The general subset sum problem is NP-complete. However, there are two algorithms, one due to Brickell and the other to Lagarias and Odlyzko, which in polynomial time solve almost all subset sum problems of sufficiently low density. Both methods rely on basis reduction algorithms to find short non-zero vectors in special lattices. The Lagarias-Odlyzko algorithm would solve almost all subset sum problems of density < 0.6463 … in polynomial time if it could invoke a polynomial-time algorithm for finding the shortest non-zero vector in a lattice. This note shows that a simple modification of that algorithm would solve almost all problems of density < 0.9408 … if it could find shortest non-zero vectors in lattices. This modification also yields dramatic improvements in practice when it is combined with known lattice basis reduction algorithms.
|Original language||English (US)|
|Title of host publication||Advances in Cryptology—EUROCRYPT 1991 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings|
|Editors||Donald W. Davies|
|Number of pages||14|
|State||Published - 1991|
|Event||Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1991 - Brighton, United Kingdom|
Duration: Apr 8 1991 → Apr 11 1991
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Other||Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1991|
|Period||4/8/91 → 4/11/91|
Bibliographical notePublisher Copyright:
© Springer-Verlag Berlin Heidelberg 1991.