期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2003
卷号：2003
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：We consider the approximate nearest neighbour search problem on the Hamming Cube \b d . We show that a randomised cell probe algorithm that uses polynomial storage and word size d O (1) requires a worst case query time of ( log log d log log log d ) . The approximation factor may be as loose as 2 log 1 − d for any fixed 0"> 0 . This generalises an earlier result on the deterministic complexity of the same problem and, more importantly, fills a major gap in the study of this problem since all earlier lower bounds either did not allow randomisation or did not allow approximation. We also give a cell probe algorithm which proves that our lower bound is optimal. Our proof uses a lower bound on the round complexity of the related communication problem. We show, additionally, that considerations of bit complexity alone cannot prove any nontrivial cell probe lower bound for the problem. This shows that the Richness Technique used in a lot of recent research around this problem would not have helped here. Our proof is based on information theoretic techniques for communication complexity, a theme that has been prominent in recent research. In particular, we make heavy use of the round elimination and message compression ideas in the recent work of Sen and Jain, Radhakrishnan, and Sen, and also introduce a new technique which we call message switching.
关键词：cell probe , Communication complexity , information theory , lower bounds , nearest neighbor
( log log d 
