2 Search Results for "Nowicki, Krzysztof"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.42
Fully-Dynamic α + 2 Arboricity Decompositions and Implicit Colouring

Authors: Aleksander B. G. Christiansen and Eva Rotenberg

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
The arboricity α of a graph is the smallest number of forests necessary to cover its edges, and an arboricity decomposition of a graph is a decomposition of its edges into forests. The best near-linear time algorithm for arboricity decomposition guarantees at most α +2 forests if the graph has arboricity α (Blumenstock and Fischer [Markus Blumenstock and Frank Fischer, 2020]). In this paper, we study arboricity decomposition for dynamic graphs, that is, graphs that are subject to insertions and deletions of edges. We give an algorithm that, provided the arboricity of the dynamic graph never exceeds α, maintains an α+2 arboricity decomposition of the graph in poly(log n,α) update time, thus matching the number of forests currently obtainable in near-linear time for static (non-changing) graphs. Our construction goes via dynamic bounded out-degree orientations, and we present a fully-dynamic algorithm that explicitly orients the edges of the dynamic graph, such that no vertex has an out-degree exceeding ⌊ (1+ε)α ⌋ + 2. Our algorithm is deterministic and has a worst-case update time of O(ε^{-6}α² log³ n). The state-of-the-art explicit, deterministic, worst-case algorithm for bounded out-degree orientations maintains a β⋅ α + log_β n out-orientation in O(β²α²+βαlog_β n) time [Tsvi Kopelowitz et al., 2014]. As a consequence, we get an algorithm that maintains an implicit vertex colouring with 4⋅ 2^α colours, in amortised poly-log n update time, and with O(α log n) worst-case query time. Thus, at the expense of log n-factors in the update time, we improve on the number of colours from 2^O(α) to O(2^α) compared to the state-of-the-art for implicit dynamic colouring [Monika Henzinger et al., 2020].
Cite as

Aleksander B. G. Christiansen and Eva Rotenberg. Fully-Dynamic α + 2 Arboricity Decompositions and Implicit Colouring. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 42:1-42:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{christiansen_et_al:LIPIcs.ICALP.2022.42,
  author =	{Christiansen, Aleksander B. G. and Rotenberg, Eva},
  title =	{{Fully-Dynamic \alpha + 2 Arboricity Decompositions and Implicit Colouring}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{42:1--42:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.42},
  URN =		{urn:nbn:de:0030-drops-163835},
  doi =		{10.4230/LIPIcs.ICALP.2022.42},
  annote =	{Keywords: Dynamic graphs, bounded arboricity, graph colouring, data structures}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2017.54
Brief Announcement: On Connectivity in the Broadcast Congested Clique

Authors: Tomasz Jurdzínski and Krzysztof Nowicki

Published in: LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

Abstract
Recently, very fast deterministic and randomized algorithms have been obtained for connectivity and minimum spanning tree in the unicast congested clique. In contrast, no solution faster than a simple parallel implementation of the Boruvka's algorithm has been known for both problems in the broadcast congested clique. In this announcement, we present the first sub-logarithmic deterministic algorithm for connected components in the broadcast congested clique.
Cite as

Tomasz Jurdzínski and Krzysztof Nowicki. Brief Announcement: On Connectivity in the Broadcast Congested Clique. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 54:1-54:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{jurdzinski_et_al:LIPIcs.DISC.2017.54,
  author =	{Jurdz{\'\i}nski, Tomasz and Nowicki, Krzysztof},
  title =	{{Brief Announcement: On Connectivity in the Broadcast Congested Clique}},
  booktitle =	{31st International Symposium on Distributed Computing (DISC 2017)},
  pages =	{54:1--54:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-053-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{91},
  editor =	{Richa, Andr\'{e}a},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.54},
  URN =		{urn:nbn:de:0030-drops-79903},
  doi =		{10.4230/LIPIcs.DISC.2017.54},
  annote =	{Keywords: congested clique, broadcast, connected components, bandwidth}
}
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