Subset sum problem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Subset sum problem" in English language version.

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mathscinet.ams.org

Garey, Michael R.; Johnson, David S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. Series of Books in the Mathematical Sciences (1st ed.). New York: W. H. Freeman and Company. ISBN 9780716710455. MR 0519066. OCLC 247570676., Section 3.1 and problem SP1 in Appendix A.3.1.
Horowitz, Ellis; Sahni, Sartaj (1974). "Computing partitions with applications to the knapsack problem" (PDF). Journal of the Association for Computing Machinery. 21 (2): 277–292. doi:10.1145/321812.321823. hdl:1813/5989. MR 0354006. S2CID 16866858. Archived (PDF) from the original on 2022-10-09.
Pisinger, David (1999). "Linear time algorithms for knapsack problems with bounded weights". Journal of Algorithms. 33 (1): 1–14. doi:10.1006/jagm.1999.1034. MR 1712690.

archive.org

Kleinberg, Jon; Tardos, Éva (2006). Algorithm Design (2nd ed.). p. 491. ISBN 0-321-37291-3.
Filmus, Yuval (30 January 2016). Answer to: "Is there a known, fast algorithm for counting all subsets that sum to below a certain number?". Theoretical Computer Science Stack Exchange. Note that Filmus' citation in support of the claim (Faliszewski, Piotr; Hemaspaandra, Lane (2009). "The complexity of power-index comparison". Theoretical Computer Science. Elsevier. 410: 101-107. DOI 10.1016/j.tcs.2008.09.034) does not in fact prove the claim, instead directing readers to another citation (Papadimitriou, Christos (1994). Computational Complexity. Addison-Wesley: Reading, MA. Chapter 9. ISBN 0-201-53082-1 — via the Internet Archive), which does not explicitly prove the claim either. Papadimitriou's proof that SSP is NP-complete via reduction of 3SAT does, however, generalize to a reduction from #3SAT to #SSP.

arxiv.org

Koiliaris, Konstantinos; Xu, Chao (2015-07-08). "A Faster Pseudopolynomial Time Algorithm for Subset Sum". arXiv:1507.02318 [cs.DS].
Bringmann, Karl (2017). "A near-linear pseudopolynomial time algorithm for subset sum". In Klein, Philip N. (ed.). Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017). SIAM. pp. 1073–1084. arXiv:1610.04712. doi:10.1137/1.9781611974782.69.

books.google.com

Hans Kellerer; Ulrich Pferschy; David Pisinger (2004). Knapsack problems. Springer. p. 97. ISBN 9783540402862.

cornell.edu

ecommons.cornell.edu

Horowitz, Ellis; Sahni, Sartaj (1974). "Computing partitions with applications to the knapsack problem" (PDF). Journal of the Association for Computing Machinery. 21 (2): 277–292. doi:10.1145/321812.321823. hdl:1813/5989. MR 0354006. S2CID 16866858. Archived (PDF) from the original on 2022-10-09.

doi.org

Horowitz, Ellis; Sahni, Sartaj (1974). "Computing partitions with applications to the knapsack problem" (PDF). Journal of the Association for Computing Machinery. 21 (2): 277–292. doi:10.1145/321812.321823. hdl:1813/5989. MR 0354006. S2CID 16866858. Archived (PDF) from the original on 2022-10-09.
Schroeppel, Richard; Shamir, Adi (1981-08-01). "A $T = O (2 n /2)$ , $S = O (2 n /4)$ algorithm for certain NP-complete problems". SIAM Journal on Computing. 10 (3): 456–464. doi:10.1137/0210033. ISSN 0097-5397.
Howgrave-Graham, Nick; Joux, Antoine (2010). "New Generic Algorithms for Hard Knapsacks". In Gilbert, Henri (ed.). Advances in Cryptology – EUROCRYPT 2010. Lecture Notes in Computer Science. Vol. 6110. Berlin, Heidelberg: Springer. pp. 235–256. doi:10.1007/978-3-642-13190-5_12. ISBN 978-3-642-13190-5.
Becker, Anja; Coron, Jean-Sébastien; Joux, Antoine (2011). "Improved Generic Algorithms for Hard Knapsacks". In Patterson, Kenneth (ed.). Advances in Cryptology – EUROCRYPT 2011. Lecture Notes in Computer Science. Vol. 6632. Berlin, Heidelberg: Springer. pp. 364–385. doi:10.1007/978-3-642-20465-4_21. ISBN 978-3-642-20465-4.
Bonnetain, Xavier; Bricout, Rémi; Schrottenloher, André; Shen, Yixin (2020). "Improved Classical and Quantum Algorithms for Subset-Sum". In Moriai, Shiho; Wang, Huaxiong (eds.). Advances in Cryptology - ASIACRYPT 2020. Lecture Notes in Computer Science. Vol. 12492. Berlin, Heidelberg: Springer. pp. 633–666. doi:10.1007/978-3-030-64834-3_22. ISBN 978-3-030-64833-6.
Pisinger, David (1999). "Linear time algorithms for knapsack problems with bounded weights". Journal of Algorithms. 33 (1): 1–14. doi:10.1006/jagm.1999.1034. MR 1712690.
Bringmann, Karl (2017). "A near-linear pseudopolynomial time algorithm for subset sum". In Klein, Philip N. (ed.). Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017). SIAM. pp. 1073–1084. arXiv:1610.04712. doi:10.1137/1.9781611974782.69.
Curtis, V. V.; Sanches, C. A. A. (January 2016). "An efficient solution to the subset-sum problem on GPU: An efficient solution to the subset-sum problem on GPU". Concurrency and Computation: Practice and Experience. 28 (1): 95–113. doi:10.1002/cpe.3636. S2CID 20927927.
Curtis, V. V.; Sanches, C. A. A. (July 2017). "A low-space algorithm for the subset-sum problem on GPU". Computers & Operations Research. 83: 120–124. doi:10.1016/j.cor.2017.02.006.
Caprara, Alberto; Kellerer, Hans; Pferschy, Ulrich (2000-02-01). "The Multiple Subset Sum Problem". SIAM Journal on Optimization. 11 (2): 308–319. doi:10.1137/S1052623498348481. ISSN 1052-6234.
Kellerer, Hans; Mansini, Renata; Pferschy, Ulrich; Speranza, Maria Grazia (2003-03-01). "An efficient fully polynomial approximation scheme for the Subset-Sum Problem". Journal of Computer and System Sciences. 66 (2): 349–370. doi:10.1016/S0022-0000(03)00006-0. ISSN 0022-0000.

dx.doi.org

Filmus, Yuval (30 January 2016). Answer to: "Is there a known, fast algorithm for counting all subsets that sum to below a certain number?". Theoretical Computer Science Stack Exchange. Note that Filmus' citation in support of the claim (Faliszewski, Piotr; Hemaspaandra, Lane (2009). "The complexity of power-index comparison". Theoretical Computer Science. Elsevier. 410: 101-107. DOI 10.1016/j.tcs.2008.09.034) does not in fact prove the claim, instead directing readers to another citation (Papadimitriou, Christos (1994). Computational Complexity. Addison-Wesley: Reading, MA. Chapter 9. ISBN 0-201-53082-1 — via the Internet Archive), which does not explicitly prove the claim either. Papadimitriou's proof that SSP is NP-complete via reduction of 3SAT does, however, generalize to a reduction from #3SAT to #SSP.

ghostarchive.org

Goodrich, Michael. "More NP complete and NP hard problems" (PDF). Archived (PDF) from the original on 2022-10-09.
Richard E. Korf, Ethan L. Schreiber, and Michael D. Moffitt (2014). "Optimal Sequential Multi-Way Number Partitioning" (PDF). Archived (PDF) from the original on 2022-10-09.{{cite web}}: CS1 maint: multiple names: authors list (link)
Horowitz, Ellis; Sahni, Sartaj (1974). "Computing partitions with applications to the knapsack problem" (PDF). Journal of the Association for Computing Machinery. 21 (2): 277–292. doi:10.1145/321812.321823. hdl:1813/5989. MR 0354006. S2CID 16866858. Archived (PDF) from the original on 2022-10-09.
"The Two-Sum Problem" (PDF). Archived (PDF) from the original on 2022-10-09.

handle.net

hdl.handle.net

Horowitz, Ellis; Sahni, Sartaj (1974). "Computing partitions with applications to the knapsack problem" (PDF). Journal of the Association for Computing Machinery. 21 (2): 277–292. doi:10.1145/321812.321823. hdl:1813/5989. MR 0354006. S2CID 16866858. Archived (PDF) from the original on 2022-10-09.

semanticscholar.org

api.semanticscholar.org

Horowitz, Ellis; Sahni, Sartaj (1974). "Computing partitions with applications to the knapsack problem" (PDF). Journal of the Association for Computing Machinery. 21 (2): 277–292. doi:10.1145/321812.321823. hdl:1813/5989. MR 0354006. S2CID 16866858. Archived (PDF) from the original on 2022-10-09.
Curtis, V. V.; Sanches, C. A. A. (January 2016). "An efficient solution to the subset-sum problem on GPU: An efficient solution to the subset-sum problem on GPU". Concurrency and Computation: Practice and Experience. 28 (1): 95–113. doi:10.1002/cpe.3636. S2CID 20927927.

siam.org

epubs.siam.org

Schroeppel, Richard; Shamir, Adi (1981-08-01). "A $T = O (2 n /2)$ , $S = O (2 n /4)$ algorithm for certain NP-complete problems". SIAM Journal on Computing. 10 (3): 456–464. doi:10.1137/0210033. ISSN 0097-5397.

stackexchange.com

cs.stackexchange.com

Filmus, Yuval (30 January 2016). Answer to: "Is there a known, fast algorithm for counting all subsets that sum to below a certain number?". Theoretical Computer Science Stack Exchange. Note that Filmus' citation in support of the claim (Faliszewski, Piotr; Hemaspaandra, Lane (2009). "The complexity of power-index comparison". Theoretical Computer Science. Elsevier. 410: 101-107. DOI 10.1016/j.tcs.2008.09.034) does not in fact prove the claim, instead directing readers to another citation (Papadimitriou, Christos (1994). Computational Complexity. Addison-Wesley: Reading, MA. Chapter 9. ISBN 0-201-53082-1 — via the Internet Archive), which does not explicitly prove the claim either. Papadimitriou's proof that SSP is NP-complete via reduction of 3SAT does, however, generalize to a reduction from #3SAT to #SSP.

uci.edu

ics.uci.edu

Goodrich, Michael. "More NP complete and NP hard problems" (PDF). Archived (PDF) from the original on 2022-10-09.

uic.edu

cs.uic.edu

Richard E. Korf, Ethan L. Schreiber, and Michael D. Moffitt (2014). "Optimal Sequential Multi-Way Number Partitioning" (PDF). Archived (PDF) from the original on 2022-10-09.{{cite web}}: CS1 maint: multiple names: authors list (link)

www3.cs.uic.edu

"The Two-Sum Problem" (PDF). Archived (PDF) from the original on 2022-10-09.

worldcat.org

search.worldcat.org

Garey, Michael R.; Johnson, David S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. Series of Books in the Mathematical Sciences (1st ed.). New York: W. H. Freeman and Company. ISBN 9780716710455. MR 0519066. OCLC 247570676., Section 3.1 and problem SP1 in Appendix A.3.1.
Schroeppel, Richard; Shamir, Adi (1981-08-01). "A $T = O (2 n /2)$ , $S = O (2 n /4)$ algorithm for certain NP-complete problems". SIAM Journal on Computing. 10 (3): 456–464. doi:10.1137/0210033. ISSN 0097-5397.
Caprara, Alberto; Kellerer, Hans; Pferschy, Ulrich (2000-02-01). "The Multiple Subset Sum Problem". SIAM Journal on Optimization. 11 (2): 308–319. doi:10.1137/S1052623498348481. ISSN 1052-6234.
Kellerer, Hans; Mansini, Renata; Pferschy, Ulrich; Speranza, Maria Grazia (2003-03-01). "An efficient fully polynomial approximation scheme for the Subset-Sum Problem". Journal of Computer and System Sciences. 66 (2): 349–370. doi:10.1016/S0022-0000(03)00006-0. ISSN 0022-0000.