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http://dx.doi.org/10.7236/JIIBC.2022.22.2.9

A Generalized Subtractive Algorithm for Subset Sum Problem  

Lee, Sang-Un (Dept. of Multimedia Eng., Gangneung-Wonju National University)
Publication Information
The Journal of the Institute of Internet, Broadcasting and Communication / v.22, no.2, 2022 , pp. 9-14 More about this Journal
Abstract
This paper presents a subset sum problem (SSP) algorithm which takes the time complexity of O(nlogn). The SSP can be classified into either super-increasing sequence or random sequence depending on the element of Set S. Additive algorithm that runs in O(nlogn) has already been proposed to and utilized for the super-increasing sequence SSP, but exhaustive Brute-Force method with time complexity of O(n2n) remains as the only viable algorithm for the random sequence SSP, which is thus considered NP-complete. The proposed subtractive algorithm basically selects a subset S comprised of values lower than target value t, then sets the subset sum less the target value as the Residual r, only to remove from S the maximum value among those lower than t. When tested on various super-increasing and random sequence SSPs, the algorithm has obtained optimal solutions running less than the cardinality of S. It can therefore be used as a general algorithm for the SSP.
Keywords
Subset Sum Problem; SSP; Residual; Subtractive Algorithm; Additive Algorithm;
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