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Documents authored by Stølting Brodal, Gerth

Document
DOI: 10.4230/LIPIcs.ISAAC.2017.12
A Simple Greedy Algorithm for Dynamic Graph Orientation

Authors: Edvin Berglin and Gerth Stølting Brodal

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)

Abstract
Graph orientations with low out-degree are one of several ways to efficiently store sparse graphs. If the graphs allow for insertion and deletion of edges, one may have to flip the orientation of some edges to prevent blowing up the maximum out-degree. We use arboricity as our sparsity measure. With an immensely simple greedy algorithm, we get parametrized trade-off bounds between out-degree and worst case number of flips, which previously only existed for amortized number of flips. We match the previous best worst-case algorithm (in O(log n) flips) for general arboricity and beat it for either constant or super-logarithmic arboricity. We also match a previous best amortized result for at least logarithmic arboricity, and give the first results with worst-case O(1) and O(sqrt(log n)) flips nearly matching degree bounds to their respective amortized solutions.
Cite as

Edvin Berglin and Gerth Stølting Brodal. A Simple Greedy Algorithm for Dynamic Graph Orientation. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 12:1-12:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{berglin_et_al:LIPIcs.ISAAC.2017.12,
  author =	{Berglin, Edvin and St{\o}lting Brodal, Gerth},
  title =	{{A Simple Greedy Algorithm for Dynamic Graph Orientation}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{12:1--12:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.12},
  URN =		{urn:nbn:de:0030-drops-82637},
  doi =		{10.4230/LIPIcs.ISAAC.2017.12},
  annote =	{Keywords: Dynamic graph algorithms, graph arboricity, edge orientations}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.21
Cache Oblivious Algorithms for Computing the Triplet Distance Between Trees

Authors: Gerth Stølting Brodal and Konstantinos Mampentzidis

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
We study the problem of computing the triplet distance between two rooted unordered trees with n labeled leafs. Introduced by Dobson 1975, the triplet distance is the number of leaf triples that induce different topologies in the two trees. The current theoretically best algorithm is an O(nlogn) time algorithm by Brodal et al. [SODA 2013]. Recently Jansson et al. proposed a new algorithm that, while slower in theory, requiring O(n log^3 n) time, in practice it outperforms the theoretically faster O(n log n) algorithm. Both algorithms do not scale to external memory. We present two cache oblivious algorithms that combine the best of both worlds. The first algorithm is for the case when the two input trees are binary trees and the second a generalized algorithm for two input trees of arbitrary degree. Analyzed in the RAM model, both algorithms require O(n log n) time, and in the cache oblivious model O(n/B log_{2}(n/M)) I/Os. Their relative simplicity and the fact that they scale to external memory makes them achieve the best practical performance. We note that these are the first algorithms that scale to external memory, both in theory and practice, for this problem.
Cite as

Gerth Stølting Brodal and Konstantinos Mampentzidis. Cache Oblivious Algorithms for Computing the Triplet Distance Between Trees. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{stltingbrodal_et_al:LIPIcs.ESA.2017.21,
  author =	{St{\o}lting Brodal, Gerth and Mampentzidis, Konstantinos},
  title =	{{Cache Oblivious Algorithms for Computing the Triplet Distance Between Trees}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{21:1--21:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.21},
  URN =		{urn:nbn:de:0030-drops-78820},
  doi =		{10.4230/LIPIcs.ESA.2017.21},
  annote =	{Keywords: Phylogenetic tree, tree comparison, triplet distance, cache oblivious algorithm}
}
Document
DOI: 10.4230/LIPIcs.STACS.2012.112
Cache-Oblivious Implicit Predecessor Dictionaries with the Working-Set Property

Authors: Gerth Stølting Brodal and Casper Kejlberg-Rasmussen

Published in: LIPIcs, Volume 14, 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)

Abstract
In this paper we present an implicit dynamic dictionary with the working-set property, supporting insert(e) and delete(e) in O(log n) time, predecessor(e) in O(log l_{p(e)}) time, successor(e) in O(log l_{s(e)}) time and search(e) in O(log min(l_{p(e)},l_{e}, l_{s(e)})) time, where n is the number of elements stored in the dictionary, l_{e} is the number of distinct elements searched for since element e was last searched for and p(e) and s(e) are the predecessor and successor of e, respectively. The time-bounds are all worst-case. The dictionary stores the elements in an array of size n using *no* additional space. In the cache-oblivious model the log is base B and the cache-obliviousness is due to our black box use of an existing cache-oblivious implicit dictionary. This is the first implicit dictionary supporting predecessor and successor searches in the working-set bound. Previous implicit structures required O(log n) time.
Cite as

Gerth Stølting Brodal and Casper Kejlberg-Rasmussen. Cache-Oblivious Implicit Predecessor Dictionaries with the Working-Set Property. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 112-123, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{stltingbrodal_et_al:LIPIcs.STACS.2012.112,
  author =	{St{\o}lting Brodal, Gerth and Kejlberg-Rasmussen, Casper},
  title =	{{Cache-Oblivious Implicit Predecessor Dictionaries with the Working-Set Property}},
  booktitle =	{29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
  pages =	{112--123},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-35-4},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{14},
  editor =	{D\"{u}rr, Christoph and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.112},
  URN =		{urn:nbn:de:0030-drops-34101},
  doi =		{10.4230/LIPIcs.STACS.2012.112},
  annote =	{Keywords: working-set property, dictionary, implicit, cache-oblivious, worst-case, external memory, I/O efficient}
}
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