TY - GEN
T1 - Improved explicit data structures in the bitprobe model
AU - Lewenstein, Moshe
AU - Munro, J. Ian
AU - Nicholson, Patrick K.
AU - Raman, Venkatesh
N1 - Funding Information: This work was supported in part by NSERC, the Canada Research Chairs program, a David Cheriton Scholarship, and a Derick Wood Graduate Scholarship.
PY - 2014
Y1 - 2014
N2 - Buhrman et al. [SICOMP 2002] studied the membership problem in the bitprobe model, presenting both randomized and deterministic schemes for storing a set of size n from a universe of size m such that membership queries on the set can be answered using t bit probes. Since then, there have been several papers focusing on deterministic schemes, especially for the first non-trivial case when n=2. The most recent, due to Radhakrishnan, Shah, and Shannigrahi [ESA 2010], describes non-explicit schemes (existential results) for t≥3 using probabilistic arguments. We describe a fully explicit scheme for n=2 that matches their space bound of Θ(m 2/5) bits for t=3 and, furthermore, improves upon it for t>3, answering their open problem. Our structure (consisting of query and storage algorithms) manipulates blocks of bits of the query element in a novel way that may be of independent interest. We also describe recursive schemes for n≥3 that improve upon all previous fully explicit schemes for a wide range of parameters.
AB - Buhrman et al. [SICOMP 2002] studied the membership problem in the bitprobe model, presenting both randomized and deterministic schemes for storing a set of size n from a universe of size m such that membership queries on the set can be answered using t bit probes. Since then, there have been several papers focusing on deterministic schemes, especially for the first non-trivial case when n=2. The most recent, due to Radhakrishnan, Shah, and Shannigrahi [ESA 2010], describes non-explicit schemes (existential results) for t≥3 using probabilistic arguments. We describe a fully explicit scheme for n=2 that matches their space bound of Θ(m 2/5) bits for t=3 and, furthermore, improves upon it for t>3, answering their open problem. Our structure (consisting of query and storage algorithms) manipulates blocks of bits of the query element in a novel way that may be of independent interest. We also describe recursive schemes for n≥3 that improve upon all previous fully explicit schemes for a wide range of parameters.
UR - http://www.scopus.com/inward/record.url?scp=84958539453&partnerID=8YFLogxK
U2 - 10.1007/978-3-662-44777-2_52
DO - 10.1007/978-3-662-44777-2_52
M3 - منشور من مؤتمر
SN - 9783662447765
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 630
EP - 641
BT - Algorithms, ESA 2014 - 22nd Annual European Symposium, Proceedings
PB - Springer Verlag
T2 - 22nd Annual European Symposium on Algorithms, ESA 2014
Y2 - 8 September 2014 through 10 September 2014
ER -