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Documents authored by Laura, Luigi

Document
DOI: 10.4230/LIPIcs.ESA.2019.50
Dynamic Dominators and Low-High Orders in DAGs

Authors: Loukas Georgiadis, Konstantinos Giannis, Giuseppe F. Italiano, Aikaterini Karanasiou, and Luigi Laura

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
We consider practical algorithms for maintaining the dominator tree and a low-high order in directed acyclic graphs (DAGs) subject to dynamic operations. Let G be a directed graph with a distinguished start vertex s. The dominator tree D of G is a tree rooted at s, such that a vertex v is an ancestor of a vertex w if and only if all paths from s to w in G include v. The dominator tree is a central tool in program optimization and code generation, and has many applications in other diverse areas including constraint programming, circuit testing, biology, and in algorithms for graph connectivity problems. A low-high order of G is a preorder of D that certifies the correctness of D, and has further applications in connectivity and path-determination problems. We first provide a practical and carefully engineered version of a recent algorithm [ICALP 2017] for maintaining the dominator tree of a DAG through a sequence of edge deletions. The algorithm runs in O(mn) total time and O(m) space, where n is the number of vertices and m is the number of edges before any deletion. In addition, we present a new algorithm that maintains a low-high order of a DAG under edge deletions within the same bounds. Both results extend to the case of reducible graphs (a class that includes DAGs). Furthermore, we present a fully dynamic algorithm for maintaining the dominator tree of a DAG under an intermixed sequence of edge insertions and deletions. Although it does not maintain the O(mn) worst-case bound of the decremental algorithm, our experiments highlight that the fully dynamic algorithm performs very well in practice. Finally, we study the practical efficiency of all our algorithms by conducting an extensive experimental study on real-world and synthetic graphs.
Cite as

Loukas Georgiadis, Konstantinos Giannis, Giuseppe F. Italiano, Aikaterini Karanasiou, and Luigi Laura. Dynamic Dominators and Low-High Orders in DAGs. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 50:1-50:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{georgiadis_et_al:LIPIcs.ESA.2019.50,
  author =	{Georgiadis, Loukas and Giannis, Konstantinos and Italiano, Giuseppe F. and Karanasiou, Aikaterini and Laura, Luigi},
  title =	{{Dynamic Dominators and Low-High Orders in DAGs}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{50:1--50:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.50},
  URN =		{urn:nbn:de:0030-drops-111715},
  doi =		{10.4230/LIPIcs.ESA.2019.50},
  annote =	{Keywords: Connectivity, dominators, low-high orders}
}
Document
DOI: 10.4230/LIPIcs.SEA.2017.27
Incremental Low-High Orders of Directed Graphs and Applications

Authors: Loukas Georgiadis, Konstantinos Giannis, Aikaterini Karanasiou, and Luigi Laura

Published in: LIPIcs, Volume 75, 16th International Symposium on Experimental Algorithms (SEA 2017)

Abstract
A flow graph G = (V, E, s) is a directed graph with a distinguished start vertex s. The dominator tree D of G is a tree rooted at s, such that a vertex v is an ancestor of a vertex w if and only if all paths from s to w include v. The dominator tree is a central tool in program optimization and code generation, and has many applications in other diverse areas including constraint programming, circuit testing, biology, and in algorithms for graph connectivity problems. A low-high order of G is a preorder d of D that certifies the correctness of D, and has further applications in connectivity and path-determination problems. In this paper we consider how to maintain efficiently a low-high order of a flow graph incrementally under edge insertions. We present algorithms that run in O(mn) total time for a sequence of edge insertions in a flow graph with n vertices, where m is the total number of edges after all insertions. These immediately provide the first incremental certifying algorithms for maintaining the dominator tree in O(mn) total time, and also imply incremental algorithms for other problems. Hence, we provide a substantial improvement over the O(m^2) straightforward algorithms, which recompute the solution from scratch after each edge insertion. Furthermore, we provide efficient implementations of our algorithms and conduct an extensive experimental study on real-world graphs taken from a variety of application areas. The experimental results show that our algorithms perform very well in practice.
Cite as

Loukas Georgiadis, Konstantinos Giannis, Aikaterini Karanasiou, and Luigi Laura. Incremental Low-High Orders of Directed Graphs and Applications. In 16th International Symposium on Experimental Algorithms (SEA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 75, pp. 27:1-27:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{georgiadis_et_al:LIPIcs.SEA.2017.27,
  author =	{Georgiadis, Loukas and Giannis, Konstantinos and Karanasiou, Aikaterini and Laura, Luigi},
  title =	{{Incremental Low-High Orders of Directed Graphs and Applications}},
  booktitle =	{16th International Symposium on Experimental Algorithms (SEA 2017)},
  pages =	{27:1--27:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-036-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{75},
  editor =	{Iliopoulos, Costas S. and Pissis, Solon P. and Puglisi, Simon J. and Raman, Rajeev},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2017.27},
  URN =		{urn:nbn:de:0030-drops-76319},
  doi =		{10.4230/LIPIcs.SEA.2017.27},
  annote =	{Keywords: connectivity, directed graphs, dominators, dynamic algorithms}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2013.15
Is Timetabling Routing Always Reliable for Public Transport?

Authors: Donatella Firmani, Giuseppe F. Italiano, Luigi Laura, and Federico Santaroni

Published in: OASIcs, Volume 33, 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2013)

Abstract
Current route planning algorithms for public transport networks are mostly based on timetable information only, i.e., they compute shortest routes under the assumption that all transit vehicles (e.g., buses, subway trains) will incur in no delays throughout their trips. Unfortunately, unavoidable and unexpected delays often prevent transit vehicles to respect their originally planned schedule. In this paper, we try to measure empirically the quality of the solutions offered by timetabling routing in a real public transport network, where unpredictable delays may happen with a certain frequency, such as the public transport network of the metropolitan area of Rome. To accomplish this task, we take the time estimates required for trips provided by a timetabling-based route planner (such as Google Transit) and compare them against the times taken by the trips according to the actual tracking of transit vehicles in the transport network, measured through the GPS data made available by the transit agency. In our experiments, the movement of transit vehicles was only mildly correlated to the timetable, giving strong evidence that in such a case timetabled routing may fail to deliver optimal or even high-quality solutions.
Cite as

Donatella Firmani, Giuseppe F. Italiano, Luigi Laura, and Federico Santaroni. Is Timetabling Routing Always Reliable for Public Transport?. In 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 33, pp. 15-26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{firmani_et_al:OASIcs.ATMOS.2013.15,
  author =	{Firmani, Donatella and Italiano, Giuseppe F. and Laura, Luigi and Santaroni, Federico},
  title =	{{Is Timetabling Routing Always Reliable for Public Transport?}},
  booktitle =	{13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{15--26},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-58-3},
  ISSN =	{2190-6807},
  year =	{2013},
  volume =	{33},
  editor =	{Frigioni, Daniele and Stiller, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2013.15},
  URN =		{urn:nbn:de:0030-drops-42415},
  doi =		{10.4230/OASIcs.ATMOS.2013.15},
  annote =	{Keywords: Shortest Path Problems, Route Planning, Timetable-based Routing, Public Transport Networks}
}
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