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Interval Selection in Data Streams: Weighted Intervals and the Insertion-Deletion Setting

Authors Jacques Dark, Adithya Diddapur, Christian Konrad



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Author Details

Jacques Dark
  • Unaffiliated Researcher, Cambridge, UK
Adithya Diddapur
  • School of Computer Science, University of Bristol, UK
Christian Konrad
  • School of Computer Science, University of Bristol, UK

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Jacques Dark, Adithya Diddapur, and Christian Konrad. Interval Selection in Data Streams: Weighted Intervals and the Insertion-Deletion Setting. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 24:1-24:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.FSTTCS.2023.24

Abstract

We study the Interval Selection problem in data streams: Given a stream of n intervals on the line, the objective is to compute a largest possible subset of non-overlapping intervals using O(|OPT|) space, where |OPT| is the size of an optimal solution. Previous work gave a 3/2-approximation for unit-length and a 2-approximation for arbitrary-length intervals [Emek et al., ICALP'12]. We extend this line of work to weighted intervals as well as to insertion-deletion streams. Our results include: 1) When considering weighted intervals, a (3/2+ε)-approximation can be achieved for unit intervals, but any constant factor approximation for arbitrary-length intervals requires space Ω(n). 2) In the insertion-deletion setting where intervals can both be added and deleted, we prove that, even without weights, computing a constant factor approximation for arbitrary-length intervals requires space Ω(n), whereas in the weighted unit-length intervals case a (2+ε)-approximation can be obtained. Our lower bound results are obtained via reductions to the recently introduced Chained-Index communication problem, further demonstrating the strength of this problem in the context of streaming geometric independent set problems.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
  • Theory of computation → Streaming models
Keywords
  • Streaming Algorithms
  • Interval Selection
  • Weighted Intervals
  • Insertion-deletion Streams

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References

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