Lokshtanov, D., Misra, P., Panolan, F. et al. (3 more authors) (2024) Meta-theorems for Parameterized Streaming Algorithms. In: Proceedings of ACM-SIAM Symposium on Discrete Algorithms (SODA24). ACM-SIAM Symposium on Discrete Algorithms (SODA24), 07-10 Jan 2024, Alexandria, Virginia, USA. Society for Industrial and Applied Mathematics (SIAM) , Philadelphia, PA , pp. 712-739. ISBN 978-1-61197-791-2
Abstract
The streaming model was introduced to parameterized complexity independently by Fafianie and Kratsch[MFCS14] and by Chitnis, Cormode, Hajiaghayi and Monemizadeh [SODA15]. Subsequently, it was broadened by Chitnis, Cormode, Esfandiari, Hajiaghayi and Monemizadeh [SPAA15] and by Chitnis, Cormode, Esfandiari, Hajiaghayi, McGregor, Monemizadeh and Vorotnikova [SODA16]. Despite its strong motivation, the applicability of the streaming model to central problems in parameterized complexity has remained, for almost a decade, quite limited. Indeed, due to simple Ω(n)-space lower bounds for many of these problems, the k⁰⁽¹⁾·polylog(n)-spacerequirement in the model is too strict.
Thus, we explore semi-streaming algorithms for parameterized graph problems, and present the first systematic study of this topic. Crucially, we aim to construct succinct representations of the input on which optimal post-processing time complexity can be achieved.
•We devise meta-theorems specifically designed for parameterized streaming and demonstrate their applicability by obtaining the first k⁰⁽¹⁾·n·polylog(n)-space streaming algorithms for well-studied problems such as Feedback Vertex Set on Tournaments,Cluster Vertex Deletion,Proper Interval Vertex DeletionandBlock Vertex Deletion. In the process, we demonstrate a fundamental connection between semi-streaming algorithms for recognizing graphs in a graph class H and semi-streaming algorithms for the problem of vertex deletion intoH.
•We present an algorithmic machinery for obtaining streaming algorithms for cut problems and exemplify this by giving the first k⁰⁽¹⁾·n·polylog(n)-space streaming algorithms for Graph Bipartitization, Multiway Cut and Subset Feedback Vertex Set
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 01 Nov 2023 11:02 |
Last Modified: | 18 Mar 2024 13:29 |
Published Version: | https://epubs.siam.org/doi/10.1137/1.9781611977912... |
Status: | Published |
Publisher: | Society for Industrial and Applied Mathematics (SIAM) |
Identification Number: | 10.1137/1.9781611977912.28 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:204783 |