Efficient approximation algorithms for the SUBSET-SUMS EQUALITY problem

Cristina Bazgan, Miklos Santha, Zsolt Tuza

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

We investigate the problem of finding two nonempty disjoint subsets of a set of n positive integers, with the objective that the sums of the numbers in the two subsets be as close as possible. In two versions of this problem, the quality of a solution is measured by the ratio and the difference of the two partial sums, respectively. Answering a problem of Woeginger and Yu (1992) in the affirmative, we give a fully polynomial-time approximation scheme for the case where the value to be optimized is the ratio between the sums of the numbers in the two sets. On the other hand, we show that in the case where the value of a solution is the positive difference between the two partial sums, the problem is not 2nk -approximable in polynomial time unless P=NP, for any constant k. In the positive direction, we give a polynomial-time algorithm that finds two subsets for which the difference of the two sums does not exceed K/nΩ(log n), where K is the greatest number in the instance.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages387-396
Number of pages10
Volume1443 LNCS
Publication statusPublished - 1998
Event25th International Colloquium on Automata, Languages and Programming, ICALP 1998 - Aalborg, Denmark
Duration: Jul 13 1998Jul 17 1998

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1443 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other25th International Colloquium on Automata, Languages and Programming, ICALP 1998
CountryDenmark
CityAalborg
Period7/13/987/17/98

Fingerprint

Approximation algorithms
Approximation Algorithms
Efficient Algorithms
Polynomials
Partial Sums
Subset
Set theory
Fully Polynomial Time Approximation Scheme
Polynomial-time Algorithm
Polynomial time
Exceed
Disjoint
Integer

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Bazgan, C., Santha, M., & Tuza, Z. (1998). Efficient approximation algorithms for the SUBSET-SUMS EQUALITY problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1443 LNCS, pp. 387-396). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1443 LNCS).

Efficient approximation algorithms for the SUBSET-SUMS EQUALITY problem. / Bazgan, Cristina; Santha, Miklos; Tuza, Zsolt.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1443 LNCS 1998. p. 387-396 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1443 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Bazgan, C, Santha, M & Tuza, Z 1998, Efficient approximation algorithms for the SUBSET-SUMS EQUALITY problem. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 1443 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1443 LNCS, pp. 387-396, 25th International Colloquium on Automata, Languages and Programming, ICALP 1998, Aalborg, Denmark, 7/13/98.
Bazgan C, Santha M, Tuza Z. Efficient approximation algorithms for the SUBSET-SUMS EQUALITY problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1443 LNCS. 1998. p. 387-396. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Bazgan, Cristina ; Santha, Miklos ; Tuza, Zsolt. / Efficient approximation algorithms for the SUBSET-SUMS EQUALITY problem. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1443 LNCS 1998. pp. 387-396 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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