TY - GEN

T1 - Cache-oblivious dynamic dictionaries with update/query tradeoffs

AU - Brodal, Gerth Stølting

AU - Demaine, Erik D.

AU - Fineman, Jeremy T.

AU - Iacono, John

AU - Langerman, Stefan

AU - Munro, J. Ian

PY - 2010

Y1 - 2010

N2 - Several existing cache-oblivious dynamic dictionaries achieve O(log B N) (or slightly better O(logB N/M)) memory transfers per operation, where N is the number of items stored, M is the memory size, and B is the block size, which matches the classic B-tree data structure. One recent structure achieves the same query bound and a sometimes-better amortized update bound of O (1/Bθ(1/log log B)2) logB N + 1/B log2 N) memory transfers. This paper presents a new data structure, the xDict, implementing predecessor queries in O(1/ε logB N/M) worst-case memory transfers and insertions and deletions in O (1/εB 1-ε logB N/M) amortized memory transfers, for any constant ε with 0 < ε < 1. For example, the xDict achieves subconstant amortized update cost when N = M B°(B1-ε), whereas the B-tree's Θ(logB N/M) is subconstant only when N = o(MB), and the previously obtained Θ (1/BΘ(1/(log log B)2) logB N + 1/B log2 N) is subconstant only when N = o(2√B). The xDict attains the optimal tradeoff between insertions and queries, even in the broader external-memory model, for the range where inserts cost between Ω(1/B lg1+ε N) and O(1/lg3 N) memory transfers.

AB - Several existing cache-oblivious dynamic dictionaries achieve O(log B N) (or slightly better O(logB N/M)) memory transfers per operation, where N is the number of items stored, M is the memory size, and B is the block size, which matches the classic B-tree data structure. One recent structure achieves the same query bound and a sometimes-better amortized update bound of O (1/Bθ(1/log log B)2) logB N + 1/B log2 N) memory transfers. This paper presents a new data structure, the xDict, implementing predecessor queries in O(1/ε logB N/M) worst-case memory transfers and insertions and deletions in O (1/εB 1-ε logB N/M) amortized memory transfers, for any constant ε with 0 < ε < 1. For example, the xDict achieves subconstant amortized update cost when N = M B°(B1-ε), whereas the B-tree's Θ(logB N/M) is subconstant only when N = o(MB), and the previously obtained Θ (1/BΘ(1/(log log B)2) logB N + 1/B log2 N) is subconstant only when N = o(2√B). The xDict attains the optimal tradeoff between insertions and queries, even in the broader external-memory model, for the range where inserts cost between Ω(1/B lg1+ε N) and O(1/lg3 N) memory transfers.

UR - http://www.scopus.com/inward/record.url?scp=77951676777&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951676777&partnerID=8YFLogxK

U2 - 10.1137/1.9781611973075.117

DO - 10.1137/1.9781611973075.117

M3 - Conference contribution

AN - SCOPUS:77951676777

SN - 9780898717013

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1448

EP - 1456

BT - Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms

PB - Association for Computing Machinery (ACM)

T2 - 21st Annual ACM-SIAM Symposium on Discrete Algorithms

Y2 - 17 January 2010 through 19 January 2010

ER -