DROPS

Volume

LIPIcs, Volume 103

17th International Symposium on Experimental Algorithms (SEA 2018)

SEA 2018, June 27-29, 2018, L'Aquila, Italy

Editors: Gianlorenzo D'Angelo

Volume

OASIcs, Volume 59

17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)

ATMOS 2017, September 7-8, 2017, Vienna, Austria

Editors: Gianlorenzo D'Angelo and Twan Dollevoet

Document

DOI: 10.4230/LIPIcs.ITCS.2026.80

FPT Approximations for Connected Maximum Coverage

Authors: Tanmay Inamdar, Satyabrata Jana, Madhumita Kundu, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract

We revisit connectivity-constrained coverage through a unifying model, Partial Connected Red-Blue Dominating Set (PartialConRBDS). Given a bipartite graph G = (R∪ B,E) with red vertices R and blue vertices B, an auxiliary connectivity graph G_{conn} on R, and integers k,t, the task is to find a set S ⊆ R with |S| ≤ k such that G_{conn}[S] is connected and S dominates at least t blue vertices. This formulation captures connected variants of Maximum Coverage [Hochbaum-Rao, Inf. Proc. Lett., 2020; D'Angelo-Delfaraz, AAMAS 2025], Partial Vertex Cover, and Partial Dominating Set [Khuller et al., SODA 2014; Lamprou et al., TCS 2021] via standard encodings. Limits to parameterized tractability. PartialConRBDS is W[1]-hard parameterized by k even under strong restrictions: it remains hard when G_{conn} is a clique or a star and the incidence graph G is 3-degenerate, or when G is K_{2,2}-free. Inapproximability. For every ε > 0, there is no polynomial-time (1, 1-1/e+ε)-approximation unless 𝖯 = NP. Moreover, under ETH, no algorithm running in f(k)⋅ n^{o(k)} time achieves an g(k)-approximation for k for any computable function g(⋅), or for any ε > 0, a (1-1/e+ε)-approximation for t. Graphical special cases. Partial Connected Dominating Set is W[2]-hard parameterized by k and inherits the same ETH-based f(k)⋅ n^{o(k)} inapproximability bound as above; Partial Connected Vertex Cover is W[1]-hard parameterized by k. These hardness boundaries delineate a natural "sweet spot" for study: within appropriate structural restrictions on the incidence graph, one can still aim for fine-grained (FPT) approximations. Our algorithms. We solve PartialConRBDS exactly by reducing it to Relaxed Directed Steiner Out-Tree in time (2e)^t ⋅ n^{𝒪(1)}. For biclique-free incidences (i.e., when G excludes K_{d,d} as an induced subgraph), we obtain two complementary parameterized schemes: - An Efficient Parameterized Approximation Scheme (EPAS) running in time 2^{𝒪(k² d/ε)}⋅ n^{𝒪(1)} that either returns a connected solution of size at most k covering at least (1-ε)t blue vertices, or correctly reports that no connected size-k solution covers t; and - A Parameterized Approximation Scheme (PAS) running in time 2^{𝒪(kd(k²+log d))}⋅ n^{𝒪(1/ε)} that either returns a connected solution of size at most (1+ε)k covering at least t blue vertices, or correctly reports that no connected size-k solution covers t. Together, these results chart the boundary between hardness and FPT-approximability for connectivity-constrained coverage.

Cite as

Tanmay Inamdar, Satyabrata Jana, Madhumita Kundu, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi. FPT Approximations for Connected Maximum Coverage. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 80:1-80:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{inamdar_et_al:LIPIcs.ITCS.2026.80,
  author =	{Inamdar, Tanmay and Jana, Satyabrata and Kundu, Madhumita and Lokshtanov, Daniel and Saurabh, Saket and Zehavi, Meirav},
  title =	{{FPT Approximations for Connected Maximum Coverage}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{80:1--80:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.80},
  URN =		{urn:nbn:de:0030-drops-253674},
  doi =		{10.4230/LIPIcs.ITCS.2026.80},
  annote =	{Keywords: Partial Dominating Set, Connectivity, Maximum Coverage, FPT Approximation, Fixed-parameter Tractability}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2025.75

Temporal Graph Realization with Bounded Stretch

Authors: George B. Mertzios, Hendrik Molter, Nils Morawietz, and Paul G. Spirakis

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract

A periodic temporal graph, in its simplest form, is a graph in which every edge appears exactly once in the first Δ time steps, and then it reappears recurrently every Δ time steps, where Δ is a given period length. This model offers a natural abstraction of transportation networks where each transportation link connects two destinations periodically. From a network design perspective, a crucial task is to assign the time-labels on the edges in a way that optimizes some criterion. In this paper we introduce a very natural optimality criterion that captures how the temporal distances of all vertex pairs are "stretched", compared to their physical distances, i.e. their distances in the underlying static (non-temporal) graph. Given a static graph G, the task is to assign to each edge one time-label between 1 and Δ such that, in the resulting periodic temporal graph with period Δ, the duration of the fastest temporal path from any vertex u to any other vertex v is at most α times the distance between u and v in G. Here, the value of α measures how much the shortest paths are allowed to be stretched once we assign the periodic time-labels. Our results span three different directions: First, we provide a series of approximation and NP-hardness results. Second, we provide approximation and fixed-parameter algorithms. Among them, we provide a simple polynomial-time algorithm (the radius-algorithm) which always guarantees an approximation strictly smaller than Δ, and which also computes the optimum stretch in some cases. Third, we consider a parameterized local search extension of the problem where we are given the temporal labeling of the graph, but we are allowed to change the time-labels of at most k edges; for this problem we prove that it is W[2]-hard but admits an XP algorithm with respect to k.

Cite as

George B. Mertzios, Hendrik Molter, Nils Morawietz, and Paul G. Spirakis. Temporal Graph Realization with Bounded Stretch. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 75:1-75:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mertzios_et_al:LIPIcs.MFCS.2025.75,
  author =	{Mertzios, George B. and Molter, Hendrik and Morawietz, Nils and Spirakis, Paul G.},
  title =	{{Temporal Graph Realization with Bounded Stretch}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{75:1--75:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.75},
  URN =		{urn:nbn:de:0030-drops-241829},
  doi =		{10.4230/LIPIcs.MFCS.2025.75},
  annote =	{Keywords: Temporal graph, periodic temporal labeling, fastest temporal path, graph realization, temporal connectivity, stretch}
}

Document

DOI: 10.4230/LIPIcs.SAND.2025.6

Dismountability in Temporal Cliques Revisited

Authors: Daniele Carnevale, Arnaud Casteigts, and Timothée Corsini

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract

A temporal graph is a graph whose edges are available only at certain points in time. It is temporally connected if the nodes can reach each other by paths that traverse the edges chronologically (temporal paths). Unlike static graphs, temporal graphs do not always admit small subsets of edges that preserve connectivity (temporal spanners) - there exist temporal graphs with Θ(n²) edges, all of which are critical. In the case of temporal cliques (the underlying graph is complete), spanners of size O(nlog n) are guaranteed. The original proof of this result by Casteigts et al. [ICALP 2019] combines a number of techniques, one of which is called dismountability. In a recent work, Angrick et al. [ESA 2024] simplified the proof and showed, among other things, that a one-sided version of dismountability can replace elegantly the second part of the proof. In this paper, we revisit methodically the dismountability principle. We start by characterizing the structure that a temporal clique must have if it is non 1-hop dismountable, then neither 1-hop nor 2-hop (i.e. non {1,2}-hop) dismountable, and finally non {1,2,3}-hop dismountable. It turns out that if a clique is k-hop dismountable for any other k, then it must also be {1,2,3}-hop dismountable, thus no additional structure can be obtained beyond this point. Interestingly, excluding 1-hop and 2-hop dismountability is already sufficient for reducing the spanner problem from cliques to extremally matched bicliques, where the O(nlog n) result is subsequently obtained. Put together with the strategy of Angrick et al., this entire result can now be recovered using only dismountability. An interesting by-product of our analysis is that any minimal counter-example to the existence of 4n spanners must satisfy the properties of non {1,2,3}-hop dismountable cliques. In the second part, we discuss further connections between dismountability and another technique called pivotability. In particular, we show that if a temporal clique is recursively k-hop dismountable, then it is also pivotable (and thus admits a 2n spanner, whatever k). We also study a family of labelings called full-range that forces both dismountability and pivotability. The latter gives some evidence that large lifetimes could be exploited more generally for the construction of spanners.

Cite as

Daniele Carnevale, Arnaud Casteigts, and Timothée Corsini. Dismountability in Temporal Cliques Revisited. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{carnevale_et_al:LIPIcs.SAND.2025.6,
  author =	{Carnevale, Daniele and Casteigts, Arnaud and Corsini, Timoth\'{e}e},
  title =	{{Dismountability in Temporal Cliques Revisited}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.6},
  URN =		{urn:nbn:de:0030-drops-230591},
  doi =		{10.4230/LIPIcs.SAND.2025.6},
  annote =	{Keywords: Dynamic networks, Temporal graphs, Reachability, Dismountability, Pivotability, Temporal spanners, Full-range graphs}
}

Document

DOI: 10.4230/LIPIcs.SAND.2025.3

Temporal Connectivity Augmentation

Authors: Thomas Bellitto, Jules Bouton Popper, and Bruno Escoffier

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract

Connectivity in temporal graphs relies on the notion of temporal paths, in which edges follow a chronological order (either strict or non-strict). In this work, we investigate the question of how to make a temporal graph connected. More precisely, we tackle the problem of finding, among a set of proposed temporal edges, the smallest subset such that its addition makes the graph temporally connected (TCA). We study the complexity of this problem and variants, under restricted lifespan of the graph, i.e. the maximum time step in the graph. Our main result on TCA is that for any fixed lifespan at least 2, it is NP-complete in both the strict and non-strict setting. We additionally provide a set of restrictions in the non-strict setting which makes the problem solvable in polynomial time and design an algorithm achieving this complexity. Interestingly, we prove that the source variant (making a given vertex a source in the augmented graph) is as difficult as TCA. On the opposite, we prove that the version where a list of connectivity demands has to be satisfied is solvable in polynomial time, when the size of the list is fixed. Finally, we highlight a variant of the previous case for which even with two pairs the problem is already NP-hard.

Cite as

Thomas Bellitto, Jules Bouton Popper, and Bruno Escoffier. Temporal Connectivity Augmentation. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bellitto_et_al:LIPIcs.SAND.2025.3,
  author =	{Bellitto, Thomas and Popper, Jules Bouton and Escoffier, Bruno},
  title =	{{Temporal Connectivity Augmentation}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{3:1--3:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.3},
  URN =		{urn:nbn:de:0030-drops-230565},
  doi =		{10.4230/LIPIcs.SAND.2025.3},
  annote =	{Keywords: Temporal graph, temporal connectivity}
}

Document

DOI: 10.4230/LIPIcs.SAND.2025.9

Spanner Enumeration for Temporal Graphs

Authors: Kazuhiro Kurita, Andrea Marino, Jason Schoeters, and Takeaki Uno

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract

A spanner of a temporal graph is a subset of edges that preserves connectivity over time between vertices. A minimal spanner is one in which no additional edges can be removed without breaking this connectivity. Our focus is on enumerating minimal spanners for a given temporal graph. We explore several variations of this problem based on the type of connectivity that must be maintained, ranging from one-to-all connectivity to one-to-all-to-one, many-to-all, and finally all-to-all connectivity. We establish that these problems become progressively harder: (i) We present a polynomial-delay enumeration algorithm for one-to-all connectivity; (ii) We prove Dual-hardness for both one-to-all-to-one and many-to-all connectivity, even in the restricted case of two-to-all; (iii) Finally, for all-to-all connectivity, we show that enumeration cannot be performed in output-polynomial time unless P = NP.

Cite as

Kazuhiro Kurita, Andrea Marino, Jason Schoeters, and Takeaki Uno. Spanner Enumeration for Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kurita_et_al:LIPIcs.SAND.2025.9,
  author =	{Kurita, Kazuhiro and Marino, Andrea and Schoeters, Jason and Uno, Takeaki},
  title =	{{Spanner Enumeration for Temporal Graphs}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.9},
  URN =		{urn:nbn:de:0030-drops-230621},
  doi =		{10.4230/LIPIcs.SAND.2025.9},
  annote =	{Keywords: temporal graphs, temporal spanners, one-to-all connectivity, all-to-all connectivity enumeration, NP-completeness, Dual-hardness, binary partition tree, flashlight search, polynomial delay}
}

Document

DOI: 10.4230/LIPIcs.SAND.2025.10

Fault Detection and Identification by Autonomous Mobile Robots

Authors: Stefano Clemente and Caterina Feletti

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract

The Look-Compute-Move model (LCM) is adopted to study swarms of mobile robots that have to solve a given problem. Robots are generally assumed to be autonomous, indistinguishable, anonymous, homogeneous and to move on the Euclidean plane. Different LCM sub-models have been theorized to study different settings and their computational power. Notably, the literature has focused on four base models (i.e., OBLOT, FSTA, FCOM, LUMI) that differ in memory and communication capabilities, and in different synchronization modes (e.g., fully synchronous FSYNCH, semi-synchronous SSYNCH). In this paper, we consider fault-prone models where robots can suffer from crash faults: each robot may irremediably stop working after an unpredictable time. We study the general Fault Detection (FD) problem which is solved by a swarm if it correctly detects whether a faulty robot exists in the swarm. The Fault Identification (FI) problem additionally requires identifying which robots are faulty. We consider 12 LCM sub-models (OBLOT, FSTA, FCOM, LUMI, combined with FSYNCH, SSYNCH, and the round-robin RROBIN) and we study the (im)possibility of designing reliable procedures to solve FD or FI. In particular, we propose three distributed algorithms so that a swarm can collectively solve FD under the models LUMI^FSYNCH, FCOM^FSYNCH, and LUMI^RROBIN.

Cite as

Stefano Clemente and Caterina Feletti. Fault Detection and Identification by Autonomous Mobile Robots. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{clemente_et_al:LIPIcs.SAND.2025.10,
  author =	{Clemente, Stefano and Feletti, Caterina},
  title =	{{Fault Detection and Identification by Autonomous Mobile Robots}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.10},
  URN =		{urn:nbn:de:0030-drops-230639},
  doi =		{10.4230/LIPIcs.SAND.2025.10},
  annote =	{Keywords: Autonomous mobile robots, Faulty robots, Look-Compute-Move, Fault detection, Fault identification, Round-robin}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2025.5

Edge-Minimum Walk of Modular Length in Polynomial Time

Authors: Antoine Amarilli, Benoît Groz, and Nicole Wein

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract

We study the problem of finding, in a directed graph, an st-walk of length r od q which is edge-minimum, i.e., uses the smallest number of distinct edges. Despite the vast literature on paths and cycles with modularity constraints, to the best of our knowledge we are the first to study this problem. Our main result is a polynomial-time algorithm that solves this task when r and q are constants. We also show how our proof technique gives an algorithm to solve a generalization of the well-known Directed Steiner Network problem, in which connections between endpoint pairs are required to satisfy modularity constraints on their length. Our algorithm is polynomial when the number of endpoint pairs and the modularity constraints on the pairs are constants. In this version of the article, proofs and examples are omitted because of space constraints. Detailed proofs are available in the full version [Antoine Amarilli et al., 2024].

Cite as

Antoine Amarilli, Benoît Groz, and Nicole Wein. Edge-Minimum Walk of Modular Length in Polynomial Time. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{amarilli_et_al:LIPIcs.ITCS.2025.5,
  author =	{Amarilli, Antoine and Groz, Beno\^{i}t and Wein, Nicole},
  title =	{{Edge-Minimum Walk of Modular Length in Polynomial Time}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{5:1--5:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.5},
  URN =		{urn:nbn:de:0030-drops-226330},
  doi =		{10.4230/LIPIcs.ITCS.2025.5},
  annote =	{Keywords: Directed Steiner Network, Modularity}
}

Document

DOI: 10.4230/LIPIcs.OPODIS.2024.12

Crash-Tolerant Perpetual Exploration with Myopic Luminous Robots on Rings

Authors: Fukuhito Ooshita, Naoki Kitamura, Ryota Eguchi, Michiko Inoue, Hirotsugu Kakugawa, Sayaka Kamei, Masahiro Shibata, and Yuichi Sudo

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract

We investigate crash-tolerant perpetual exploration algorithms by myopic luminous robots on ring networks. Myopic robots mean that they can observe nodes only within a certain fixed distance ϕ, and luminous robots mean that they have light devices that can emit a color from a set of colors. The goal of perpetual exploration is to ensure that robots, starting from specific initial positions and colors, move in such a way that every node is visited by at least one robot infinitely often. As a main contribution, we clarify the tight necessary and sufficient number of robots to realize perpetual exploration when at most f robots crash. In the fully synchronous model, we prove that f+2 robots are necessary and sufficient for any ϕ ≥ 1. In the semi-synchronous and asynchronous models, we prove that 3f+3 (resp., 2f+2) robots are necessary and sufficient if ϕ = 1 (resp., ϕ ≥ 2).

Cite as

Fukuhito Ooshita, Naoki Kitamura, Ryota Eguchi, Michiko Inoue, Hirotsugu Kakugawa, Sayaka Kamei, Masahiro Shibata, and Yuichi Sudo. Crash-Tolerant Perpetual Exploration with Myopic Luminous Robots on Rings. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ooshita_et_al:LIPIcs.OPODIS.2024.12,
  author =	{Ooshita, Fukuhito and Kitamura, Naoki and Eguchi, Ryota and Inoue, Michiko and Kakugawa, Hirotsugu and Kamei, Sayaka and Shibata, Masahiro and Sudo, Yuichi},
  title =	{{Crash-Tolerant Perpetual Exploration with Myopic Luminous Robots on Rings}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.12},
  URN =		{urn:nbn:de:0030-drops-225486},
  doi =		{10.4230/LIPIcs.OPODIS.2024.12},
  annote =	{Keywords: mobile robots, crash faults, LCM model, exploration}
}

@InProceedings{ooshita_et_al:LIPIcs.OPODIS.2024.12,
  author =	{Ooshita, Fukuhito and Kitamura, Naoki and Eguchi, Ryota and Inoue, Michiko and Kakugawa, Hirotsugu and Kamei, Sayaka and Shibata, Masahiro and Sudo, Yuichi},
  title =	{{Crash-Tolerant Perpetual Exploration with Myopic Luminous Robots on Rings}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.12},
  URN =		{urn:nbn:de:0030-drops-225486},
  doi =		{10.4230/LIPIcs.OPODIS.2024.12},
  annote =	{Keywords: mobile robots, crash faults, LCM model, exploration}
}

Document

DOI: 10.4230/OASIcs.ATMOS.2024.7

Improved Algorithms for the Capacitated Team Orienteering Problem

Authors: Gianlorenzo D'Angelo, Mattia D'Emidio, Esmaeil Delfaraz, and Gabriele Di Stefano

Published in: OASIcs, Volume 123, 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)

Abstract

We study the Capacitated Team Orienteering Problem, where a fleet of vehicles with capacities have to meet customers with known demands and prizes for a single commodity. The objective is to maximize the total prize and to assign a sequence of customers to each vehicle while keeping the total distance traveled within a given budget and such that the total demand served by each vehicle does not exceed its capacity. The problem has been widely studied both from a theoretical and a practical point of view. The contribution of this paper is twofold: (1) We advance the theoretical knowledge on the problem by providing new approximation algorithms that achieve, under some natural assumption, improved approximation ratios compared to the current best algorithms; (2) We propose four efficient heuristics that outperform the current state-of-the-art practical methods in the sense that they compute solutions that collect nearly the same prize in a significantly smaller running time. We also experimentally test the scalability of the new heuristics, showing that their running time increases approximately linearly with the size of the input, allowing us to process large graphs which were not possible to analyze before.

Cite as

Gianlorenzo D'Angelo, Mattia D'Emidio, Esmaeil Delfaraz, and Gabriele Di Stefano. Improved Algorithms for the Capacitated Team Orienteering Problem. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dangelo_et_al:OASIcs.ATMOS.2024.7,
  author =	{D'Angelo, Gianlorenzo and D'Emidio, Mattia and Delfaraz, Esmaeil and Di Stefano, Gabriele},
  title =	{{Improved Algorithms for the Capacitated Team Orienteering Problem}},
  booktitle =	{24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
  pages =	{7:1--7:17},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-350-8},
  ISSN =	{2190-6807},
  year =	{2024},
  volume =	{123},
  editor =	{Bouman, Paul C. and Kontogiannis, Spyros C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.7},
  URN =		{urn:nbn:de:0030-drops-211957},
  doi =		{10.4230/OASIcs.ATMOS.2024.7},
  annote =	{Keywords: Vehicle Routing, Approximation algorithms, Algorithm Engineering}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2022.9

Budgeted Out-Tree Maximization with Submodular Prizes

Authors: Gianlorenzo D'Angelo, Esmaeil Delfaraz, and Hugo Gilbert

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

Abstract

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.

Cite as

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

DOI: 10.4230/LIPIcs.ESA.2022.19

Sparse Temporal Spanners with Low Stretch

Authors: Davide Bilò, Gianlorenzo D'Angelo, Luciano Gualà, Stefano Leucci, and Mirko Rossi

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

Abstract

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.

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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

DOI: 10.4230/LIPIcs.STACS.2022.12

Single-Source Shortest p-Disjoint Paths: Fast Computation and Sparse Preservers

Authors: Davide Bilò, Gianlorenzo D'Angelo, Luciano Gualà, Stefano Leucci, Guido Proietti, and Mirko Rossi

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

Abstract

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.

Cite as

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}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2021.59

Improved Approximation Factor for Adaptive Influence Maximization via Simple Greedy Strategies

Authors: Gianlorenzo D'Angelo, Debashmita Poddar, and Cosimo Vinci

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

Abstract

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.

Cite as

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}
}

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