A novel and efficient algorithm to solve subset sum problem
B. Sinchev, A.B. Sinchev, J. Akzhanova, A.M. Mukhanova, and, Y.Issekeshev

TL;DR
This paper introduces a new algorithm for the subset sum problem with improved time and memory complexity, applicable to all NP-complete problems and potentially impacting the P vs NP question.
Contribution
The paper presents an analytical algorithm with significantly better complexity for subset sum, applicable to all NP-complete problems, and proposes a parallel computing methodology for larger instances.
Findings
Algorithm has time complexity O(C(n,k))
Memory complexity is O(C(n,k))
Applicable to real-world NP-complete problems
Abstract
In this paper we suggest analytical methods and associated algorithms for determining the sum of the subsets of the set (subset sum problem). Our algorithm has time complexity (, which significantly improves upon all known algorithms. This algorithm is applicable to all NP-complete problems. Moreover, the algorithm has memory complexity , which makes our algorithm applicable to real-world problems. At first, we show how to use the algorithm for small dimensions . After that we establish a general methodology for . The main idea is to split the original set (the algorithm becomes even faster with sorted sets) into smaller subsets and use parallel computing. This approach might be a significant breakthrough towards finding an efficient solution to -complete problems. As a result, it opens a way to prove the…
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Taxonomy
TopicsMachine Learning and Data Classification · Text and Document Classification Technologies · Graph Labeling and Dimension Problems
