TY - GEN
T1 - An almost linear-time algorithm for the dense subset-sum problem
AU - Galil, Zvi
AU - Margalit, Oded
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1991.
PY - 1991/1/1
Y1 - 1991/1/1
N2 - This paper describes a new approach for solving a large subproblem of the subset-sum problem. It is useful for solving other NP-hard integer programming problems. The limits and potential of this approach are investigated. The approach yields an algorithm for solving the dense version of the subset-sum problem. It runs in time O(l log l), where l 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.
AB - This paper describes a new approach for solving a large subproblem of the subset-sum problem. It is useful for solving other NP-hard integer programming problems. The limits and potential of this approach are investigated. The approach yields an algorithm for solving the dense version of the subset-sum problem. It runs in time O(l log l), where l 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.
UR - http://www.scopus.com/inward/record.url?scp=84982306730&partnerID=8YFLogxK
U2 - 10.1007/3-540-54233-7_177
DO - 10.1007/3-540-54233-7_177
M3 - Conference contribution
AN - SCOPUS:84982306730
SN - 9783540542339
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 719
EP - 727
BT - Automata, Languages and Programming - 18th International Colloquium, Proceedings
A2 - Albert, Javier Leach
A2 - Artalejo, Mario Rodriguez
A2 - Monien, Burkhard
PB - Springer Verlag
T2 - 18th International Colloqulum on Automata, Languages, and Programming, ICALP 1991
Y2 - 8 July 1991 through 12 July 1991
ER -