Homomorphic hashing for sparse coefficient extraction

Authors:
Petteri Kaski;Mikko Koivisto;Jesper Nederlof
Affiliations:
Helsinki Institute for Information Technology HIIT, Department of Information and Computer Science, Aalto University, Finland;Helsinki Institute for Information Technology HIIT, Department of Computer Science, University of Helsinki, Finland;Utrecht University, Utrecht, The Netherlands
Venue:
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Year:
2012

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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.