NDLI: An Almost Linear-Time Algorithm for the Dense Subset-Sum Problem

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Galil, Zvi Margalit, Oded
Copyright Year	1991
Abstract	This paper describes a new approach for solving the subset-sum problem. It is useful for solving other NP-hard problems. The limits and potential of this approach are discussed. The approach yields an algorithm for solving the dense version of the subset-sum problem. It runs in time $O(\ell \log \ell )$, where $\ell $ is the bound on the size of the elements. But for dense enough inputs and target numbers near the middle sum, it runs in time $O(m)$, where m is the number of elements. Consequently, it improves the previously best algorithms by at least one order of magnitude and sometimes by two. The algorithm yields a characterization of the set of subset sums as a collection of arithmetic progressions with the same difference. This characterization is derived by elementary number-theoretic and algorithmic techniques. Such a characterization was first obtained by using analytic number theory and yielded inferior algorithms.
Starting Page	1157
Ending Page	1189
Page Count	33
File Format	PDF
ISSN	00975397
DOI	10.1137/0220072
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	6
Volume Number	20
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-13
Access Restriction	Subscribed
Subject Keyword	NP-hard integer programming subset-sum Partitions of integers dense problems Permutations, words, matrices
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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