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Succinct Coverage Oracles

In this paper, we identify a fundamental algorithmic problem that we term succinct dynamic covering (SDC), arising in many modern-day web applications, including ad-serving and online recommendation systems in eBay and Netflix. Roughly speaking, SDC applies two restrictions to the well-studied Max-Coverage problem: Given an integer k, X={1,2,...,n} and I={S_1, ..., S_m}, S_i a subset of X, find a subset J of I, such that |J| <= k and the union of S in J is as large as possible. The two restrictions applied by SDC are: (1) Dynamic: At query-time, we are given a query Q, a subset of X, and our goal is to find J such that the intersection of Q with the union of S in J is as large as possible; (2) Space-constrained: We don&#39;t have enough space to store (and process) the entire input; specifically, we have o(mn), and maybe as little as O((m+n)polylog(mn)) space. The goal of SDC is to maintain a small data structure so as to answer most dynamic queries with high accuracy. We call such a scheme a Coverage Oracle. We present algorithms and complexity results for coverage oracles. We present deterministic and probabilistic near-tight upper and lower bounds on the approximation ratio of S