Succinct Coverage Oracles
Ioannis Antonellis, Anish Das Sarma, Shaddin Dughmi

TL;DR
This paper introduces the succinct dynamic covering problem, a space-efficient approach to approximate maximum coverage in dynamic, space-constrained settings, with algorithms and bounds for coverage oracles.
Contribution
It formulates the SDC problem, analyzes the space-approximation tradeoff, and provides algorithms with near-tight bounds for coverage oracles under space constraints.
Findings
Lower bounds show constant-factor approximations need Omega(mn) space
Upper bounds provide explicit space-approximation tradeoffs
Algorithms achieve high accuracy with limited space
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 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'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…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Data Management and Algorithms · Optimization and Search Problems
