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Parameterized Dynamic Data Structure for Split Completion

Authors Konrad Majewski , Michał Pilipczuk , Anna Zych-Pawlewicz

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ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Data structures design and analysis
Keywords
  • parameterized complexity
  • dynamic data structures
  • split graphs

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Abstract

We design a randomized data structure that, for a fully dynamic graph G updated by edge insertions and deletions and integers k, d fixed upon initialization, maintains the answer to the Split Completion problem: whether one can add k edges to G to obtain a split graph. The data structure can be initialized on an edgeless n-vertex graph in time n ⋅ (k d ⋅ log n)^{𝒪(1)}, and the amortized time complexity of an update is 5^k ⋅ (k d ⋅ log n)^{𝒪(1)}. The answer provided by the data structure is correct with probability 1-𝒪(n^{-d}).

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Konrad Majewski, Michał Pilipczuk, and Anna Zych-Pawlewicz. Parameterized Dynamic Data Structure for Split Completion. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 87:1-87:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ESA.2024.87

Author Details

Konrad Majewski
  • Institute of Informatics, University of Warsaw, Poland
Michał Pilipczuk
  • Institute of Informatics, University of Warsaw, Poland
Anna Zych-Pawlewicz
  • Institute of Informatics, University of Warsaw, Poland

Funding

This work is a part of project BOBR that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 948057).

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