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Recent years have seen a significant increase in our understanding of high-dimensional nearest neighbor search (NNS) for distances like the lscr1 and lscr2 norms. By contrast, our understanding of the lscrinfin norm is now where it was (exactly) 10 years ago. In FOCSpsila98, Indyk proved the following unorthodox result: there is a data structure (in fact, a decision tree) of size O(nrho), for any...
Two decision problems are presented that arise from reversing the operation of a distance-based indexing tree. Whereas similarity search finds points in the tree given a query point, reverse similarity search begins with a set of constraints like those defining a leaf and generates a point meeting the constraints. These problems derive from robust hashing, a technique used in similarity search and...
The bugbear of model checking is the explosion in the number of states as the number of processes increases. Industrial-sized problems are often intractable for model checkers. We modify the most popular model checker in use today, SPIN, by replacing its internal verification search engine by a guided, random-walk based simulator. The resulting tool is called RANSPIN. The guiding mechanism used in...
We establish new lower bounds on the complexity of several searching problems. We show that the time for solving the partial sum problem on n points in d dimensions is at least proportional to (log n/log 2m/n)d-1 in both the worst and average cases; m denotes the amount of storage used. This bound is provably tight for m = Ω(nlogcn) and any c ≫ d- 1. We also prove a lower bound of Ω(n(log n/log log...
We introduce a new technique for solving problems of the following form: preprocess a set of objects so that those satisfying a given property with respect to a query object can be listed very effectively. Among well-known problems to fall into this category we find range query, point enclosure, intersection, near-neighbor problems, etc. The approach which we take is very general and rests on a new...
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