none of them could generate universal and light code. In this paper, we present a new deterministic algorithm based on a novel data arrangement, which could generate such code and return all solutions. If n is small enough, it is efficient for usual purpose. We also present a probabilistic version with one-sided error and a greedy algorithm which could generate a solution with minimized variance.
Cite
@article{arxiv.1807.02611,
title = {New Algorithms for Subset Sum Problem},
author = {Zhengjun Cao and Lihua Liu},
journal= {arXiv preprint arXiv:1807.02611},
year = {2018}
}