8 Search Results for "Viennot, Laurent"

Document
DOI: 10.4230/LIPIcs.STACS.2024.13
Temporalizing Digraphs via Linear-Size Balanced Bi-Trees

Authors: Stéphane Bessy, Stéphan Thomassé, and Laurent Viennot

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
In a directed graph D on vertex set v₁,… ,v_n, a forward arc is an arc v_iv_j where i < j. A pair v_i,v_j is forward connected if there is a directed path from v_i to v_j consisting of forward arcs. In the Forward Connected Pairs Problem (FCPP), the input is a strongly connected digraph D, and the output is the maximum number of forward connected pairs in some vertex enumeration of D. We show that FCPP is in APX, as one can efficiently enumerate the vertices of D in order to achieve a quadratic number of forward connected pairs. For this, we construct a linear size balanced bi-tree T (an out-branching and an in-branching with same size and same root which are vertex disjoint in the sense that they share no vertex apart from their common root). The existence of such a T was left as an open problem (Brunelli, Crescenzi, Viennot, Networks 2023) motivated by the study of temporal paths in temporal networks. More precisely, T can be constructed in quadratic time (in the number of vertices) and has size at least n/3. The algorithm involves a particular depth-first search tree (Left-DFS) of independent interest, and shows that every strongly connected directed graph has a balanced separator which is a circuit. Remarkably, in the request version RFCPP of FCPP, where the input is a strong digraph D and a set of requests R consisting of pairs {x_i,y_i}, there is no constant c > 0 such that one can always find an enumeration realizing c.|R| forward connected pairs {x_i,y_i} (in either direction).
Cite as

Stéphane Bessy, Stéphan Thomassé, and Laurent Viennot. Temporalizing Digraphs via Linear-Size Balanced Bi-Trees. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 13:1-13:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bessy_et_al:LIPIcs.STACS.2024.13,
  author =	{Bessy, St\'{e}phane and Thomass\'{e}, St\'{e}phan and Viennot, Laurent},
  title =	{{Temporalizing Digraphs via Linear-Size Balanced Bi-Trees}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{13:1--13:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.13},
  URN =		{urn:nbn:de:0030-drops-197235},
  doi =		{10.4230/LIPIcs.STACS.2024.13},
  annote =	{Keywords: digraph, temporal graph, temporalization, bi-tree, #1\{in-branching, out-branching, in-tree, out-tree\}, forward connected pairs, left-maximal DFS}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.35
Collective Tree Exploration via Potential Function Method

Authors: Romain Cosson and Laurent Massoulié

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
We study the problem of collective tree exploration (CTE) in which a team of k agents is tasked to traverse all the edges of an unknown tree as fast as possible, assuming complete communication between the agents [FGKP06]. In this paper, we present an algorithm performing collective tree exploration in 2n/k+𝒪(kD) rounds, where n is the number of nodes in the tree, and D is the tree depth. This leads to a competitive ratio of 𝒪(√k), the first polynomial improvement over the 𝒪(k) ratio of depth-first search. Our analysis holds for an asynchronous generalization of collective tree exploration. It relies on a game with robots at the leaves of a continuously growing tree extending the "tree-mining game" of [C23] and resembling the "evolving tree game" of [BCR22]. Another surprising consequence of our results is the existence of algorithms {𝒜_k}_{k ∈ ℕ} for layered tree traversal (LTT) with cost at most 2L/k+𝒪(kD), where L is the sum of all edge lengths. For the case of layered trees of width w and unit edge lengths, our guarantee is thus in 𝒪(√wD).
Cite as

Romain Cosson and Laurent Massoulié. Collective Tree Exploration via Potential Function Method. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 35:1-35:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cosson_et_al:LIPIcs.ITCS.2024.35,
  author =	{Cosson, Romain and Massouli\'{e}, Laurent},
  title =	{{Collective Tree Exploration via Potential Function Method}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{35:1--35:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.35},
  URN =		{urn:nbn:de:0030-drops-195638},
  doi =		{10.4230/LIPIcs.ITCS.2024.35},
  annote =	{Keywords: collective exploration, online algorithms, evolving tree, competitive analysis}
}
Document
DOI: 10.4230/LIPIcs.DISC.2023.14
Efficient Collaborative Tree Exploration with Breadth-First Depth-Next

Authors: Romain Cosson, Laurent Massoulié, and Laurent Viennot

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)

Abstract
We study the problem of collaborative tree exploration introduced by Fraigniaud, Gasieniec, Kowalski, and Pelc [Pierre Fraigniaud et al., 2006] where a team of k agents is tasked to collectively go through all the edges of an unknown tree as fast as possible and return to the root. Denoting by n the total number of nodes and by D the tree depth, the 𝒪(n/log(k)+D) algorithm of [Pierre Fraigniaud et al., 2006] achieves a 𝒪(k/log(k)) competitive ratio with respect to the cost of offline exploration which is at least max{{2n/k,2D}}. Brass, Cabrera-Mora, Gasparri, and Xiao [Peter Brass et al., 2011] study an alternative performance criterion, the competitive overhead with respect to the cost of offline exploration, with their 2n/k+𝒪((D+k)^k) guarantee. In this paper, we introduce "Breadth-First Depth-Next" (BFDN), a novel and simple algorithm that performs collaborative tree exploration in 2n/k+𝒪(D²log(k)) rounds, thus outperforming [Peter Brass et al., 2011] for all values of (n,D,k) and being order-optimal for trees of depth D = o(√n). Our analysis relies on a two-player game reflecting a problem of online resource allocation that could be of independent interest. We extend the guarantees of BFDN to: scenarios with limited memory and communication, adversarial setups where robots can be blocked, and exploration of classes of non-tree graphs. Finally, we provide a recursive version of BFDN with a runtime of 𝒪_𝓁(n/k^{1/𝓁}+log(k) D^{1+1/𝓁}) for parameter 𝓁 ≥ 1, thereby improving performance for trees with large depth.
Cite as

Romain Cosson, Laurent Massoulié, and Laurent Viennot. Efficient Collaborative Tree Exploration with Breadth-First Depth-Next. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cosson_et_al:LIPIcs.DISC.2023.14,
  author =	{Cosson, Romain and Massouli\'{e}, Laurent and Viennot, Laurent},
  title =	{{Efficient Collaborative Tree Exploration with Breadth-First Depth-Next}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{14:1--14:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.14},
  URN =		{urn:nbn:de:0030-drops-191409},
  doi =		{10.4230/LIPIcs.DISC.2023.14},
  annote =	{Keywords: collaborative exploration, online algorithms, trees, adversarial game, competitive analysis, robot swarms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.37
Revisiting the Random Subset Sum Problem

Authors: Arthur Carvalho Walraven Da Cunha, Francesco d'Amore, Frédéric Giroire, Hicham Lesfari, Emanuele Natale, and Laurent Viennot

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
The average properties of the well-known Subset Sum Problem can be studied by means of its randomised version, where we are given a target value z, random variables X_1, …, X_n, and an error parameter ε > 0, and we seek a subset of the X_is whose sum approximates z up to error ε. In this setup, it has been shown that, under mild assumptions on the distribution of the random variables, a sample of size 𝒪(log(1/ε)) suffices to obtain, with high probability, approximations for all values in [-1/2, 1/2]. Recently, this result has been rediscovered outside the algorithms community, enabling meaningful progress in other fields. In this work, we present an alternative proof for this theorem, with a more direct approach and resourcing to more elementary tools.
Cite as

Arthur Carvalho Walraven Da Cunha, Francesco d'Amore, Frédéric Giroire, Hicham Lesfari, Emanuele Natale, and Laurent Viennot. Revisiting the Random Subset Sum Problem. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 37:1-37:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dacunha_et_al:LIPIcs.ESA.2023.37,
  author =	{Da Cunha, Arthur Carvalho Walraven and d'Amore, Francesco and Giroire, Fr\'{e}d\'{e}ric and Lesfari, Hicham and Natale, Emanuele and Viennot, Laurent},
  title =	{{Revisiting the Random Subset Sum Problem}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{37:1--37:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.37},
  URN =		{urn:nbn:de:0030-drops-186905},
  doi =		{10.4230/LIPIcs.ESA.2023.37},
  annote =	{Keywords: Random subset sum, Randomised method, Subset-sum, Combinatorics}
}
Document
DOI: 10.4230/LIPIcs.SAND.2023.4
Computing Temporal Reachability Under Waiting-Time Constraints in Linear Time

Authors: Filippo Brunelli and Laurent Viennot

Published in: LIPIcs, Volume 257, 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)

Abstract
This paper proposes a simple algorithm for computing single-source reachability in a temporal graph under waiting-time constraints, that is when waiting at each node is bounded by some time constraints. Given a space-time representation of a temporal graph, and a source node, the algorithm computes in linear-time which nodes and temporal edges are reachable through a constrained temporal walk from the source.
Cite as

Filippo Brunelli and Laurent Viennot. Computing Temporal Reachability Under Waiting-Time Constraints in Linear Time. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 4:1-4:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{brunelli_et_al:LIPIcs.SAND.2023.4,
  author =	{Brunelli, Filippo and Viennot, Laurent},
  title =	{{Computing Temporal Reachability Under Waiting-Time Constraints in Linear Time}},
  booktitle =	{2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)},
  pages =	{4:1--4:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-275-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{257},
  editor =	{Doty, David and Spirakis, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2023.4},
  URN =		{urn:nbn:de:0030-drops-179402},
  doi =		{10.4230/LIPIcs.SAND.2023.4},
  annote =	{Keywords: temporal reachability, temporal graph, temporal path, temporal walk, waiting-time constraints, restless temporal walk, linear time}
}
Document
DOI: 10.4230/LIPIcs.SEA.2021.11
On Computing the Diameter of (Weighted) Link Streams

Authors: Marco Calamai, Pierluigi Crescenzi, and Andrea Marino

Published in: LIPIcs, Volume 190, 19th International Symposium on Experimental Algorithms (SEA 2021)

Abstract
A weighted link stream is a pair (V,𝔼) comprising V, the set of nodes, and 𝔼, the list of temporal edges (u,v,t,λ), where u,v are two nodes in V, t is the starting time of the temporal edge, and λ is its travel time. By making use of this model, different notions of diameter can be defined, which refer to the following distances: earliest arrival time, latest departure time, fastest time, and shortest time. After proving that any of these diameters cannot be computed in time sub-quadratic with respect to the number of temporal edges, we propose different algorithms (inspired by the approach used for computing the diameter of graphs) which allow us to compute, in practice very efficiently, the diameter of quite large real-world weighted link stream for several definitions of the diameter. Indeed, all the proposed algorithms require very often a very low number of single source (or target) best path computations. We verify the effectiveness of our approach by means of an extensive set of experiments on real-world link streams. We also experimentally prove that the temporal version of the well-known 2-sweep technique, for computing a lower bound on the diameter of a graph, is quite effective in the case of weighted link stream, by returning very often tight bounds.
Cite as

Marco Calamai, Pierluigi Crescenzi, and Andrea Marino. On Computing the Diameter of (Weighted) Link Streams. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{calamai_et_al:LIPIcs.SEA.2021.11,
  author =	{Calamai, Marco and Crescenzi, Pierluigi and Marino, Andrea},
  title =	{{On Computing the Diameter of (Weighted) Link Streams}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{11:1--11:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-185-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{190},
  editor =	{Coudert, David and Natale, Emanuele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.11},
  URN =		{urn:nbn:de:0030-drops-137836},
  doi =		{10.4230/LIPIcs.SEA.2021.11},
  annote =	{Keywords: Temporal graph, shortest path, diameter}
}
Document
Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management
DOI: 10.4230/LIPIcs.ICALP.2019.143
Exploiting Hopsets: Improved Distance Oracles for Graphs of Constant Highway Dimension and Beyond

Authors: Siddharth Gupta, Adrian Kosowski, and Laurent Viennot

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

Abstract
For fixed h >= 2, we consider the task of adding to a graph G a set of weighted shortcut edges on the same vertex set, such that the length of a shortest h-hop path between any pair of vertices in the augmented graph is exactly the same as the original distance between these vertices in G. A set of shortcut edges with this property is called an exact h-hopset and may be applied in processing distance queries on graph G. In particular, a 2-hopset directly corresponds to a distributed distance oracle known as a hub labeling. In this work, we explore centralized distance oracles based on 3-hopsets and display their advantages in several practical scenarios. In particular, for graphs of constant highway dimension, and more generally for graphs of constant skeleton dimension, we show that 3-hopsets require exponentially fewer shortcuts per node than any previously described distance oracle, and also offer a speedup in query time when compared to simple oracles based on a direct application of 2-hopsets. Finally, we consider the problem of computing minimum-size h-hopset (for any h >= 2) for a given graph G, showing a polylogarithmic-factor approximation for the case of unique shortest path graphs. When h=3, for a given bound on the space used by the distance oracle, we provide a construction of hopset achieving polylog approximation both for space and query time compared to the optimal 3-hopset oracle given the space bound.
Cite as

Siddharth Gupta, Adrian Kosowski, and Laurent Viennot. Exploiting Hopsets: Improved Distance Oracles for Graphs of Constant Highway Dimension and Beyond. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 143:1-143:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{gupta_et_al:LIPIcs.ICALP.2019.143,
  author =	{Gupta, Siddharth and Kosowski, Adrian and Viennot, Laurent},
  title =	{{Exploiting Hopsets: Improved Distance Oracles for Graphs of Constant Highway Dimension and Beyond}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{143:1--143:15},
  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.2019.143},
  URN =		{urn:nbn:de:0030-drops-107199},
  doi =		{10.4230/LIPIcs.ICALP.2019.143},
  annote =	{Keywords: Hopsets, Distance Oracles, Graph Algorithms, Data Structures}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2017.15
Decomposing a Graph into Shortest Paths with Bounded Eccentricity

Authors: Etienne Birmelé, Fabien de Montgolfier, Léo Planche, and Laurent Viennot

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)

Abstract
We introduce the problem of hub-laminar decomposition which generalizes that of computing a shortest path with minimum eccentricity (MESP). Intuitively, it consists in decomposing a graph into several paths that collectively have small eccentricity and meet only near their extremities. The problem is related to computing an isometric cycle with minimum eccentricity (MEIC). It is also linked to DNA reconstitution in the context of metagenomics in biology. We show that a graph having such a decomposition with long enough paths can be decomposed in polynomial time with approximated guaranties on the parameters of the decomposition. Moreover, such a decomposition with few paths allows to compute a compact representation of distances with additive distortion. We also show that having an isometric cycle with small eccentricity is related to the possibility of embedding the graph in a cycle with low distortion.
Cite as

Etienne Birmelé, Fabien de Montgolfier, Léo Planche, and Laurent Viennot. Decomposing a Graph into Shortest Paths with Bounded Eccentricity. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 15:1-15:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{birmele_et_al:LIPIcs.ISAAC.2017.15,
  author =	{Birmel\'{e}, Etienne and de Montgolfier, Fabien and Planche, L\'{e}o and Viennot, Laurent},
  title =	{{Decomposing a Graph into Shortest Paths with Bounded Eccentricity}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{15:1--15:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.15},
  URN =		{urn:nbn:de:0030-drops-82621},
  doi =		{10.4230/LIPIcs.ISAAC.2017.15},
  annote =	{Keywords: Graph Decomposition, Graph Clustering, Distance Labeling, BFS, MESP}
}
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