Results 1 
5 of
5
Lower Bound Techniques for Data Structures
, 2008
"... We describe new techniques for proving lower bounds on datastructure problems, with the following broad consequences:
â¢ the first Î©(lgn) lower bound for any dynamic problem, improving on a bound that had been standing since 1989;
â¢ for static data structures, the first separation between linea ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
We describe new techniques for proving lower bounds on datastructure problems, with the following broad consequences:
â¢ the first Î©(lgn) lower bound for any dynamic problem, improving on a bound that had been standing since 1989;
â¢ for static data structures, the first separation between linear and polynomial space. Specifically, for some problems that have constant query time when polynomial space is allowed, we can show Î©(lg n/ lg lg n) bounds when the space is O(n Â· polylog n).
Using these techniques, we analyze a variety of central datastructure problems, and obtain improved lower bounds for the following:
â¢ the partialsums problem (a fundamental application of augmented binary search trees);
â¢ the predecessor problem (which is equivalent to IP lookup in Internet routers);
â¢ dynamic trees and dynamic connectivity;
â¢ orthogonal range stabbing;
â¢ orthogonal range counting, and orthogonal range reporting;
â¢ the partial match problem (searching with wildcards);
â¢ (1 + Îµ)approximate near neighbor on the hypercube;
â¢ approximate nearest neighbor in the lâ metric.
Our new techniques lead to surprisingly nontechnical proofs. For several problems, we obtain simpler proofs for bounds that were already known.
Web www.itu.dk Generalized static orthogonal range searching in less space
, 2003
"... less space ..."
(Show Context)
Ph.D. thesis
"... Data structures for orthogonal intersection searching and other problems ..."
(Show Context)
(Really) Tight bounds for dispatching binary
"... Abstract. We consider binary dispatching problem originating from object oriented programming. We want to preprocess a hierarchy of classes and collection of methods so that given a function call in the runtime we are able to retrieve the most specialized implementation which can be invoked with t ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We consider binary dispatching problem originating from object oriented programming. We want to preprocess a hierarchy of classes and collection of methods so that given a function call in the runtime we are able to retrieve the most specialized implementation which can be invoked with the actual types of the arguments. This problem has been thoroughly studied for the case of mono dispatching [7,4], where the methods take just one argument, resulting in (expected) O(log logm) query time after just linear preprocessing. For the binary dispatching, where the methods take exactly two arguments, logarithmic query time is possible [5], even if the structure is allowed to take linear space [1]. Unfortunately, constructing such structure requires as much as (expected) Θ(m(log logm)2) time [1,9]. Using a different idea we are able to construct in (deterministic) linear time and space a structure allowing dispatching binary methods in the same logarithmic time. Then we show how to improve the query time to just O ( logm log logm), which is easily seen to be optimal as a consequence of some already known lower bounds if we want to keep the size of the resulting structure close to linear. Keywords: method dispatching, persistent data structures, rectangle geometry 1