Composing equipotent teams

Cieliebak, M; Eidenbenz, S; Pagourtzis, A

dc.contributor.author	Cieliebak, M	en
dc.contributor.author	Eidenbenz, S	en
dc.contributor.author	Pagourtzis, A	en
dc.date.accessioned	2014-03-01T01:18:46Z
dc.date.available	2014-03-01T01:18:46Z
dc.date.issued	2003	en
dc.identifier.issn	0302-9743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15192
dc.subject	Computational Complexity	en
dc.subject	Polynomial Time	en
dc.subject	Polynomial Time Algorithm	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.title	Composing equipotent teams	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/978-3-540-45077-1_10	en
heal.identifier.secondary	http://dx.doi.org/10.1007/978-3-540-45077-1_10	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	We study the computational complexity of k EQUAL SUM SUBSETS, in which we need to find k disjoint subsets of a given set of numbers such that the elements in each subset add up to the same sum. This problem is known to be NP-complete. We obtain several variations by considering different requirements as to how to compose teams of equal strength to play a tournament. We present: - A pseudo-polynomial time algorithm for k EQUAL SUM SUBSETS with k = O(1) and a proof of strong NP-completeness for k = Ω(n). - A polynomial-time algorithm under the additional requirement that the subsets should be of equal cardinality c = O(1), and a pseudo-polynomial time algorithm for the variation where the common cardinality is part of the input or not specified at all, which we proof NP-complete. - A pseudo-polynomial time algorithm for the variation where we look for two equal sum subsets such that certain pairs of numbers are not allowed to appear in the same subset. Our results are a first step towards determining the dividing lines between polynomial time solvability, pseudo-polynomial time solvability, and strong NP-completeness of subset-sum related problems; we leave an interesting set of questions that need to be answered in order to obtain the complete picture. © Springer-Verlag Berlin Heidelberg 2003.	en
heal.publisher	SPRINGER-VERLAG BERLIN	en
heal.journalName	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)	en
heal.bookName	LECTURE NOTES IN COMPUTER SCIENCE	en
dc.identifier.doi	10.1007/978-3-540-45077-1_10	en
dc.identifier.isi	ISI:000185822800010	en
dc.identifier.volume	2751	en
dc.identifier.spage	98	en
dc.identifier.epage	108	en