
Separating Adaptive Streaming from Oblivious Streaming
We present a streaming problem for which every adversariallyrobust stre...
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A Quantum Advantage for a Natural Streaming Problem
Data streaming, in which a large dataset is received as a "stream" of up...
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Approximate Convex Hull of Data Streams
Given a finite set of points P ⊆R^d, we would like to find a small subse...
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Small Space Stream Summary for Matroid Center
In the matroid center problem, which generalizes the kcenter problem, w...
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The Partition Spanning Forest Problem
Given a set of colored points in the plane, we ask if there exists a cro...
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An Efficient SemiStreaming PTAS for Tournament Feedback ArcSet with Few Passes
We present the first semistreaming PTAS for the minimum feedback arc se...
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Adaptive Deep Forest for Online Learning from Drifting Data Streams
Learning from data streams is among the most vital fields of contemporar...
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Streaming Algorithms for Geometric Steiner Forest
We consider a natural generalization of the Steiner tree problem, the Steiner forest problem, in the Euclidean plane: the input is a multiset X ⊆ℝ^2, partitioned into k color classes C_1, C_2, …, C_k ⊆ X. The goal is to find a minimumcost Euclidean graph G such that every color class C_i is connected in G. We study this Steiner forest problem in the streaming setting, where the stream consists of insertions and deletions of points to X. Each input point x∈ X arrives with its color 𝖼𝗈𝗅𝗈𝗋(x) ∈ [k], and as usual for dynamic geometric streams, the input points are restricted to the discrete grid {0, …, Δ}^2. We design a singlepass streaming algorithm that uses poly(k ·logΔ) space and time, and estimates the cost of an optimal Steiner forest solution within ratio arbitrarily close to the famous Euclidean Steiner ratio α_2 (currently 1.1547 ≤α_2 ≤ 1.214). Our approach relies on a novel combination of streaming techniques, like sampling and linear sketching, with the classical dynamicprogramming framework for geometric optimization problems, which usually requires large memory and has so far not been applied in the streaming setting. We complement our streaming algorithm for the Steiner forest problem with simple arguments showing that any finite approximation requires Ω(k) bits of space. In addition, our approximation ratio is currently the best even for streaming Steiner tree, i.e., k=1.
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