Bipartite Synthesis Method applied to the Subset Sum Problem demonstrates capability as decision and optimization tool

TL;DR

This paper presents a deterministic Bipartite Synthesis Method for the Subset Sum Problem, achieving near-optimal worst-case performance and offering potential advantages over existing algorithms for decision and optimization tasks.

Contribution

Introduces a new deterministic algorithm based on the Bipartite Synthesis Method with competitive worst-case complexity for the Subset Sum Problem.

Findings

Achieves worst-case complexity around O(2^{0.5n})

Demonstrates potential for broader decision and optimization applications

Can be integrated with existing methods for improved performance

Abstract

This paper introduces a deterministic algorithm for solving an instance of the Subset Sum Problem based on a new method entitled the Bipartite Synthesis Method. The algorithm is described and shown to have worst-case limiting performance over similar to the best deterministic algorithms achieving run time complexity on the order of O(2^0.5n). This algorithm is representative of a more expansive capability that might convey significant advantages over existing deterministic or probabilistic methods, and it is amenable to blending with existing methods. The method introduced can be applied to a variety of decision and optimization problems.