The 43rd Annual IEEE Symposium on Foundations of Computer Science (FOCS'02) Implicit B-Trees: New Results for the Dictionary Problem Vancouver, BC, Canada November 16-November 19 ISBN: 0-7695-1822-2
We reopen the issue of finding an implicit data structure for the dictionary problem. In particular, we examine the problem of maintaining n data values in the first n locations of an array in such a way that we can efficiently perform the operations insert, delete and search. No information other than n and the data is to be retained; and the only operations which we may perform on the data values (other than reads and writes) are comparisons. Our structure supports these operations in 0(\log ^2 n/\log \log n) time, marking the first improvement on the problem since the mid 1980?s. En route we develop a number of space efficient techniques for handling segments of a large array in a memory hierarchy. We achieve a cost of 0(\log _B n) block transfers like in regular B-trees, under the realistic assumption that a block stores B = \Omega (\log n) keys, so that reporting r consecutive keys in sorted order has a cost of 0(\log _B n + {r \mathord{\left/ {\vphantom {r B}} \right. \kern-\nulldelimiterspace} B}) block transfers. Being implicit, our B-tree occupies exactly \left\lceil {{\raise0.7ex\hbox{$n$} \!\mathord{\left/ {\vphantom n B}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$B$}}} \right\rceil blocks after each update.
Citation:
Gianni Franceschini, Roberto Grossi, J. Ian Munro, Linda Pagli, "Implicit B-Trees: New Results for the Dictionary Problem," focs, pp.145, The 43rd Annual IEEE Symposium on Foundations of Computer Science (FOCS'02), 2002 Usage of this product signifies your acceptance of the Terms of Use. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||