ABSTRACT
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 such as in eBay, Netflix, and Amazon. Roughly speaking, SDC applies two restrictions to the well-studied Max-Coverage problem [14]: Given an integer k, X={1,2,...,n}and I={S_1,...,S_m}, S_i subseteq X, find |J| subseteq I, such that |J| < k and (union_S_in_J S) is as large as possible. The two restrictions applied by SDC are: (1)Dynamic: At query-time, we are given a query Q subseteq X, and our goal is to find J such that Q bigcap (union_S_J S) is as large as possible; Space-constrained: We don'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. A solution to SDC maintains a small data structure, and uses this datastructure 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 SDC as a function of the amount of space available to the oracle. Our lower bound results show that to obtain constant-factor approximations we need Omega(mn) space. Fortunately, our upper bounds present an explicit tradeoff between space and approximation ratio, allowing us to determine the amount of space needed to guarantee certain accuracy.
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Index Terms
- Dynamic covering for recommendation systems
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