Abstract
We study classes of Dynamic Programming (DP) algorithms which, due to their algebraic definitions, are closely related to coefficient extraction methods. DP algorithms can easily be modified to exploit sparseness in the DP table through memorization. Coefficient extraction techniques on the other hand are both space-efficient and parallelisable, but no tools have been available to exploit sparseness. We investigate the systematic use of homomorphic hash functions to combine the best of these methods and obtain improved space-efficient algorithms for problems including LINEAR SAT, SET PARTITION and SUBSET SUM. Our algorithms run in time proportional to the number of nonzero entries of the last segment of the DP table, which presents a strict improvement over sparse DP. The last property also gives an improved algorithm for CNF SAT and SET COVER with sparse projections.
| Original language | English |
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| Title of host publication | Parameterized and Exact Computation (7th International Symposium, IPEC 2012, Ljubljana, Slovenia, September 12-14, 2012. Proceedings) |
| Editors | D. Thilikos, G.J. Woeginger |
| Place of Publication | Berlin |
| Publisher | Springer |
| Pages | 147-158 |
| ISBN (Print) | 978-3-642-33292-0 |
| DOIs | |
| Publication status | Published - 2012 |
| Externally published | Yes |
| Event | 7th International Symposium on Parameterized and Exact Computation, IPEC 2012 - Ljubljana, Slovenia Duration: 12 Sep 2012 → 14 Sep 2012 Conference number: 7 http://ipec2012.isoftcloud.gr |
Publication series
| Name | Lecture Notes in Computer Science |
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| Volume | 7535 |
| ISSN (Print) | 0302-9743 |
Conference
| Conference | 7th International Symposium on Parameterized and Exact Computation, IPEC 2012 |
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| Abbreviated title | IPEC 2012 |
| Country/Territory | Slovenia |
| City | Ljubljana |
| Period | 12/09/12 → 14/09/12 |
| Internet address |