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Documents authored by Setzer, Alexander

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Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management
DOI: 10.4230/LIPIcs.ICALP.2019.150
On the Complexity of Local Graph Transformations

Authors: Christian Scheideler and Alexander Setzer

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
We consider the problem of transforming a given graph G_s into a desired graph G_t by applying a minimum number of primitives from a particular set of local graph transformation primitives. These primitives are local in the sense that each node can apply them based on local knowledge and by affecting only its 1-neighborhood. Although the specific set of primitives we consider makes it possible to transform any (weakly) connected graph into any other (weakly) connected graph consisting of the same nodes, they cannot disconnect the graph or introduce new nodes into the graph, making them ideal in the context of supervised overlay network transformations. We prove that computing a minimum sequence of primitive applications (even centralized) for arbitrary G_s and G_t is NP-hard, which we conjecture to hold for any set of local graph transformation primitives satisfying the aforementioned properties. On the other hand, we show that this problem admits a polynomial time algorithm with a constant approximation ratio.
Cite as

Christian Scheideler and Alexander Setzer. On the Complexity of Local Graph Transformations. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 150:1-150:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{scheideler_et_al:LIPIcs.ICALP.2019.150,
  author =	{Scheideler, Christian and Setzer, Alexander},
  title =	{{On the Complexity of Local Graph Transformations}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{150:1--150:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.150},
  URN =		{urn:nbn:de:0030-drops-107266},
  doi =		{10.4230/LIPIcs.ICALP.2019.150},
  annote =	{Keywords: Graphs transformations, NP-hardness, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2015.24
Towards Establishing Monotonic Searchability in Self-Stabilizing Data Structures

Authors: Christian Scheideler, Alexander Setzer, and Thim Strothmann

Published in: LIPIcs, Volume 46, 19th International Conference on Principles of Distributed Systems (OPODIS 2015)

Abstract
Distributed applications are commonly based on overlay networks interconnecting their sites so that they can exchange information. For these overlay networks to preserve their functionality, they should be able to recover from various problems like membership changes or faults. Various self-stabilizing overlay networks have already been proposed in recent years, which have the advantage of being able to recover from any illegal state, but none of these networks can give any guarantees on its functionality while the recovery process is going on. We initiate research on overlay networks that are not only self-stabilizing but that also ensure that searchability is maintained while the recovery process is going on, as long as there are no corrupted messages in the system. More precisely, once a search message from node u to another node v is successfully delivered, all future search messages from u to v succeed as well. We call this property monotonic searchability. We show that in general it is impossible to provide monotonic searchability if corrupted messages are present in the system, which justifies the restriction to system states without corrupted messages. Furthermore, we provide a self-stabilizing protocol for the line for which we can also show monotonic searchability. It turns out that even for the line it is non-trivial to achieve this property. Additionally, we extend our protocol to deal with node departures in terms of the Finite Departure Problem of Foreback et al. (SSS 2014). This makes our protocol even capable of handling node dynamics.
Cite as

Christian Scheideler, Alexander Setzer, and Thim Strothmann. Towards Establishing Monotonic Searchability in Self-Stabilizing Data Structures. In 19th International Conference on Principles of Distributed Systems (OPODIS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 46, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{scheideler_et_al:LIPIcs.OPODIS.2015.24,
  author =	{Scheideler, Christian and Setzer, Alexander and Strothmann, Thim},
  title =	{{Towards Establishing Monotonic Searchability in Self-Stabilizing Data Structures}},
  booktitle =	{19th International Conference on Principles of Distributed Systems (OPODIS 2015)},
  pages =	{24:1--24:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-98-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{46},
  editor =	{Anceaume, Emmanuelle and Cachin, Christian and Potop-Butucaru, Maria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2015.24},
  URN =		{urn:nbn:de:0030-drops-66135},
  doi =		{10.4230/LIPIcs.OPODIS.2015.24},
  annote =	{Keywords: Topological Self-Stabilization, Monotonic Searchability, Node Departures}
}
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