A polynomial approximation scheme for the subset sum problem

• Published in: Discrete Applied Mathematics Vol. 57; no. 2; pp. 243 - 253
• Main Authors: Soma, Nei Yoshihiro, Zinober, Alan Solon Ivor, Yanasse, Horacio Hideki, Harley, Peter John
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Lausanne Elsevier B.V 24.02.1995; Amsterdam Elsevier; New York, NY
• Subjects: Applied sciences; Exact sciences and technology; Flows in networks. Combinatorial problems; Heuristic; Operational research and scientific management; Operational research. Management science; Polynomial approximation scheme; Subset sum; Polynomial approximation scheme; Heuristic; Subset sum; Approximation; Algorithm complexity; Heuristic method; Polynomial time
• ISSN: 0166-218X; 1872-6771
• DOI: 10.1016/0166-218X(94)00106-N

The subset sum problem is defined as: given a set of n + 1 positive integers, a 1, a 2,…, a n and b, find a subset of the a i 's such that their sum is the closest to b without exceeding the value b. We propose a variation of the well-known polynomial approximation scheme of Martello and Toth for this problem. From a practical point of view the suggested algorithm has a better experimental error behaviour and comparable running time. It is also shown that in the worst theoretical case both algorithms yield the same error.