4 Search Results for "Dueholm Hansen, Thomas"


Document
ARRIVAL: Next Stop in CLS

Authors: Bernd Gärtner, Thomas Dueholm Hansen, Pavel Hubácek, Karel Král, Hagar Mosaad, and Veronika Slívová

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)


Abstract
We study the computational complexity of Arrival, a zero-player game on n-vertex switch graphs introduced by Dohrau, Gärtner, Kohler, Matousek, and Welzl. They showed that the problem of deciding termination of this game is contained in NP n coNP. Karthik C. S. recently introduced a search variant of Arrival and showed that it is in the complexity class PLS. In this work, we significantly improve the known upper bounds for both the decision and the search variants of Arrival. First, we resolve a question suggested by Dohrau et al. and show that the decision variant of Arrival is in UP n coUP. Second, we prove that the search variant of Arrival is contained in CLS. Third, we give a randomized O(1.4143^n)-time algorithm to solve both variants. Our main technical contributions are (a) an efficiently verifiable characterization of the unique witness for termination of the Arrival game, and (b) an efficient way of sampling from the state space of the game. We show that the problem of finding the unique witness is contained in CLS, whereas it was previously conjectured to be FPSPACE-complete. The efficient sampling procedure yields the first algorithm for the problem that has expected runtime O(c^n) with c<2.

Cite as

Bernd Gärtner, Thomas Dueholm Hansen, Pavel Hubácek, Karel Král, Hagar Mosaad, and Veronika Slívová. ARRIVAL: Next Stop in CLS. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 60:1-60:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{gartner_et_al:LIPIcs.ICALP.2018.60,
  author =	{G\"{a}rtner, Bernd and Hansen, Thomas Dueholm and Hub\'{a}cek, Pavel and Kr\'{a}l, Karel and Mosaad, Hagar and Sl{\'\i}vov\'{a}, Veronika},
  title =	{{ARRIVAL: Next Stop in CLS}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{60:1--60:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.60},
  URN =		{urn:nbn:de:0030-drops-90641},
  doi =		{10.4230/LIPIcs.ICALP.2018.60},
  annote =	{Keywords: CLS, switch graphs, zero-player game, UP n coUP}
}
Document
Decremental Data Structures for Connectivity and Dominators in Directed Graphs

Authors: Loukas Georgiadis, Thomas Dueholm Hansen, Giuseppe F. Italiano, Sebastian Krinninger, and Nikos Parotsidis

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)


Abstract
We introduce a new dynamic data structure for maintaining the strongly connected components (SCCs) of a directed graph (digraph) under edge deletions, so as to answer a rich repertoire of connectivity queries. Our main technical contribution is a decremental data structure that supports sensitivity queries of the form "are u and v strongly connected in the graph G \ w?", for any triple of vertices u, v, w, while G undergoes deletions of edges. Our data structure processes a sequence of edge deletions in a digraph with $n$ vertices in O(m n log n) total time and O(n^2 log n) space, where m is the number of edges before any deletion, and answers the above queries in constant time. We can leverage our data structure to obtain decremental data structures for many more types of queries within the same time and space complexity. For instance for edge-related queries, such as testing whether two query vertices u and v are strongly connected in G \ e, for some query edge e. As another important application of our decremental data structure, we provide the first nontrivial algorithm for maintaining the dominator tree of a flow graph under edge deletions. We present an algorithm that processes a sequence of edge deletions in a flow graph in O(m n log n) total time and O(n^2 log n) space. For reducible flow graphs we provide an O(mn)-time and O(m + n)-space algorithm. We give a conditional lower bound that provides evidence that these running times may be tight up to subpolynomial factors.

Cite as

Loukas Georgiadis, Thomas Dueholm Hansen, Giuseppe F. Italiano, Sebastian Krinninger, and Nikos Parotsidis. Decremental Data Structures for Connectivity and Dominators in Directed Graphs. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 42:1-42:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


Copy BibTex To Clipboard

@InProceedings{georgiadis_et_al:LIPIcs.ICALP.2017.42,
  author =	{Georgiadis, Loukas and Dueholm Hansen, Thomas and Italiano, Giuseppe F. and Krinninger, Sebastian and Parotsidis, Nikos},
  title =	{{Decremental Data Structures for Connectivity and Dominators in Directed Graphs}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{42:1--42:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.42},
  URN =		{urn:nbn:de:0030-drops-74455},
  doi =		{10.4230/LIPIcs.ICALP.2017.42},
  annote =	{Keywords: dynamic graph algorithms, decremental algorithms, dominator tree, strong connectivity under failures}
}
Document
Improved Algorithms for Computing the Cycle of Minimum Cost-to-Time Ratio in Directed Graphs

Authors: Karl Bringmann, Thomas Dueholm Hansen, and Sebastian Krinninger

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)


Abstract
We study the problem of finding the cycle of minimum cost-to-time ratio in a directed graph with n nodes and m edges. This problem has a long history in combinatorial optimization and has recently seen interesting applications in the context of quantitative verification. We focus on strongly polynomial algorithms to cover the use-case where the weights are relatively large compared to the size of the graph. Our main result is an algorithm with running time ~O(m^{3/4} n^{3/2}), which gives the first improvement over Megiddo's ~O(n^3) algorithm [JACM'83] for sparse graphs (We use the notation ~O(.) to hide factors that are polylogarithmic in n.) We further demonstrate how to obtain both an algorithm with running time n^3/2^{Omega(sqrt(log n)} on general graphs and an algorithm with running time ~O(n) on constant treewidth graphs. To obtain our main result, we develop a parallel algorithm for negative cycle detection and single-source shortest paths that might be of independent interest.

Cite as

Karl Bringmann, Thomas Dueholm Hansen, and Sebastian Krinninger. Improved Algorithms for Computing the Cycle of Minimum Cost-to-Time Ratio in Directed Graphs. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 124:1-124:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


Copy BibTex To Clipboard

@InProceedings{bringmann_et_al:LIPIcs.ICALP.2017.124,
  author =	{Bringmann, Karl and Dueholm Hansen, Thomas and Krinninger, Sebastian},
  title =	{{Improved Algorithms for Computing the Cycle of Minimum Cost-to-Time Ratio in Directed Graphs}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{124:1--124:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.124},
  URN =		{urn:nbn:de:0030-drops-74398},
  doi =		{10.4230/LIPIcs.ICALP.2017.124},
  annote =	{Keywords: quantitative verification and synthesis, parametric search, shortest paths, negative cycle detection}
}
Document
Random-Edge Is Slower Than Random-Facet on Abstract Cubes

Authors: Thomas Dueholm Hansen and Uri Zwick

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)


Abstract
Random-Edge and Random-Facet are two very natural randomized pivoting rules for the simplex algorithm. The behavior of Random-Facet is fairly well understood. It performs an expected sub-exponential number of pivoting steps on any linear program, or more generally, on any Acyclic Unique Sink Orientation (AUSO) of an arbitrary polytope, making it the fastest known pivoting rule for the simplex algorithm. The behavior of Random-Edge is much less understood. We show that in the AUSO setting, Random-Edge is slower than Random-Facet. To do that, we construct AUSOs of the n-dimensional hypercube on which Random-Edge performs an expected number of 2^{Omega(sqrt(n*log(n)))} steps. This improves on a 2^{Omega(sqrt^3(n))} lower bound of Matoušek and Szabó. As Random-Facet performs an expected number of 2^{O(sqrt(n)} steps on any n-dimensional AUSO, this established our result. Improving our 2^{Omega(sqrt(n*log(n)))} lower bound seems to require radically new techniques.

Cite as

Thomas Dueholm Hansen and Uri Zwick. Random-Edge Is Slower Than Random-Facet on Abstract Cubes. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 51:1-51:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


Copy BibTex To Clipboard

@InProceedings{hansen_et_al:LIPIcs.ICALP.2016.51,
  author =	{Hansen, Thomas Dueholm and Zwick, Uri},
  title =	{{Random-Edge Is Slower Than Random-Facet on Abstract Cubes}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{51:1--51:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.51},
  URN =		{urn:nbn:de:0030-drops-63316},
  doi =		{10.4230/LIPIcs.ICALP.2016.51},
  annote =	{Keywords: Linear programming, the Simplex Algorithm, Pivoting rules, Acyclic Unique Sink Orientations}
}
  • Refine by Author
  • 2 Dueholm Hansen, Thomas
  • 2 Hansen, Thomas Dueholm
  • 2 Krinninger, Sebastian
  • 1 Bringmann, Karl
  • 1 Georgiadis, Loukas
  • Show More...

  • Refine by Classification
  • 1 Theory of computation → Problems, reductions and completeness

  • Refine by Keyword
  • 1 Acyclic Unique Sink Orientations
  • 1 CLS
  • 1 Linear programming
  • 1 Pivoting rules
  • 1 UP n coUP
  • Show More...

  • Refine by Type
  • 4 document

  • Refine by Publication Year
  • 2 2017
  • 1 2016
  • 1 2018

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail