Diverse near neighbor problem
Author(s)Abbar, Sofiane; Amer-Yahia, Sihem; Indyk, Piotr; Mahabadi, Sepideh; Varadarajan, Kasturi R.
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Motivated by the recent research on diversity-aware search, we investigate the k-diverse near neighbor reporting problem. The problem is defined as follows: given a query point q, report the maximum diversity set S of k points in the ball of radius r around q. The diversity of a set S is measured by the minimum distance between any pair of points in $S$ (the higher, the better). We present two approximation algorithms for the case where the points live in a d-dimensional Hamming space. Our algorithms guarantee query times that are sub-linear in n and only polynomial in the diversity parameter k, as well as the dimension d. For low values of k, our algorithms achieve sub-linear query times even if the number of points within distance r from a query $q$ is linear in $n$. To the best of our knowledge, these are the first known algorithms of this type that offer provable guarantees.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Proceedings of the 29th annual symposium on Symposuim on computational geometry (SoCG '13)
Association for Computing Machinery (ACM)
Sofiane Abbar, Sihem Amer-Yahia, Piotr Indyk, Sepideh Mahabadi, and Kasturi R. Varadarajan. 2013. Diverse near neighbor problem. In Proceedings of the twenty-ninth annual symposium on Computational geometry (SoCG '13). ACM, New York, NY, USA, 207-214.
Author's final manuscript