-
Upload Video
videos in mp4/mov/flv
close
Upload video
Note: publisher must agree to add uploaded document -
Upload Slides
slides or other attachment
close
Upload Slides
Note: publisher must agree to add uploaded document -
Feedback
help us improve
close
Feedback
Please help us improve your experience by sending us a comment, question or concern
Please help transcribe this video using our simple transcription tool. You need to be logged in to do so.
Description
In this paper we show how the complexity of performing nearest neighbor (NNS) search on a metric space is related to the expansion of the metric space. Given a metric space we look at the graph obtained by connecting every pair of points within a certain distance $r$ . We then look at various notions of expansion in this graph relating them to the cell probe complexity of NNS for randomized and deterministic, exact and approximate algorithms. For example if the graph has node expansion $Phi$ then we show that any deterministic $t$-probe data structure for $n$ points must use space $S$ where $(St/n)^t > Phi$. We show similar results for randomized algorithms as well. These relationships can be used to derive most of the known lower bounds in the well known metric spaces such as $l_1$, $l_2$, $l_infty$ by simply computing their expansion. In the process, we strengthen and generalize our previous results~cite{PTW08}. Additionally, we unify the approach in~cite{PTW08} and the communication complexity based approach. Our work reduces the problem of proving cell probe lower bounds of near neighbor search to computing the appropriate expansion paramete