20 Search Results for "Aj�b�d�, George O."

Document
Invited Talk
DOI: 10.4230/LIPIcs.MFCS.2023.5
Sliding into the Future: Investigating Sliding Windows in Temporal Graphs (Invited Talk)

Authors: Nina Klobas, George B. Mertzios, and Paul G. Spirakis

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
Graphs are fundamental tools for modelling relations among objects in various scientific fields. However, traditional static graphs have limitations when it comes to capturing the dynamic nature of real-world systems. To overcome this limitation, temporal graphs have been introduced as a framework to model graphs that change over time. In temporal graphs the edges among vertices appear and disappear at specific time steps, reflecting the temporal dynamics of the observed system, which allows us to analyse time dependent patterns and processes. In this paper we focus on the research related to sliding time windows in temporal graphs. Sliding time windows offer a way to analyse specific time intervals within the lifespan of a temporal graph. By sliding the window along the timeline, we can examine the graph’s characteristics and properties within different time periods. This paper provides an overview of the research on sliding time windows in temporal graphs. Although progress has been made in this field, there are still many interesting questions and challenges to be explored. We discuss some of the open problems and highlight their potential for future research.
Cite as

Nina Klobas, George B. Mertzios, and Paul G. Spirakis. Sliding into the Future: Investigating Sliding Windows in Temporal Graphs (Invited Talk). In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 5:1-5:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{klobas_et_al:LIPIcs.MFCS.2023.5,
  author =	{Klobas, Nina and Mertzios, George B. and Spirakis, Paul G.},
  title =	{{Sliding into the Future: Investigating Sliding Windows in Temporal Graphs}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{5:1--5:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.5},
  URN =		{urn:nbn:de:0030-drops-185397},
  doi =		{10.4230/LIPIcs.MFCS.2023.5},
  annote =	{Keywords: Temporal Graphs, Sliding Time Windows}
}
Document
DOI: 10.4230/DagRep.12.6.1
Theories of Programming (Dagstuhl Seminar 22231)

Authors: Thomas D. LaToza, Amy Ko, David C. Shepherd, Dag Sjøberg, and Benjamin Xie

Published in: Dagstuhl Reports, Volume 12, Issue 6 (2023)

Abstract
Much of computer science research focuses on techniques to make programming easier, better, less error prone, more powerful, and even more just. But rarely do we try to explain any of these challenges. Why is programming hard? Why is it slow? Why is it error prone? Why is it powerful? How does it do harm? These why and how questions are what motivated the Dagstuhl Seminar 22231 on Theories of Programming. This seminar brought together 28 CS researchers from domains most concerned with programming human and social activities: software engineering, programming languages, human-computer interaction, and computing education. Together, we sketched new theories of programming and considered the role of theories more broadly in programming.
Cite as

Thomas D. LaToza, Amy Ko, David C. Shepherd, Dag Sjøberg, and Benjamin Xie. Theories of Programming (Dagstuhl Seminar 22231). In Dagstuhl Reports, Volume 12, Issue 6, pp. 1-13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{latoza_et_al:DagRep.12.6.1,
  author =	{LaToza, Thomas D. and Ko, Amy and Shepherd, David C. and Sj{\o}berg, Dag and Xie, Benjamin},
  title =	{{Theories of Programming (Dagstuhl Seminar 22231)}},
  pages =	{1--13},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{12},
  number =	{6},
  editor =	{LaToza, Thomas D. and Ko, Amy and Shepherd, David C. and Sj{\o}berg, Dag and Xie, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.12.6.1},
  URN =		{urn:nbn:de:0030-drops-174533},
  doi =		{10.4230/DagRep.12.6.1},
  annote =	{Keywords: computing education, human-computer interaction, programming languages, software engineering, theories of programming}
}
Document
DOI: 10.4230/DagRep.12.1.1
Mobility Data Science (Dagstuhl Seminar 22021)

Authors: Mohamed Mokbel, Mahmoud Sakr, Li Xiong, Andreas Züfle, Jussara Almeida, Taylor Anderson, Walid Aref, Gennady Andrienko, Natalia Andrienko, Yang Cao, Sanjay Chawla, Reynold Cheng, Panos Chrysanthis, Xiqi Fei, Gabriel Ghinita, Anita Graser, Dimitrios Gunopulos, Christian Jensen, Joon-Sook Kim, Kyoung-Sook Kim, Peer Kröger, John Krumm, Johannes Lauer, Amr Magdy, Mario Nascimento, Siva Ravada, Matthias Renz, Dimitris Sacharidis, Cyrus Shahabi, Flora Salim, Mohamed Sarwat, Maxime Schoemans, Bettina Speckmann, Egemen Tanin, Yannis Theodoridis, Kristian Torp, Goce Trajcevski, Marc van Kreveld, Carola Wenk, Martin Werner, Raymond Wong, Song Wu, Jianqiu Xu, Moustafa Youssef, Demetris Zeinalipour, Mengxuan Zhang, and Esteban Zimányi

Published in: Dagstuhl Reports, Volume 12, Issue 1 (2022)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 22021 "Mobility Data Science". This seminar was held January 9-14, 2022, including 47 participants from industry and academia. The goal of this Dagstuhl Seminar was to create a new research community of mobility data science in which the whole is greater than the sum of its parts by bringing together established leaders as well as promising young researchers from all fields related to mobility data science. Specifically, this report summarizes the main results of the seminar by (1) defining Mobility Data Science as a research domain, (2) by sketching its agenda in the coming years, and by (3) building a mobility data science community. (1) Mobility data science is defined as spatiotemporal data that additionally captures the behavior of moving entities (human, vehicle, animal, etc.). To understand, explain, and predict behavior, we note that a strong collaboration with research in behavioral and social sciences is needed. (2) Future research directions for mobility data science described in this report include a) mobility data acquisition and privacy, b) mobility data management and analysis, and c) applications of mobility data science. (3) We identify opportunities towards building a mobility data science community, towards collaborations between academic and industry, and towards a mobility data science curriculum.
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Mohamed Mokbel, Mahmoud Sakr, Li Xiong, Andreas Züfle, Jussara Almeida, Taylor Anderson, Walid Aref, Gennady Andrienko, Natalia Andrienko, Yang Cao, Sanjay Chawla, Reynold Cheng, Panos Chrysanthis, Xiqi Fei, Gabriel Ghinita, Anita Graser, Dimitrios Gunopulos, Christian Jensen, Joon-Sook Kim, Kyoung-Sook Kim, Peer Kröger, John Krumm, Johannes Lauer, Amr Magdy, Mario Nascimento, Siva Ravada, Matthias Renz, Dimitris Sacharidis, Cyrus Shahabi, Flora Salim, Mohamed Sarwat, Maxime Schoemans, Bettina Speckmann, Egemen Tanin, Yannis Theodoridis, Kristian Torp, Goce Trajcevski, Marc van Kreveld, Carola Wenk, Martin Werner, Raymond Wong, Song Wu, Jianqiu Xu, Moustafa Youssef, Demetris Zeinalipour, Mengxuan Zhang, and Esteban Zimányi. Mobility Data Science (Dagstuhl Seminar 22021). In Dagstuhl Reports, Volume 12, Issue 1, pp. 1-34, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Article{mokbel_et_al:DagRep.12.1.1,
  author =	{Mokbel, Mohamed and Sakr, Mahmoud and Xiong, Li and Z\"{u}fle, Andreas and Almeida, Jussara and Anderson, Taylor and Aref, Walid and Andrienko, Gennady and Andrienko, Natalia and Cao, Yang and Chawla, Sanjay and Cheng, Reynold and Chrysanthis, Panos and Fei, Xiqi and Ghinita, Gabriel and Graser, Anita and Gunopulos, Dimitrios and Jensen, Christian and Kim, Joon-Sook and Kim, Kyoung-Sook and Kr\"{o}ger, Peer and Krumm, John and Lauer, Johannes and Magdy, Amr and Nascimento, Mario and Ravada, Siva and Renz, Matthias and Sacharidis, Dimitris and Shahabi, Cyrus and Salim, Flora and Sarwat, Mohamed and Schoemans, Maxime and Speckmann, Bettina and Tanin, Egemen and Theodoridis, Yannis and Torp, Kristian and Trajcevski, Goce and van Kreveld, Marc and Wenk, Carola and Werner, Martin and Wong, Raymond and Wu, Song and Xu, Jianqiu and Youssef, Moustafa and Zeinalipour, Demetris and Zhang, Mengxuan and Zim\'{a}nyi, Esteban},
  title =	{{Mobility Data Science (Dagstuhl Seminar 22021)}},
  pages =	{1--34},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2022},
  volume =	{12},
  number =	{1},
  editor =	{Mokbel, Mohamed and Sakr, Mahmoud and Xiong, Li and Z\"{u}fle, Andreas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.12.1.1},
  URN =		{urn:nbn:de:0030-drops-169190},
  doi =		{10.4230/DagRep.12.1.1},
  annote =	{Keywords: Spatio-temporal, Tracking, Privacy, Behavior, Data cleaning, Data management, Analytics}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.24
Reconstructing Decision Trees

Authors: Guy Blanc, Jane Lange, and Li-Yang Tan

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

Abstract
We give the first reconstruction algorithm for decision trees: given queries to a function f that is opt-close to a size-s decision tree, our algorithm provides query access to a decision tree T where: - T has size S := s^O((log s)²/ε³); - dist(f,T) ≤ O(opt)+ε; - Every query to T is answered with poly((log s)/ε)⋅ log n queries to f and in poly((log s)/ε)⋅ n log n time. This yields a tolerant tester that distinguishes functions that are close to size-s decision trees from those that are far from size-S decision trees. The polylogarithmic dependence on s in the efficiency of our tester is exponentially smaller than that of existing testers. Since decision tree complexity is well known to be related to numerous other boolean function properties, our results also provide a new algorithm for reconstructing and testing these properties.
Cite as

Guy Blanc, Jane Lange, and Li-Yang Tan. Reconstructing Decision Trees. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{blanc_et_al:LIPIcs.ICALP.2022.24,
  author =	{Blanc, Guy and Lange, Jane and Tan, Li-Yang},
  title =	{{Reconstructing Decision Trees}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{24:1--24:17},
  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.2022.24},
  URN =		{urn:nbn:de:0030-drops-163653},
  doi =		{10.4230/LIPIcs.ICALP.2022.24},
  annote =	{Keywords: Property reconstruction, property testing, tolerant testing, decision trees}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2021.4
Covariant Conversions (CoCo): A Design Pattern for Type-Safe Modular Software Evolution in Object-Oriented Systems

Authors: Jan Bessai, George T. Heineman, and Boris Düdder

Published in: LIPIcs, Volume 194, 35th European Conference on Object-Oriented Programming (ECOOP 2021)

Abstract
Software evolution is an essential challenge for all software engineers, typically addressed solely using code versioning systems and language-specific code analysis tools. Most versioning systems view the evolution of a system as a directed acyclic graph of steps, with independent branches that could be merged. What these systems fail to provide is the ability to ensure stable APIs or that each subsequent evolution represents a cohesive extension yielding a valid system. Modular software evolution ensures that APIs remain stable, which is achieved by ensuring that only additional methods, fields, and data types are added, while treating existing modules through blackbox interfaces. Even with these restrictions, it must be possible to add new variations, fields, and methods without extensive duplication of prior module code. In contrast to most literature, our focus is on ensuring modular software evolution using mainstream object-oriented programming languages, instead of resorting to novel language extensions. We present a novel CoCo design pattern that supports type-safe covariantly overridden convert methods to transform earlier data type instances into their newest evolutionary representation to access operations that had been added later. CoCo supports both binary methods and producer methods. We validate and contrast our approach using a well-known compiler construction case study that other researchers have also investigated for modular evolution. Our resulting implementation relies on less boilerplate code, is completely type-safe, and allows clients to use normal object-oriented calling conventions. We also compare CoCo with existing approaches to the Expression Problem. We conclude by discussing how CoCo could change the direction of currently proposed Java language extensions to support closed-world assumptions about data types, as borrowed from functional programming.
Cite as

Jan Bessai, George T. Heineman, and Boris Düdder. Covariant Conversions (CoCo): A Design Pattern for Type-Safe Modular Software Evolution in Object-Oriented Systems. In 35th European Conference on Object-Oriented Programming (ECOOP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 194, pp. 4:1-4:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bessai_et_al:LIPIcs.ECOOP.2021.4,
  author =	{Bessai, Jan and Heineman, George T. and D\"{u}dder, Boris},
  title =	{{Covariant Conversions (CoCo): A Design Pattern for Type-Safe Modular Software Evolution in Object-Oriented Systems}},
  booktitle =	{35th European Conference on Object-Oriented Programming (ECOOP 2021)},
  pages =	{4:1--4:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-190-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{194},
  editor =	{M{\o}ller, Anders and Sridharan, Manu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2021.4},
  URN =		{urn:nbn:de:0030-drops-140476},
  doi =		{10.4230/LIPIcs.ECOOP.2021.4},
  annote =	{Keywords: Expression problem, software evolution, type safety, producer method, binary method}
}
Document
DOI: 10.4230/LIPIcs.DISC.2020.9
Spread of Information and Diseases via Random Walks in Sparse Graphs

Authors: George Giakkoupis, Hayk Saribekyan, and Thomas Sauerwald

Published in: LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)

Abstract
We consider a natural network diffusion process, modeling the spread of information or infectious diseases. Multiple mobile agents perform independent simple random walks on an n-vertex connected graph G. The number of agents is linear in n and the walks start from the stationary distribution. Initially, a single vertex has a piece of information (or a virus). An agent becomes informed (or infected) the first time it visits some vertex with the information (or virus); thereafter, the agent informs (infects) all vertices it visits. Giakkoupis et al. [George Giakkoupis et al., 2019] have shown that the spreading time, i.e., the time before all vertices are informed, is asymptotically and w.h.p. the same as in the well-studied randomized rumor spreading process, on any d-regular graph with d = Ω(log n). The case of sub-logarithmic degree was left open, and is the main focus of this paper. First, we observe that the equivalence shown in [George Giakkoupis et al., 2019] does not hold for small d: We give an example of a 3-regular graph with logarithmic diameter for which the expected spreading time is Ω(log² n/log log n), whereas randomized rumor spreading is completed in time Θ(log n), w.h.p. Next, we show a general upper bound of Õ(d ⋅ diam(G) + log³ n /d), w.h.p., for the spreading time on any d-regular graph. We also provide a version of the bound based on the average degree, for non-regular graphs. Next, we give tight analyses for specific graph families. We show that the spreading time is O(log n), w.h.p., for constant-degree regular expanders. For the binary tree, we show an upper bound of O(log n⋅ log log n), w.h.p., and prove that this is tight, by giving a matching lower bound for the cover time of the tree by n random walks. Finally, we show a bound of O(diam(G)), w.h.p., for k-dimensional grids (k ≥ 1 is constant), by adapting a technique by Kesten and Sidoravicius [Kesten and Sidoravicius, 2003; Kesten and Sidoravicius, 2005].
Cite as

George Giakkoupis, Hayk Saribekyan, and Thomas Sauerwald. Spread of Information and Diseases via Random Walks in Sparse Graphs. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{giakkoupis_et_al:LIPIcs.DISC.2020.9,
  author =	{Giakkoupis, George and Saribekyan, Hayk and Sauerwald, Thomas},
  title =	{{Spread of Information and Diseases via Random Walks in Sparse Graphs}},
  booktitle =	{34th International Symposium on Distributed Computing (DISC 2020)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-168-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{179},
  editor =	{Attiya, Hagit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.9},
  URN =		{urn:nbn:de:0030-drops-130873},
  doi =		{10.4230/LIPIcs.DISC.2020.9},
  annote =	{Keywords: parallel random walks, information dissemination, infectious diseases}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.27
Exact and Approximate Algorithms for Computing a Second Hamiltonian Cycle

Authors: Argyrios Deligkas, George B. Mertzios, Paul G. Spirakis, and Viktor Zamaraev

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
In this paper we consider the following total functional problem: Given a cubic Hamiltonian graph G and a Hamiltonian cycle C₀ of G, how can we compute a second Hamiltonian cycle C₁ ≠ C₀ of G? Cedric Smith and William Tutte proved in 1946, using a non-constructive parity argument, that such a second Hamiltonian cycle always exists. Our main result is a deterministic algorithm which computes the second Hamiltonian cycle in O(n⋅2^0.299862744n) = O(1.23103ⁿ) time and in linear space, thus improving the state of the art running time of O*(2^0.3n) = O(1.2312ⁿ) for solving this problem (among deterministic algorithms running in polynomial space). Whenever the input graph G does not contain any induced cycle C₆ on 6 vertices, the running time becomes O(n⋅ 2^0.2971925n) = O(1.22876ⁿ). Our algorithm is based on a fundamental structural property of Thomason’s lollipop algorithm, which we prove here for the first time. In the direction of approximating the length of a second cycle in a (not necessarily cubic) Hamiltonian graph G with a given Hamiltonian cycle C₀ (where we may not have guarantees on the existence of a second Hamiltonian cycle), we provide a linear-time algorithm computing a second cycle with length at least n - 4α (√n+2α)+8, where α = (Δ-2)/(δ-2) and δ,Δ are the minimum and the maximum degree of the graph, respectively. This approximation result also improves the state of the art.
Cite as

Argyrios Deligkas, George B. Mertzios, Paul G. Spirakis, and Viktor Zamaraev. Exact and Approximate Algorithms for Computing a Second Hamiltonian Cycle. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 27:1-27:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{deligkas_et_al:LIPIcs.MFCS.2020.27,
  author =	{Deligkas, Argyrios and Mertzios, George B. and Spirakis, Paul G. and Zamaraev, Viktor},
  title =	{{Exact and Approximate Algorithms for Computing a Second Hamiltonian Cycle}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{27:1--27:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.27},
  URN =		{urn:nbn:de:0030-drops-126953},
  doi =		{10.4230/LIPIcs.MFCS.2020.27},
  annote =	{Keywords: Hamiltonian cycle, cubic graph, exact algorithm, approximation algorithm}
}
Document
Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management
DOI: 10.4230/LIPIcs.ICALP.2019.131
How Fast Can We Reach a Target Vertex in Stochastic Temporal Graphs?

Authors: Eleni C. Akrida, George B. Mertzios, Sotiris Nikoletseas, Christoforos Raptopoulos, Paul G. Spirakis, and Viktor Zamaraev

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

Abstract
Temporal graphs are used to abstractly model real-life networks that are inherently dynamic in nature, in the sense that the network structure undergoes discrete changes over time. Given a static underlying graph G=(V,E), a temporal graph on G is a sequence of snapshots {G_t=(V,E_t) subseteq G: t in N}, one for each time step t >= 1. In this paper we study stochastic temporal graphs, i.e. stochastic processes G={G_t subseteq G: t in N} whose random variables are the snapshots of a temporal graph on G. A natural feature of stochastic temporal graphs which can be observed in various real-life scenarios is a memory effect in the appearance probabilities of particular edges; that is, the probability an edge e in E appears at time step t depends on its appearance (or absence) at the previous k steps. In this paper we study the hierarchy of models memory-k, k >= 0, which address this memory effect in an edge-centric network evolution: every edge of G has its own probability distribution for its appearance over time, independently of all other edges. Clearly, for every k >= 1, memory-(k-1) is a special case of memory-k. However, in this paper we make a clear distinction between the values k=0 ("no memory") and k >= 1 ("some memory"), as in some cases these models exhibit a fundamentally different computational behavior for these values of k, as our results indicate. For every k >= 0 we investigate the computational complexity of two naturally related, but fundamentally different, temporal path (or journey) problems: {Minimum Arrival} and {Best Policy}. In the first problem we are looking for the expected arrival time of a foremost journey between two designated vertices {s},{y}. In the second one we are looking for the expected arrival time of the best policy for actually choosing a particular {s}-{y} journey. We present a detailed investigation of the computational landscape of both problems for the different values of memory k. Among other results we prove that, surprisingly, {Minimum Arrival} is strictly harder than {Best Policy}; in fact, for k=0, {Minimum Arrival} is #P-hard while {Best Policy} is solvable in O(n^2) time.
Cite as

Eleni C. Akrida, George B. Mertzios, Sotiris Nikoletseas, Christoforos Raptopoulos, Paul G. Spirakis, and Viktor Zamaraev. How Fast Can We Reach a Target Vertex in Stochastic Temporal Graphs?. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 131:1-131:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{akrida_et_al:LIPIcs.ICALP.2019.131,
  author =	{Akrida, Eleni C. and Mertzios, George B. and Nikoletseas, Sotiris and Raptopoulos, Christoforos and Spirakis, Paul G. and Zamaraev, Viktor},
  title =	{{How Fast Can We Reach a Target Vertex in Stochastic Temporal Graphs?}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{131:1--131:14},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.131},
  URN =		{urn:nbn:de:0030-drops-107071},
  doi =		{10.4230/LIPIcs.ICALP.2019.131},
  annote =	{Keywords: Temporal network, stochastic temporal graph, temporal path, #P-hard problem, polynomial-time approximation scheme}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.46
The Power of Linear-Time Data Reduction for Maximum Matching

Authors: George B. Mertzios, André Nichterlein, and Rolf Niedermeier

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
Finding maximum-cardinality matchings in undirected graphs is arguably one of the most central graph primitives. For m-edge and n-vertex graphs, it is well-known to be solvable in O(m\sqrt{n}) time; however, for several applications this running time is still too slow. We investigate how linear-time (and almost linear-time) data reduction (used as preprocessing) can alleviate the situation. More specifically, we focus on linear-time kernelization. We start a deeper and systematic study both for general graphs and for bipartite graphs. Our data reduction algorithms easily comply (in form of preprocessing) with every solution strategy (exact, approximate, heuristic), thus making them attractive in various settings.
Cite as

George B. Mertzios, André Nichterlein, and Rolf Niedermeier. The Power of Linear-Time Data Reduction for Maximum Matching. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 46:1-46:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{mertzios_et_al:LIPIcs.MFCS.2017.46,
  author =	{Mertzios, George B. and Nichterlein, Andr\'{e} and Niedermeier, Rolf},
  title =	{{The Power of Linear-Time Data Reduction for Maximum Matching}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{46:1--46:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.46},
  URN =		{urn:nbn:de:0030-drops-81166},
  doi =		{10.4230/LIPIcs.MFCS.2017.46},
  annote =	{Keywords: Maximum-cardinality matching, bipartite graphs, linear-time algorithms, kernelization, parameterized complexity analysis, FPT in P}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.136
On the Transformation Capability of Feasible Mechanisms for Programmable Matter

Authors: Othon Michail, George Skretas, and Paul G. Spirakis

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

Abstract
In this work, we study theoretical models of programmable matter systems. The systems under consideration consist of spherical modules, kept together by magnetic forces and able to perform two minimal mechanical operations (or movements): rotate around a neighbor and slide over a line. In terms of modeling, there are n nodes arranged in a 2-dimensional grid and forming some initial shape. The goal is for the initial shape A to transform to some target shape B by a sequence of movements. Most of the paper focuses on transformability questions, meaning whether it is in principle feasible to transform a given shape to another. We first consider the case in which only rotation is available to the nodes. Our main result is that deciding whether two given shapes A and B can be transformed to each other is in P. We then insist on rotation only and impose the restriction that the nodes must maintain global connectivity throughout the transformation. We prove that the corresponding transformability question is in PSPACE and study the problem of determining the minimum seeds that can make feasible otherwise infeasible transformations. Next we allow both rotations and slidings and prove universality: any two connected shapes A,B of the same number of nodes, can be transformed to each other without breaking connectivity. The worst-case number of movements of the generic strategy is Theta(n^2). We improve this to O(n) parallel time, by a pipelining strategy, and prove optimality of both by matching lower bounds. We next turn our attention to distributed transformations. The nodes are now distributed processes able to perform communicate-compute-move rounds. We provide distributed algorithms for a general type of transformation.
Cite as

Othon Michail, George Skretas, and Paul G. Spirakis. On the Transformation Capability of Feasible Mechanisms for Programmable Matter. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 136:1-136:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{michail_et_al:LIPIcs.ICALP.2017.136,
  author =	{Michail, Othon and Skretas, George and Spirakis, Paul G.},
  title =	{{On the Transformation Capability of Feasible Mechanisms for Programmable Matter}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{136:1--136:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.136},
  URN =		{urn:nbn:de:0030-drops-74341},
  doi =		{10.4230/LIPIcs.ICALP.2017.136},
  annote =	{Keywords: programmable matter, transformation, reconfigurable robotics, shape formation, complexity, distributed algorithms}
}
Document
DOI: 10.4230/OASIcs.CMN.2016.14
Appraisal of Computational Model for Yorùbá Folktale Narrative

Authors: O. Deborah Ninan, George O. Ajíbádé, and Odetunji A. Odéjobí

Published in: OASIcs, Volume 53, 7th Workshop on Computational Models of Narrative (CMN 2016)

Abstract
Our effort at developing computational models for African narratives, particularly those of Yorùbá folktales, is challenged by the diversity in concepts and methodologies in the discipline. This motivated us to pause and consider the various computational models of narratives in the literature. This is with a view to finding the most appropriate or otherwise adapt a closely related one for the purpose. Thorndyke's story grammar was among the models of narrative in the literature which were appraised, found close in structure and was adapted for the modelling of Yorùbá folktales narrative. In conclusion we found that the modified version of Thorndyke's model was appropriate for modelling Yorùbá folktales narrative.
Cite as

O. Deborah Ninan, George O. Ajíbádé, and Odetunji A. Odéjobí. Appraisal of Computational Model for Yorùbá Folktale Narrative. In 7th Workshop on Computational Models of Narrative (CMN 2016). Open Access Series in Informatics (OASIcs), Volume 53, pp. 14:1-14:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{ninan_et_al:OASIcs.CMN.2016.14,
  author =	{Ninan, O. Deborah and Aj{\'\i}b\'{a}d\'{e}, George O. and Od\'{e}job{\'\i}, Odetunji A.},
  title =	{{Appraisal of Computational Model for Yor\`{u}b\'{a} Folktale Narrative}},
  booktitle =	{7th Workshop on Computational Models of Narrative (CMN 2016)},
  pages =	{14:1--14:11},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-020-0},
  ISSN =	{2190-6807},
  year =	{2016},
  volume =	{53},
  editor =	{Miller, Ben and Lieto, Antonio and Ronfard, R\'{e}mi and Ware, Stephen G. and Finlayson, Mark A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.CMN.2016.14},
  URN =		{urn:nbn:de:0030-drops-67158},
  doi =		{10.4230/OASIcs.CMN.2016.14},
  annote =	{Keywords: Computational, Modelling, Grammar, Folktales, Yor\`{u}b\'{a}}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2016.6
The Densest k-Subhypergraph Problem

Authors: Eden Chlamtac, Michael Dinitz, Christian Konrad, Guy Kortsarz, and George Rabanca

Published in: LIPIcs, Volume 60, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)

Abstract
The Densest k-Subgraph (DkS) problem, and its corresponding minimization problem Smallest p-Edge Subgraph (SpES), have come to play a central role in approximation algorithms. This is due both to their practical importance, and their usefulness as a tool for solving and establishing approximation bounds for other problems. These two problems are not well understood, and it is widely believed that they do not an admit a subpolynomial approximation ratio (although the best known hardness results do not rule this out). In this paper we generalize both DkS and SpES from graphs to hypergraphs. We consider the Densest k-Subhypergraph problem (given a hypergraph (V, E), find a subset W subseteq V of k vertices so as to maximize the number of hyperedges contained in W) and define the Minimum p-Union problem (given a hypergraph, choose p of the hyperedges so as to minimize the number of vertices in their union). We focus in particular on the case where all hyperedges have size 3, as this is the simplest non-graph setting. For this case we provide an O(n^{4(4-sqrt{3})/13 + epsilon}) <= O(n^{0.697831+epsilon})-approximation (for arbitrary constant epsilon > 0) for Densest k-Subhypergraph and an ~O(n^{2/5})-approximation for Minimum p-Union. We also give an O(sqrt{m})-approximation for Minimum p-Union in general hypergraphs. Finally, we examine the interesting special case of interval hypergraphs (instances where the vertices are a subset of the natural numbers and the hyperedges are intervals of the line) and prove that both problems admit an exact polynomial time solution on these instances.
Cite as

Eden Chlamtac, Michael Dinitz, Christian Konrad, Guy Kortsarz, and George Rabanca. The Densest k-Subhypergraph Problem. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 60, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{chlamtac_et_al:LIPIcs.APPROX-RANDOM.2016.6,
  author =	{Chlamtac, Eden and Dinitz, Michael and Konrad, Christian and Kortsarz, Guy and Rabanca, George},
  title =	{{The Densest k-Subhypergraph Problem}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-018-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{60},
  editor =	{Jansen, Klaus and Mathieu, Claire and Rolim, Jos\'{e} D. P. and Umans, Chris},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2016.6},
  URN =		{urn:nbn:de:0030-drops-66298},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2016.6},
  annote =	{Keywords: Hypergraphs, Approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.146
Bounds on the Voter Model in Dynamic Networks

Authors: Petra Berenbrink, George Giakkoupis, Anne-Marie Kermarrec, and Frederik Mallmann-Trenn

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

Abstract
In the voter model, each node of a graph has an opinion, and in every round each node chooses independently a random neighbour and adopts its opinion. We are interested in the consensus time, which is the first point in time where all nodes have the same opinion. We consider dynamic graphs in which the edges are rewired in every round (by an adversary) giving rise to the graph sequence G_1, G_2, ..., where we assume that G_i has conductance at least phi_i. We assume that the degrees of nodes don't change over time as one can show that the consensus time can become super-exponential otherwise. In the case of a sequence of d-regular graphs, we obtain asymptotically tight results. Even for some static graphs, such as the cycle, our results improve the state of the art. Here we show that the expected number of rounds until all nodes have the same opinion is bounded by O(m/(d_{min}*phi)), for any graph with m edges, conductance phi, and degrees at least d_{min}. In addition, we consider a biased dynamic voter model, where each opinion i is associated with a probability P_i, and when a node chooses a neighbour with that opinion, it adopts opinion i with probability P_i (otherwise the node keeps its current opinion). We show for any regular dynamic graph, that if there is an epsilon > 0 difference between the highest and second highest opinion probabilities, and at least Omega(log(n)) nodes have initially the opinion with the highest probability, then all nodes adopt w.h.p. that opinion. We obtain a bound on the convergence time, which becomes O(log(n)/phi) for static graphs.
Cite as

Petra Berenbrink, George Giakkoupis, Anne-Marie Kermarrec, and Frederik Mallmann-Trenn. Bounds on the Voter Model in Dynamic Networks. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 146:1-146:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{berenbrink_et_al:LIPIcs.ICALP.2016.146,
  author =	{Berenbrink, Petra and Giakkoupis, George and Kermarrec, Anne-Marie and Mallmann-Trenn, Frederik},
  title =	{{Bounds on the Voter Model in Dynamic Networks}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{146:1--146:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.146},
  URN =		{urn:nbn:de:0030-drops-62901},
  doi =		{10.4230/LIPIcs.ICALP.2016.146},
  annote =	{Keywords: Voting, Distributed Computing, Conductance, Dynamic Graphs, Consensus}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2016.68
Stably Computing Order Statistics with Arithmetic Population Protocols

Authors: George B. Mertzios, Sotiris E. Nikoletseas, Christoforos L. Raptopoulos, and Paul G. Spirakis

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract
In this paper we initiate the study of populations of agents with very limited capabilities that are globally able to compute order statistics of their arithmetic input values via pair-wise meetings. To this extent, we introduce the Arithmetic Population Protocol (APP) model, embarking from the well known Population Protocol (PP) model and inspired by two recent papers in which states are treated as integer numbers. In the APP model, every agent has a state from a set Q of states, as well as a fixed number of registers (independent of the size of the population), each of which can store an element from a totally ordered set S of samples. Whenever two agents interact with each other, they update their states and the values stored in their registers according to a joint transition function. This transition function is also restricted; it only allows (a) comparisons and (b) copy / paste operations for the sample values that are stored in the registers of the two interacting agents. Agents can only meet in pairs via a fair scheduler and are required to eventually converge to the same output value of the function that the protocol globally and stably computes. We present two different APPs for stably computing the median of the input values, initially stored on the agents of the population. Our first APP, in which every agent has 3 registers and no states, stably computes (with probability 1) the median under any fair scheduler in any strongly connected directed (or connected undirected) interaction graph. Under the probabilistic scheduler, we show that our protocol stably computes the median in O(n^6) number of interactions in a connected undirected interaction graph of n agents. Our second APP, in which every agent has 2 registers and O(n^2 log{n}) states, computes to the correct median of the input with high probability in O(n^3 log{n}) interactions, assuming the probabilistic scheduler and the complete interaction graph. Finally we present a third APP which, for any k, stably computes the k-th smallest element of the input of the population under any fair scheduler and in any strongly connected directed (or connected undirected) interaction graph. In this APP every agent has 2 registers and n states. Upon convergence every agent has a different state; all these states provide a total ordering of the agents with respect to their input values.
Cite as

George B. Mertzios, Sotiris E. Nikoletseas, Christoforos L. Raptopoulos, and Paul G. Spirakis. Stably Computing Order Statistics with Arithmetic Population Protocols. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 68:1-68:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{mertzios_et_al:LIPIcs.MFCS.2016.68,
  author =	{Mertzios, George B. and Nikoletseas, Sotiris E. and Raptopoulos, Christoforos L. and Spirakis, Paul G.},
  title =	{{Stably Computing Order Statistics with Arithmetic Population Protocols}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{68:1--68:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.68},
  URN =		{urn:nbn:de:0030-drops-64805},
  doi =		{10.4230/LIPIcs.MFCS.2016.68},
  annote =	{Keywords: arithmetic population protocols, order statistics, median, k-minimum element}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2015.102
Polynomial Fixed-parameter Algorithms: A Case Study for Longest Path on Interval Graphs

Authors: Archontia C. Giannopoulou, George B. Mertzios, and Rolf Niedermeier

Published in: LIPIcs, Volume 43, 10th International Symposium on Parameterized and Exact Computation (IPEC 2015)

Abstract
We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus on a fundamental graph problem: Longest Path; it is NP-hard in general but known to be solvable in O(n^4) time on n-vertex interval graphs. We show how to solve Longest Path on Interval Graphs, parameterized by vertex deletion number k to proper interval graphs, in O(k^9n) time. Notably, Longest Path is trivially solvable in linear time on proper interval graphs, and the parameter value k can be approximated up to a factor of 4 in linear time. From a more general perspective, we believe that using parameterized complexity analysis for polynomial-time solvable problems offers a very fertile ground for future studies for all sorts of algorithmic problems. It may enable a refined understanding of efficiency aspects for polynomial-time solvable problems, similarly to what classical parameterized complexity analysis does for NP-hard problems.
Cite as

Archontia C. Giannopoulou, George B. Mertzios, and Rolf Niedermeier. Polynomial Fixed-parameter Algorithms: A Case Study for Longest Path on Interval Graphs. In 10th International Symposium on Parameterized and Exact Computation (IPEC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 43, pp. 102-113, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{giannopoulou_et_al:LIPIcs.IPEC.2015.102,
  author =	{Giannopoulou, Archontia C. and Mertzios, George B. and Niedermeier, Rolf},
  title =	{{Polynomial Fixed-parameter Algorithms: A Case Study for Longest Path on Interval Graphs}},
  booktitle =	{10th International Symposium on Parameterized and Exact Computation (IPEC 2015)},
  pages =	{102--113},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-92-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{43},
  editor =	{Husfeldt, Thore and Kanj, Iyad},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2015.102},
  URN =		{urn:nbn:de:0030-drops-55750},
  doi =		{10.4230/LIPIcs.IPEC.2015.102},
  annote =	{Keywords: fixed-parameter algorithm, preprocessing, data reduction, polynomial-time algorithm, longest path problem, interval graphs, proper interval vertex del}
}
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