eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-12
24:1
24:17
10.4230/LIPIcs.FSTTCS.2023.24
article
Interval Selection in Data Streams: Weighted Intervals and the Insertion-Deletion Setting
Dark, Jacques
1
Diddapur, Adithya
2
Konrad, Christian
2
https://orcid.org/0000-0003-1802-4011
Unaffiliated Researcher, Cambridge, UK
School of Computer Science, University of Bristol, UK
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol284-fsttcs2023/LIPIcs.FSTTCS.2023.24/LIPIcs.FSTTCS.2023.24.pdf
Streaming Algorithms
Interval Selection
Weighted Intervals
Insertion-deletion Streams