Document

**Published in:** LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

We consider a variant of the prize collecting Steiner tree problem in which we are given a directed graph D = (V,A), a monotone submodular prize function p:2^V → ℝ^+ ∪ {0}, a cost function c:V → ℤ^+, a root vertex r ∈ V, and a budget B. The aim is to find an out-subtree T of D rooted at r that costs at most B and maximizes the prize function. We call this problem Directed Rooted Submodular Tree (DRST).
For the case of undirected graphs and additive prize functions, Moss and Rabani [SIAM J. Comput. 2007] gave an algorithm that guarantees an O(log|V|)-approximation factor if a violation by a factor 2 of the budget constraint is allowed. Bateni et al. [SIAM J. Comput. 2018] improved the budget violation factor to 1+ε at the cost of an additional approximation factor of O(1/ε²), for any ε ∈ (0,1]. For directed graphs, Ghuge and Nagarajan [SODA 2020] gave an optimal quasi-polynomial time O({log n'}/{log log n'})-approximation algorithm, where n' is the number of vertices in an optimal solution, for the case in which the costs are associated to the edges.
In this paper, we give a polynomial time algorithm for DRST that guarantees an approximation factor of O(√B/ε³) at the cost of a budget violation of a factor 1+ε, for any ε ∈ (0,1]. The same result holds for the edge-cost case, to the best of our knowledge this is the first polynomial time approximation algorithm for this case. We further show that the unrooted version of DRST can be approximated to a factor of O(√B) without budget violation, which is an improvement over the factor O(Δ √B) given in [Kuo et al. IEEE/ACM Trans. Netw. 2015] for the undirected and unrooted case, where Δ is the maximum degree of the graph. Finally, we provide some new/improved approximation bounds for several related problems, including the additive-prize version of DRST, the maximum budgeted connected set cover problem, and the budgeted sensor cover problem.

Gianlorenzo D'Angelo, Esmaeil Delfaraz, and Hugo Gilbert. Budgeted Out-Tree Maximization with Submodular Prizes. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dangelo_et_al:LIPIcs.ISAAC.2022.9, author = {D'Angelo, Gianlorenzo and Delfaraz, Esmaeil and Gilbert, Hugo}, title = {{Budgeted Out-Tree Maximization with Submodular Prizes}}, booktitle = {33rd International Symposium on Algorithms and Computation (ISAAC 2022)}, pages = {9:1--9:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-258-7}, ISSN = {1868-8969}, year = {2022}, volume = {248}, editor = {Bae, Sang Won and Park, Heejin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.9}, URN = {urn:nbn:de:0030-drops-172945}, doi = {10.4230/LIPIcs.ISAAC.2022.9}, annote = {Keywords: Prize Collecting Steiner Tree, Directed graphs, Approximation Algorithms, Budgeted Problem} }

Document

**Published in:** LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

A temporal graph is an undirected graph G = (V,E) along with a function λ : E → ℕ^+ that assigns a time-label to each edge in E. A path in G such that the traversed time-labels are non-decreasing is called a temporal path. Accordingly, the distance from u to v is the minimum length (i.e., the number of edges) of a temporal path from u to v. A temporal α-spanner of G is a (temporal) subgraph H that preserves the distances between any pair of vertices in V, up to a multiplicative stretch factor of α. The size of H is measured as the number of its edges.
In this work, we study the size-stretch trade-offs of temporal spanners. In particular we show that temporal cliques always admit a temporal (2k-1)-spanner with Õ(kn^{1+1/k}) edges, where k > 1 is an integer parameter of choice. Choosing k = ⌊log n⌋, we obtain a temporal O(log n)-spanner with Õ(n) edges that has almost the same size (up to logarithmic factors) as the temporal spanner given in [Casteigts et al., JCSS 2021] which only preserves temporal connectivity.
We then turn our attention to general temporal graphs. Since Ω(n²) edges might be needed by any connectivity-preserving temporal subgraph [Axiotis et al., ICALP'16], we focus on approximating distances from a single source. We show that Õ(n/log(1+ε)) edges suffice to obtain a stretch of (1+ε), for any small ε > 0. This result is essentially tight in the following sense: there are temporal graphs G for which any temporal subgraph preserving exact distances from a single-source must use Ω(n²) edges. Interestingly enough, our analysis can be extended to the case of additive stretch for which we prove an upper bound of Õ(n² / β) on the size of any temporal β-additive spanner, which we show to be tight up to polylogarithmic factors.
Finally, we investigate how the lifetime of G, i.e., the number of its distinct time-labels, affects the trade-off between the size and the stretch of a temporal spanner.

Davide Bilò, Gianlorenzo D'Angelo, Luciano Gualà, Stefano Leucci, and Mirko Rossi. Sparse Temporal Spanners with Low Stretch. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bilo_et_al:LIPIcs.ESA.2022.19, author = {Bil\`{o}, Davide and D'Angelo, Gianlorenzo and Gual\`{a}, Luciano and Leucci, Stefano and Rossi, Mirko}, title = {{Sparse Temporal Spanners with Low Stretch}}, booktitle = {30th Annual European Symposium on Algorithms (ESA 2022)}, pages = {19:1--19:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-247-1}, ISSN = {1868-8969}, year = {2022}, volume = {244}, editor = {Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva 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.2022.19}, URN = {urn:nbn:de:0030-drops-169575}, doi = {10.4230/LIPIcs.ESA.2022.19}, annote = {Keywords: temporal spanners, temporal graphs, graph sparsification, approximate distances} }

Document

**Published in:** LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Let G be a directed graph with n vertices, m edges, and non-negative edge costs. Given G, a fixed source vertex s, and a positive integer p, we consider the problem of computing, for each vertex t≠ s, p edge-disjoint paths of minimum total cost from s to t in G. Suurballe and Tarjan [Networks, 1984] solved the above problem for p = 2 by designing a O(m+nlog n) time algorithm which also computes a sparse single-source 2-multipath preserver, i.e., a subgraph containing 2 edge-disjoint paths of minimum total cost from s to every other vertex of G. The case p ≥ 3 was left as an open problem.
We study the general problem (p ≥ 2) and prove that any graph admits a sparse single-source p-multipath preserver with p(n-1) edges. This size is optimal since the in-degree of each non-root vertex v must be at least p. Moreover, we design an algorithm that requires O(pn² (p + log n)) time to compute both p edge-disjoint paths of minimum total cost from the source to all other vertices and an optimal-size single-source p-multipath preserver. The running time of our algorithm outperforms that of a natural approach that solves n-1 single-pair instances using the well-known successive shortest paths algorithm by a factor of Θ(m/(np)) and is asymptotically near optimal if p = O(1) and m = Θ(n²). Our results extend naturally to the case of p vertex-disjoint paths.

Davide Bilò, Gianlorenzo D'Angelo, Luciano Gualà, Stefano Leucci, Guido Proietti, and Mirko Rossi. Single-Source Shortest p-Disjoint Paths: Fast Computation and Sparse Preservers. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 12:1-12:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bilo_et_al:LIPIcs.STACS.2022.12, author = {Bil\`{o}, Davide and D'Angelo, Gianlorenzo and Gual\`{a}, Luciano and Leucci, Stefano and Proietti, Guido and Rossi, Mirko}, title = {{Single-Source Shortest p-Disjoint Paths: Fast Computation and Sparse Preservers}}, booktitle = {39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)}, pages = {12:1--12:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-222-8}, ISSN = {1868-8969}, year = {2022}, volume = {219}, editor = {Berenbrink, Petra and Monmege, Benjamin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.12}, URN = {urn:nbn:de:0030-drops-158221}, doi = {10.4230/LIPIcs.STACS.2022.12}, annote = {Keywords: multipath spanners, graph sparsification, edge-disjoint paths, min-cost flow} }

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Track A: Algorithms, Complexity and Games

**Published in:** LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

In the adaptive influence maximization problem, we are given a social network and a budget k, and we iteratively select k nodes, called seeds, in order to maximize the expected number of nodes that are reached by an influence cascade that they generate according to a stochastic model for influence diffusion. The decision on the next seed to select is based on the observed cascade of previously selected seeds. We focus on the myopic feedback model, in which we can only observe which neighbors of previously selected seeds have been influenced and on the independent cascade model, where each edge is associated with an independent probability of diffusing influence. While adaptive policies are strictly stronger than non-adaptive ones, in which all the seeds are selected beforehand, the latter are much easier to design and implement and they provide good approximation factors if the adaptivity gap, the ratio between the adaptive and the non-adaptive optima, is small. Previous works showed that the adaptivity gap is at most 4, and that simple adaptive or non-adaptive greedy algorithms guarantee an approximation of 1/4 (1-1/e) ≈ 0.158 for the adaptive optimum. This is the best approximation factor known so far for the adaptive influence maximization problem with myopic feedback.
In this paper, we directly analyze the approximation factor of the non-adaptive greedy algorithm, without passing through the adaptivity gap, and show an improved bound of 1/2 (1-1/e) ≈ 0.316. Therefore, the adaptivity gap is at most 2e/e-1 ≈ 3.164. To prove these bounds, we introduce a new approach to relate the greedy non-adaptive algorithm to the adaptive optimum. The new approach does not rely on multi-linear extensions or random walks on optimal decision trees, which are commonly used techniques in the field. We believe that it is of independent interest and may be used to analyze other adaptive optimization problems. Finally, we also analyze the adaptive greedy algorithm, and show that guarantees an improved approximation factor of 1-1/(√{e)}≈ 0.393.

Gianlorenzo D'Angelo, Debashmita Poddar, and Cosimo Vinci. Improved Approximation Factor for Adaptive Influence Maximization via Simple Greedy Strategies. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 59:1-59:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{dangelo_et_al:LIPIcs.ICALP.2021.59, author = {D'Angelo, Gianlorenzo and Poddar, Debashmita and Vinci, Cosimo}, title = {{Improved Approximation Factor for Adaptive Influence Maximization via Simple Greedy Strategies}}, booktitle = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)}, pages = {59:1--59:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-195-5}, ISSN = {1868-8969}, year = {2021}, volume = {198}, editor = {Bansal, Nikhil and Merelli, Emanuela and Worrell, James}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.59}, URN = {urn:nbn:de:0030-drops-141282}, doi = {10.4230/LIPIcs.ICALP.2021.59}, annote = {Keywords: Adaptive Optimization, Influence Maximization, Submodular Optimization, Stochastic Optimization} }

Document

**Published in:** LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

In this paper we consider a generalization of the well-known budgeted maximum coverage problem. We are given a ground set of elements and a set of bins. The goal is to find a subset of elements along with an associated set of bins, such that the overall cost is at most a given budget, and the profit is maximized. Each bin has its own cost and the cost of each element depends on its associated bin. The profit is measured by a monotone submodular function over the elements.
We first present an algorithm that guarantees an approximation factor of 1/2(1-1/e^alpha), where alpha <= 1 is the approximation factor of an algorithm for a sub-problem. We give two polynomial-time algorithms to solve this sub-problem. The first one gives us alpha=1- epsilon if the costs satisfies a specific condition, which is fulfilled in several relevant cases, including the unitary costs case and the problem of maximizing a monotone submodular function under a knapsack constraint. The second one guarantees alpha=1-1/e-epsilon for the general case. The gap between our approximation guarantees and the known inapproximability bounds is 1/2.
We extend our algorithm to a bi-criterion approximation algorithm in which we are allowed to spend an extra budget up to a factor beta >= 1 to guarantee a 1/2(1-1/e^(alpha beta))-approximation. If we set beta=1/(alpha)ln (1/(2 epsilon)), the algorithm achieves an approximation factor of 1/2-epsilon, for any arbitrarily small epsilon>0.

Francesco Cellinese, Gianlorenzo D'Angelo, Gianpiero Monaco, and Yllka Velaj. Generalized Budgeted Submodular Set Function Maximization. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{cellinese_et_al:LIPIcs.MFCS.2018.31, author = {Cellinese, Francesco and D'Angelo, Gianlorenzo and Monaco, Gianpiero and Velaj, Yllka}, title = {{Generalized Budgeted Submodular Set Function Maximization}}, booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)}, pages = {31:1--31:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-086-6}, ISSN = {1868-8969}, year = {2018}, volume = {117}, editor = {Potapov, Igor and Spirakis, Paul and Worrell, James}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.31}, URN = {urn:nbn:de:0030-drops-96138}, doi = {10.4230/LIPIcs.MFCS.2018.31}, annote = {Keywords: Submodular set function, Approximation algorithms, Budgeted Maximum Coverage} }

Document

Complete Volume

**Published in:** LIPIcs, Volume 103, 17th International Symposium on Experimental Algorithms (SEA 2018)

LIPIcs, Volume 103, SEA'18, Complete Volume

17th International Symposium on Experimental Algorithms (SEA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 103, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@Proceedings{dangelo:LIPIcs.SEA.2018, title = {{LIPIcs, Volume 103, SEA'18, Complete Volume}}, booktitle = {17th International Symposium on Experimental Algorithms (SEA 2018)}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-070-5}, ISSN = {1868-8969}, year = {2018}, volume = {103}, editor = {D'Angelo, Gianlorenzo}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2018}, URN = {urn:nbn:de:0030-drops-92438}, doi = {10.4230/LIPIcs.SEA.2018}, annote = {Keywords: Theory of computation, Design and analysis of algorithms} }

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Front Matter

**Published in:** LIPIcs, Volume 103, 17th International Symposium on Experimental Algorithms (SEA 2018)

Gianlorenzo

17th International Symposium on Experimental Algorithms (SEA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 103, pp. 0:i-0:xi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{dangelo:LIPIcs.SEA.2018.0, author = {D'Angelo, Gianlorenzo}, title = {{Front Matter, Table of Contents, Preface, Conference Organization}}, booktitle = {17th International Symposium on Experimental Algorithms (SEA 2018)}, pages = {0:i--0:xi}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-070-5}, ISSN = {1868-8969}, year = {2018}, volume = {103}, editor = {D'Angelo, Gianlorenzo}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2018.0}, URN = {urn:nbn:de:0030-drops-89357}, doi = {10.4230/LIPIcs.SEA.2018.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization} }

Document

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

The Independent Cascade Model (ICM) is a widely studied model that aims to capture the dynamics of the information diffusion in social networks and in general complex networks. In this model, we can distinguish between active nodes which spread the information and inactive ones. The process starts from a set of initially active nodes called seeds. Recursively, currently active nodes can activate their neighbours according to a probability distribution on the set of edges. After a certain number of these recursive cycles, a large number of nodes might become active. The process terminates when no further node gets activated.
Starting from the work of Domingos and Richardson [Domingos et al. 2001], several studies have been conducted with the aim of shaping a given diffusion process so as to maximize the number of activated nodes at the end of the process. One of the most studied problems has been formalized by Kempe et al. and consists in finding a set of initial seeds that maximizes the expected number of active nodes under a budget constraint [Kempe et al. 2003].
In this paper we study a generalization of the problem of Kempe et al. in which we are allowed to spend part of the budget to create new edges incident to the seeds. That is, the budget can be spent to buy seeds or edges according to a cost function. The problem does not admin a PTAS, unless P=NP. We propose two approximation algorithms: the former one gives an approximation ratio that depends on the edge costs and increases when these costs are high; the latter algorithm gives a constant approximation guarantee which is greater than that of the first algorithm when the edge costs can be small.

Gianlorenzo D'Angelo, Lorenzo Severini, and Yllka Velaj. Selecting Nodes and Buying Links to Maximize the Information Diffusion in a Network. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 75:1-75:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{dangelo_et_al:LIPIcs.MFCS.2017.75, author = {D'Angelo, Gianlorenzo and Severini, Lorenzo and Velaj, Yllka}, title = {{Selecting Nodes and Buying Links to Maximize the Information Diffusion in a Network}}, booktitle = {42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)}, pages = {75:1--75:14}, 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.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.75}, URN = {urn:nbn:de:0030-drops-80853}, doi = {10.4230/LIPIcs.MFCS.2017.75}, annote = {Keywords: Approximation algorithms, information diffusion, complex networks, independent cascade model, network augmentation} }

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Complete Volume

**Published in:** OASIcs, Volume 59, 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)

OASIcs, Volume 59, ATMOS'17, Complete Volume

17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017). Open Access Series in Informatics (OASIcs), Volume 59, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@Proceedings{dangelo_et_al:OASIcs.ATMOS.2017, title = {{OASIcs, Volume 59, ATMOS'17, Complete Volume}}, booktitle = {17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-042-2}, ISSN = {2190-6807}, year = {2017}, volume = {59}, editor = {D'Angelo, Gianlorenzo and Dollevoet, Twan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2017}, URN = {urn:nbn:de:0030-drops-79109}, doi = {10.4230/OASIcs.ATMOS.2017}, annote = {Keywords: Analysis of Algorithms and Problem Complexity, Optimization, Combinatorics, Graph Theory, Applications} }

Document

Front Matter

**Published in:** OASIcs, Volume 59, 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)

Front Matter, Table of Contents, Preface, Organization

17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017). Open Access Series in Informatics (OASIcs), Volume 59, pp. 0:i-0:x, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{dangelo_et_al:OASIcs.ATMOS.2017.0, author = {D'Angelo, Gianlorenzo and Dollevoet, Twan}, title = {{Front Matter, Table of Contents, Preface, Organization}}, booktitle = {17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)}, pages = {0:i--0:x}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-042-2}, ISSN = {2190-6807}, year = {2017}, volume = {59}, editor = {D'Angelo, Gianlorenzo and Dollevoet, Twan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2017.0}, URN = {urn:nbn:de:0030-drops-78872}, doi = {10.4230/OASIcs.ATMOS.2017.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Organization} }

Document

**Published in:** LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

We are considering distributed network computing, in which computing entities are connected by a network modeled as a connected graph. These entities are located at the nodes of the graph, and they exchange information by message-passing along its edges. In this context, we are adopting the classical framework for local distributed decision, in which nodes must collectively decide whether their network configuration satisfies some given boolean predicate, by having each node interacting with the nodes in its vicinity only. A network configuration is accepted if and only if every node individually accepts. It is folklore that not every Turing-decidable network property (e.g., whether the network is planar) can be decided locally whenever the computing entities are Turing machines (TM). On the other hand, it is known that every Turing-decidable network property can be decided locally if nodes are running non-deterministic Turing machines (NTM). However, this holds only if the nodes have the ability to guess the identities of the nodes currently in the network. That is, for different sets of identities assigned to the nodes, the correct guesses of the nodes might be different. If one asks the nodes to use the same guess in the same network configuration even with different identity assignments, i.e., to perform identity-oblivious guesses, then it is known that not every Turing-decidable network property can be decided locally.
In this paper, we show that every Turing-decidable network property can be decided locally if nodes are running alternating Turing machines (ATM), and this holds even if nodes are bounded to perform identity-oblivious guesses. More specifically, we show that, for every network property, there is a local algorithm for ATMs, with at most 2 alternations, that decides that property. To this aim, we define a hierarchy of classes of decision tasks where the lowest level contains tasks solvable with TMs, the first level those solvable with NTMs, and level k contains those tasks solvable with ATMs with k alternations. We characterize the entire hierarchy, and show that it collapses in the second level. In addition, we show separation results between the classes of network properties that are locally decidable with TMs, NTMs, and ATMs. Finally, we establish the existence of completeness results for each of these classes, using novel notions of local reduction.

Alkida Balliu, Gianlorenzo D'Angelo, Pierre Fraigniaud, and Dennis Olivetti. What Can Be Verified Locally?. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{balliu_et_al:LIPIcs.STACS.2017.8, author = {Balliu, Alkida and D'Angelo, Gianlorenzo and Fraigniaud, Pierre and Olivetti, Dennis}, title = {{What Can Be Verified Locally?}}, booktitle = {34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)}, pages = {8:1--8:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-028-6}, ISSN = {1868-8969}, year = {2017}, volume = {66}, editor = {Vollmer, Heribert and Vall\'{e}e, Brigitte}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.8}, URN = {urn:nbn:de:0030-drops-70253}, doi = {10.4230/LIPIcs.STACS.2017.8}, annote = {Keywords: Distributed Network Computing, Distributed Algorithm, Distributed Decision, Locality} }

Document

**Published in:** OASIcs, Volume 42, 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2014)

Many efforts have been done in the last years to model public transport timetables in order to find optimal routes. The proposed models can be classified into two types: those representing the timetable as an array, and those representing it as a graph. The array-based models have been shown to be very effective in terms of query time, while the graph-based models usually answer queries by computing shortest paths, and hence they are suitable to be used in combination with speed-up techniques developed for road networks.
In this paper, we focus on the dynamic behavior of graph-based models considering the case where transportation systems are subject to delays with respect to the given timetable. We make three contributions: (i) we give a simplified and optimized update routine for the well-known time-expanded model along with an engineered query algorithm; (ii) we propose a new graph-based model tailored for handling dynamic updates; (iii) we assess the effectiveness of the proposed models and algorithms by an experimental study, which shows that both models require negligible update time and a query time which is comparable to that required by some array-based models.

Alessio Cionini, Gianlorenzo D'Angelo, Mattia D'Emidio, Daniele Frigioni, Kalliopi Giannakopoulou, Andreas Paraskevopoulos, and Christos Zaroliagis. Engineering Graph-Based Models for Dynamic Timetable Information Systems. In 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 42, pp. 46-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{cionini_et_al:OASIcs.ATMOS.2014.46, author = {Cionini, Alessio and D'Angelo, Gianlorenzo and D'Emidio, Mattia and Frigioni, Daniele and Giannakopoulou, Kalliopi and Paraskevopoulos, Andreas and Zaroliagis, Christos}, title = {{Engineering Graph-Based Models for Dynamic Timetable Information Systems}}, booktitle = {14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems}, pages = {46--61}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-939897-75-0}, ISSN = {2190-6807}, year = {2014}, volume = {42}, editor = {Funke, Stefan and Mihal\'{a}k, Mat\'{u}s}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2014.46}, URN = {urn:nbn:de:0030-drops-47522}, doi = {10.4230/OASIcs.ATMOS.2014.46}, annote = {Keywords: Timetabling, dynamic updates, queries, shortest paths} }

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**Published in:** OASIcs, Volume 12, 9th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'09) (2009)

Computation of quickest paths has undergoing a rapid development in recent
years. It turns out that many high-performance route planning algorithms are
made up of several basic ingredients. However, not all of those ingredients have
been analyzed in a \emph{dynamic} scenario where edge weights change after
preprocessing. In this work, we present how one of those ingredients, i.e.,
Arc-Flags can be applied in dynamic scenarios

Emanuele Berrettini, Gianlorenzo D'Angelo, and Daniel Delling. Arc-Flags in Dynamic Graphs. In 9th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'09). Open Access Series in Informatics (OASIcs), Volume 12, pp. 1-18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{berrettini_et_al:OASIcs.ATMOS.2009.2149, author = {Berrettini, Emanuele and D'Angelo, Gianlorenzo and Delling, Daniel}, title = {{Arc-Flags in Dynamic Graphs}}, booktitle = {9th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'09)}, pages = {1--18}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-939897-11-8}, ISSN = {2190-6807}, year = {2009}, volume = {12}, editor = {Clausen, Jens and Di Stefano, Gabriele}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2009.2149}, URN = {urn:nbn:de:0030-drops-21490}, doi = {10.4230/OASIcs.ATMOS.2009.2149}, annote = {Keywords: Shortest Path, Speed-Up Technique, Dynamic Graph Algorithm Shortest Path, Speed-Up Technique, Dynamic Graph Algorithm} }

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**Published in:** OASIcs, Volume 7, 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07) (2007)

In this paper we provide efficient robust algorithms for shunting
problems concerning the reordering of train cars over a hump. In
particular, we study algorithms able to cope with small
disruptions, as temporary and local availability and/or
malfunctioning of key resources that can occur and affect planned
operations. To this aim, a definition of robust algorithm is
provided. Performances of the proposed algorithms are measured by
the notion of price of robustness. Various scenarios are
considered, and interesting results are presented.

Serafino Cicerone, Gianlorenzo D'Angelo, Gabriele Di Stefano, Daniele Frigioni, and Alfredo Navarra. 12. Robust Algorithms and Price of Robustness in Shunting Problems. In 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07). Open Access Series in Informatics (OASIcs), Volume 7, pp. 175-190, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{cicerone_et_al:OASIcs.ATMOS.2007.1175, author = {Cicerone, Serafino and D'Angelo, Gianlorenzo and Di Stefano, Gabriele and Frigioni, Daniele and Navarra, Alfredo}, title = {{12. Robust Algorithms and Price of Robustness in Shunting Problems}}, booktitle = {7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07)}, pages = {175--190}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-939897-04-0}, ISSN = {2190-6807}, year = {2007}, volume = {7}, editor = {Ahuja, Ravindra K. and Liebchen, Christian and Mesa, Juan A.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2007.1175}, URN = {urn:nbn:de:0030-drops-11755}, doi = {10.4230/OASIcs.ATMOS.2007.1175}, annote = {Keywords: } }

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**Published in:** OASIcs, Volume 7, 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07) (2007)

In railways systems the timetable is typically represented as a
weighted digraph on which itinerary queries are answered by
shortest path algorithms, usually running Dijkstra's algorithm.
Due to the continuously growing size of real-world graphs, there
is a constant need for faster algorithms and many techniques have
been devised to heuristically speed up Dijkstra's algorithm. One
of these techniques is the multi-level overlay graph, that
has been recently introduced and shown to be experimentally
efficient, especially when applied to timetable information.
In many practical application major disruptions to the normal
operation cannot be completely avoided because of the complexity
of the underlying systems. Timetable information
update after disruptions is considered one of the weakest points
in current railway systems, and this determines the need for an
effective online redesign and update of the shortest paths
information as a consequence of disruptions.
In this paper, we make a step forward toward this direction by
showing some theoretical properties of multi-level overlay graphs
that lead us to the definition of a new data structure for the
dynamic maintenance of a multi-level overlay graph of a given
graph G while weight decrease or weight increase operations are
performed on G. Our solution is theoretically faster than the
recomputation from scratch and allows fast queries.

Francesco Bruera, Serafino Cicerone, Gianlorenzo D'Angelo, Gabriele Di Stefano, and Daniele Frigioni. 15. Maintenance of Multi-level Overlay Graphs for Timetable Queries. In 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07). Open Access Series in Informatics (OASIcs), Volume 7, pp. 226-242, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{bruera_et_al:OASIcs.ATMOS.2007.1171, author = {Bruera, Francesco and Cicerone, Serafino and D'Angelo, Gianlorenzo and Di Stefano, Gabriele and Frigioni, Daniele}, title = {{15. Maintenance of Multi-level Overlay Graphs for Timetable Queries}}, booktitle = {7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07)}, pages = {226--242}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-939897-04-0}, ISSN = {2190-6807}, year = {2007}, volume = {7}, editor = {Ahuja, Ravindra K. and Liebchen, Christian and Mesa, Juan A.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2007.1171}, URN = {urn:nbn:de:0030-drops-11717}, doi = {10.4230/OASIcs.ATMOS.2007.1171}, annote = {Keywords: Timetable Queries, Speed-up techniques for shortest paths, Dynamic maintenance of shortest paths} }