Succinct Data Structures for Approximating Convex Functions with Applications
نویسندگان
چکیده
We study data structures for providing ε-approximations of convex functions whose slopes are bounded from above and below by n and −n, respectively. The structures we describe have size O((1/ε) log n) and can answer queries in O(log(1/ε) + log log n) time. We also give an informationtheoretic lower-bound, that shows it is impossible to obtain structures of size O(1/ε) for approximating this class of convex functions. Finally, we show that our structures have applications to efficiently solving problems in clustering and facility location.
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