41 Search Results for "Natale, Emanuele"

Volume

LIPIcs, Volume 190

19th International Symposium on Experimental Algorithms (SEA 2021)

SEA 2021, June 7-9, 2021, Nice, France

Editors: David Coudert and Emanuele Natale

Document
DOI: 10.4230/LIPIcs.STACS.2026.6
Threshold-Driven Streaming Graph: Expansion and Rumor Spreading

Authors: Flora Angileri, Andrea Clementi, Emanuele Natale, Michele Salvi, and Isabella Ziccardi

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
A randomized distributed algorithm called RAES was introduced in [Becchetti et al., 2020] to extract a bounded-degree expander from a dense n-vertex expander graph G = (V, E). The algorithm relies on a simple threshold-based procedure. A key assumption in [Becchetti et al., 2020] is that the input graph G is static - i.e., both its vertex set V and edge set E remain unchanged throughout the process - while the analysis of raes in dynamic models is left as a major open question. In this work, we investigate the behavior of RAES under a dynamic graph model induced by a streaming node-churn process (also known as the sliding window model), where, at each discrete round, a new node joins the graph and the oldest node departs. This process yields a bounded-degree dynamic graph 𝒢 = {G_t = (V_t, E_t) : t ∈ ℕ} that captures essential characteristics of peer-to-peer networks - specifically, node churn and threshold on the number of connections each node can manage. We prove that every snapshot G_t in the dynamic graph sequence has good expansion properties with high probability. Furthermore, we leverage this property to establish a logarithmic upper bound on the completion time of the well-known PUSH and PULL rumor spreading protocols over the dynamic graph 𝒢.
Cite as

Flora Angileri, Andrea Clementi, Emanuele Natale, Michele Salvi, and Isabella Ziccardi. Threshold-Driven Streaming Graph: Expansion and Rumor Spreading. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 6:1-6:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{angileri_et_al:LIPIcs.STACS.2026.6,
  author =	{Angileri, Flora and Clementi, Andrea and Natale, Emanuele and Salvi, Michele and Ziccardi, Isabella},
  title =	{{Threshold-Driven Streaming Graph: Expansion and Rumor Spreading}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{6:1--6:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.6},
  URN =		{urn:nbn:de:0030-drops-254957},
  doi =		{10.4230/LIPIcs.STACS.2026.6},
  annote =	{Keywords: Distributed Algorithms, Randomized Algorithms, Dynamic Random Graphs, Graph Expansion, Rumor Spreading}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.27
On the h-Majority Dynamics with Many Opinions

Authors: Francesco d'Amore, Niccolò D'Archivio, George Giakkoupis, and Emanuele Natale

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
We present the first upper bound on the convergence time to consensus of the well-known h-majority dynamics with k opinions, in the synchronous setting, for h and k that are both non-constant values. We suppose that, at the beginning of the process, there is some initial additive bias towards some plurality opinion, that is, there is an opinion that is supported by x nodes while any other opinion is supported by strictly fewer nodes. We prove that, with high probability, if the bias is ω(√x) and the initial plurality opinion is supported by at least x = ω(log n) nodes, then the process converges to plurality consensus in O(log n) rounds whenever h = ω(n log n / x). A main corollary is the following: if k = o(n / log n) and the process starts from an almost-balanced configuration with an initial bias of magnitude ω(√{n/k}) towards the initial plurality opinion, then any function h = ω(k log n) suffices to guarantee convergence to consensus in O(log n) rounds, with high probability. Our upper bound shows that the lower bound of Ω(k / h²) rounds to reach consensus given by Becchetti et al. (2017) cannot be pushed further than Ω̃(k / h). Moreover, the bias we require is asymptotically smaller than the Ω(√{nlog n}) bias that guarantees plurality consensus in the 3-majority dynamics: in our case, the required bias is at most any (arbitrarily small) function in ω(√x) for any value of k ≥ 2.
Cite as

Francesco d'Amore, Niccolò D'Archivio, George Giakkoupis, and Emanuele Natale. On the h-Majority Dynamics with Many Opinions. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 27:1-27:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{damore_et_al:LIPIcs.DISC.2025.27,
  author =	{d'Amore, Francesco and D'Archivio, Niccol\`{o} and Giakkoupis, George and Natale, Emanuele},
  title =	{{On the h-Majority Dynamics with Many Opinions}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{27:1--27:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.27},
  URN =		{urn:nbn:de:0030-drops-248448},
  doi =		{10.4230/LIPIcs.DISC.2025.27},
  annote =	{Keywords: Distributed Algorithms, Randomized Algorithms, Markov Chains, Consensus Problem, Opinion dynamics, Plurality Consensus}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2025.53
Brief Announcement: Maintaining a Bounded Degree Expander in Dynamic Peer-To-Peer Networks

Authors: Antonio Cruciani

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
We study the problem of maintaining robust and sparse overlay networks in fully distributed settings where nodes continuously join and leave the system. This scenario closely models real-world unstructured peer-to-peer networks, where maintaining a well-connected yet low-degree communication graph is crucial. We generalize a recent protocol by Becchetti et al. [SODA 2020] that relies on a simple randomized connection strategy to build an expander topology with high probability to a dynamic networks with churn setting. In this work, the network dynamism is governed by an oblivious adversary that controls which nodes join and leave the system in each round. The adversary has full knowledge of the system and unbounded computational power, but cannot see the random choices made by the protocol. Our analysis builds on the framework of Augustine et al. [FOCS 2015], and shows that our distributed algorithm maintains a constant-degree expander graph with high probability, despite a continuous adversarial churn with a rate of up to 𝒪(n/polylog(n)) per round, where n is the stable network size. The protocol and proof techniques are not new, but together they resolve a specific open problem raised in prior work. The result is a simple, fully distributed, and churn-resilient protocol with provable guarantees that align with observed empirical behavior.
Cite as

Antonio Cruciani. Brief Announcement: Maintaining a Bounded Degree Expander in Dynamic Peer-To-Peer Networks. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 53:1-53:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cruciani:LIPIcs.DISC.2025.53,
  author =	{Cruciani, Antonio},
  title =	{{Brief Announcement: Maintaining a Bounded Degree Expander in Dynamic Peer-To-Peer Networks}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{53:1--53:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.53},
  URN =		{urn:nbn:de:0030-drops-248691},
  doi =		{10.4230/LIPIcs.DISC.2025.53},
  annote =	{Keywords: Peer-to-peer network, dynamic network, churn, distributed algorithm, randomized algorithm}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2025.60
Brief Announcement: Distributed Sparsest Cut via Eigenvalue Estimation

Authors: Yannic Maus and Tijn de Vos

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
We give new, improved bounds for approximating the sparsest cut value or in other words the conductance ϕ of a graph in the CONGEST model. As our main result, we present an algorithm running in O(log² n/ϕ) rounds in which every vertex outputs a value ̃ ϕ satisfying ϕ ≤ ̃ ϕ ≤ √{2.01ϕ}. In most regimes, our algorithm improves significantly over the previously fastest algorithm for the problem [Chen, Meierhans, Probst Gutenberg, Saranurak; SODA 25]. Additionally, our result generalizes to k-way conductance. We obtain these results, by approximating the eigenvalues of the normalized Laplacian matrix L: = I-Deg^{-1/2}ADeg^ {-1/2}, where, A is the adjacency matrix and Deg is the diagonal matrix with the weighted degrees on the diagonal. We show our algorithms are near-optimal by proving a lower bound for computing the smallest non-trivial eigenvalue of L, even in the stronger LOCAL model The previous state of the art sparsest cut algorithm is in the technical realm of expander decompositions. Our algorithms, on the other hand, are relatively simple and easy to implement. At the core, they rely on the well-known power method, which comes down to repeatedly multiplying the Laplacian with a vector. This operation can be performed in a single round in the CONGEST model. All our algorithms apply to weighted, undirected graphs. Our lower bounds apply even in unweighted graphs.
Cite as

Yannic Maus and Tijn de Vos. Brief Announcement: Distributed Sparsest Cut via Eigenvalue Estimation. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 60:1-60:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{maus_et_al:LIPIcs.DISC.2025.60,
  author =	{Maus, Yannic and de Vos, Tijn},
  title =	{{Brief Announcement: Distributed Sparsest Cut via Eigenvalue Estimation}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{60:1--60:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.60},
  URN =		{urn:nbn:de:0030-drops-248763},
  doi =		{10.4230/LIPIcs.DISC.2025.60},
  annote =	{Keywords: CONGEST, Sparsest Cut, Laplacian, Eigenvalues, Spectral Graph Theory}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.8
A Simple Integer Successor-Delete Data Structure

Authors: Gerth Stølting Brodal

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract
We consider a simple decremental data structure for maintaining a set of integers, that supports initializing the set to {1,2,…,n} followed by d deletions and s successor queries in arbitrary order in total 𝒪(n+d+s⋅(1+log_{max(2,s/n)} min(s,n))) time. The data structure consists of a single array of n integers. A straightforward modification allows the data structure to also support p predecessor and r range queries, with a total output k, in total 𝒪(n+d+k+q ⋅ (1+log_{max(2,q/n)} min(q,n))) time, where q = s+p+r. The data structure is essentially a special case of the classic union-find data structure with path compression but with unweighted linking (i.e., without linking by rank or size), that is known to achieve logarithmic amortized time bounds (Tarjan and van Leeuwen, 1984). In this paper we study the efficiency of this simple data structure, and compare it to other, theoretically superior, data structures.
Cite as

Gerth Stølting Brodal. A Simple Integer Successor-Delete Data Structure. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{brodal:LIPIcs.SEA.2025.8,
  author =	{Brodal, Gerth St{\o}lting},
  title =	{{A Simple Integer Successor-Delete Data Structure}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.8},
  URN =		{urn:nbn:de:0030-drops-232461},
  doi =		{10.4230/LIPIcs.SEA.2025.8},
  annote =	{Keywords: Successor queries, deletions, interval union-find, union-find}
}
Document
Survey
DOI: 10.4230/TGDK.1.1.11
How Does Knowledge Evolve in Open Knowledge Graphs?

Authors: Axel Polleres, Romana Pernisch, Angela Bonifati, Daniele Dell'Aglio, Daniil Dobriy, Stefania Dumbrava, Lorena Etcheverry, Nicolas Ferranti, Katja Hose, Ernesto Jiménez-Ruiz, Matteo Lissandrini, Ansgar Scherp, Riccardo Tommasini, and Johannes Wachs

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract
Openly available, collaboratively edited Knowledge Graphs (KGs) are key platforms for the collective management of evolving knowledge. The present work aims t o provide an analysis of the obstacles related to investigating and processing specifically this central aspect of evolution in KGs. To this end, we discuss (i) the dimensions of evolution in KGs, (ii) the observability of evolution in existing, open, collaboratively constructed Knowledge Graphs over time, and (iii) possible metrics to analyse this evolution. We provide an overview of relevant state-of-the-art research, ranging from metrics developed for Knowledge Graphs specifically to potential methods from related fields such as network science. Additionally, we discuss technical approaches - and their current limitations - related to storing, analysing and processing large and evolving KGs in terms of handling typical KG downstream tasks.
Cite as

Axel Polleres, Romana Pernisch, Angela Bonifati, Daniele Dell'Aglio, Daniil Dobriy, Stefania Dumbrava, Lorena Etcheverry, Nicolas Ferranti, Katja Hose, Ernesto Jiménez-Ruiz, Matteo Lissandrini, Ansgar Scherp, Riccardo Tommasini, and Johannes Wachs. How Does Knowledge Evolve in Open Knowledge Graphs?. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 11:1-11:59, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{polleres_et_al:TGDK.1.1.11,
  author =	{Polleres, Axel and Pernisch, Romana and Bonifati, Angela and Dell'Aglio, Daniele and Dobriy, Daniil and Dumbrava, Stefania and Etcheverry, Lorena and Ferranti, Nicolas and Hose, Katja and Jim\'{e}nez-Ruiz, Ernesto and Lissandrini, Matteo and Scherp, Ansgar and Tommasini, Riccardo and Wachs, Johannes},
  title =	{{How Does Knowledge Evolve in Open Knowledge Graphs?}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{11:1--11:59},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.11},
  URN =		{urn:nbn:de:0030-drops-194855},
  doi =		{10.4230/TGDK.1.1.11},
  annote =	{Keywords: KG evolution, temporal KG, versioned KG, dynamic KG}
}
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.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
Complete Volume
DOI: 10.4230/LIPIcs.SEA.2021
LIPIcs, Volume 190, SEA 2021, Complete Volume

Authors: David Coudert and Emanuele Natale

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

Abstract
LIPIcs, Volume 190, SEA 2021, Complete Volume
Cite as

19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 1-434, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@Proceedings{coudert_et_al:LIPIcs.SEA.2021,
  title =	{{LIPIcs, Volume 190, SEA 2021, Complete Volume}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{1--434},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021},
  URN =		{urn:nbn:de:0030-drops-137716},
  doi =		{10.4230/LIPIcs.SEA.2021},
  annote =	{Keywords: LIPIcs, Volume 190, SEA 2021, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.SEA.2021.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: David Coudert and Emanuele Natale

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

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{coudert_et_al:LIPIcs.SEA.2021.0,
  author =	{Coudert, David and Natale, Emanuele},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{0:i--0:xii},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.0},
  URN =		{urn:nbn:de:0030-drops-137722},
  doi =		{10.4230/LIPIcs.SEA.2021.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.SEA.2021.1
Engineering Nearly Linear-Time Algorithms for Small Vertex Connectivity

Authors: Max Franck and Sorrachai Yingchareonthawornchai

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

Abstract
Vertex connectivity is a well-studied concept in graph theory with numerous applications. A graph is k-connected if it remains connected after removing any k-1 vertices. The vertex connectivity of a graph is the maximum k such that the graph is k-connected. There is a long history of algorithmic development for efficiently computing vertex connectivity. Recently, two near linear-time algorithms for small k were introduced by [Forster et al. SODA 2020]. Prior to that, the best known algorithm was one by [Henzinger et al. FOCS'96] with quadratic running time when k is small. In this paper, we study the practical performance of the algorithms by Forster et al. In addition, we introduce a new heuristic on a key subroutine called local cut detection, which we call degree counting. We prove that the new heuristic improves space-efficiency (which can be good for caching purposes) and allows the subroutine to terminate earlier. According to experimental results on random graphs with planted vertex cuts, random hyperbolic graphs, and real world graphs with vertex connectivity between 4 and 15, the degree counting heuristic offers a factor of 2-4 speedup over the original non-degree counting version for most of our data. It also outperforms the previous state-of-the-art algorithm by Henzinger et al. even on relatively small graphs.
Cite as

Max Franck and Sorrachai Yingchareonthawornchai. Engineering Nearly Linear-Time Algorithms for Small Vertex Connectivity. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{franck_et_al:LIPIcs.SEA.2021.1,
  author =	{Franck, Max and Yingchareonthawornchai, Sorrachai},
  title =	{{Engineering Nearly Linear-Time Algorithms for Small Vertex Connectivity}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{1:1--1:18},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.1},
  URN =		{urn:nbn:de:0030-drops-137735},
  doi =		{10.4230/LIPIcs.SEA.2021.1},
  annote =	{Keywords: Algorithm Engineering, Algorithmic Graph Theory, Sublinear Algorithms}
}
Document
DOI: 10.4230/LIPIcs.SEA.2021.2
Parallel Five-Cycle Counting Algorithms

Authors: Louisa Ruixue Huang, Jessica Shi, and Julian Shun

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

Abstract
Counting the frequency of subgraphs in large networks is a classic research question that reveals the underlying substructures of these networks for important applications. However, subgraph counting is a challenging problem, even for subgraph sizes as small as five, due to the combinatorial explosion in the number of possible occurrences. This paper focuses on the five-cycle, which is an important special case of five-vertex subgraph counting and one of the most difficult to count efficiently. We design two new parallel five-cycle counting algorithms and prove that they are work-efficient and achieve polylogarithmic span. Both algorithms are based on computing low out-degree orientations, which enables the efficient computation of directed two-paths and three-paths, and the algorithms differ in the ways in which they use this orientation to eliminate double-counting. We develop fast multicore implementations of the algorithms and propose a work scheduling optimization to improve their performance. Our experiments on a variety of real-world graphs using a 36-core machine with two-way hyper-threading show that our algorithms achieves 10-46x self-relative speed-up, outperform our serial benchmarks by 10-32x, and outperform the previous state-of-the-art serial algorithm by up to 818x.
Cite as

Louisa Ruixue Huang, Jessica Shi, and Julian Shun. Parallel Five-Cycle Counting Algorithms. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 2:1-2:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{huang_et_al:LIPIcs.SEA.2021.2,
  author =	{Huang, Louisa Ruixue and Shi, Jessica and Shun, Julian},
  title =	{{Parallel Five-Cycle Counting Algorithms}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{2:1--2:18},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.2},
  URN =		{urn:nbn:de:0030-drops-137749},
  doi =		{10.4230/LIPIcs.SEA.2021.2},
  annote =	{Keywords: Cycle counting, parallel algorithms, graph algorithms}
}
Document
DOI: 10.4230/LIPIcs.SEA.2021.3
Fast and Robust Vectorized In-Place Sorting of Primitive Types

Authors: Mark Blacher, Joachim Giesen, and Lars Kühne

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

Abstract
Modern CPUs provide single instruction-multiple data (SIMD) instructions. SIMD instructions process several elements of a primitive data type simultaneously in fixed-size vectors. Classical sorting algorithms are not directly expressible in SIMD instructions. Accelerating sorting algorithms with SIMD instruction is therefore a creative endeavor. A promising approach for sorting with SIMD instructions is to use sorting networks for small arrays and Quicksort for large arrays. In this paper we improve vectorization techniques for sorting networks and Quicksort. In particular, we show how to use the full capacity of vector registers in sorting networks and how to make vectorized Quicksort robust with respect to different key distributions. To demonstrate the performance of our techniques we implement an in-place hybrid sorting algorithm for the data type int with AVX2 intrinsics. Our implementation is at least 30% faster than state-of-the-art high-performance sorting alternatives.
Cite as

Mark Blacher, Joachim Giesen, and Lars Kühne. Fast and Robust Vectorized In-Place Sorting of Primitive Types. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{blacher_et_al:LIPIcs.SEA.2021.3,
  author =	{Blacher, Mark and Giesen, Joachim and K\"{u}hne, Lars},
  title =	{{Fast and Robust Vectorized In-Place Sorting of Primitive Types}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{3:1--3:16},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.3},
  URN =		{urn:nbn:de:0030-drops-137758},
  doi =		{10.4230/LIPIcs.SEA.2021.3},
  annote =	{Keywords: Quicksort, Sorting Networks, Vectorization, SIMD, AVX2}
}
Document
DOI: 10.4230/LIPIcs.SEA.2021.4
Minimum Scan Cover and Variants - Theory and Experiments

Authors: Kevin Buchin, Sándor P. Fekete, Alexander Hill, Linda Kleist, Irina Kostitsyna, Dominik Krupke, Roel Lambers, and Martijn Struijs

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

Abstract
We consider a spectrum of geometric optimization problems motivated by contexts such as satellite communication and astrophysics. In the problem Minimum Scan Cover with Angular Costs, we are given a graph G that is embedded in Euclidean space. The edges of G need to be scanned, i.e., probed from both of their vertices. In order to scan their edge, two vertices need to face each other; changing the heading of a vertex incurs some cost in terms of energy or rotation time that is proportional to the corresponding rotation angle. Our goal is to compute schedules that minimize the following objective functions: (i) in Minimum Makespan Scan Cover (MSC-MS), this is the time until all edges are scanned; (ii) in Minimum Total Energy Scan Cover (MSC-TE), the sum of all rotation angles; (iii) in Minimum Bottleneck Energy Scan Cover (MSC-BE), the maximum total rotation angle at one vertex. Previous theoretical work on MSC-MS revealed a close connection to graph coloring and the cut cover problem, leading to hardness and approximability results. In this paper, we present polynomial-time algorithms for 1D instances of MSC-TE and MSC-BE, but NP-hardness proofs for bipartite 2D instances. For bipartite graphs in 2D, we also give 2-approximation algorithms for both MSC-TE and MSC-BE. Most importantly, we provide a comprehensive study of practical methods for all three problems. We compare three different mixed-integer programming and two constraint programming approaches, and show how to compute provably optimal solutions for geometric instances with up to 300 edges. Additionally, we compare the performance of different meta-heuristics for even larger instances.
Cite as

Kevin Buchin, Sándor P. Fekete, Alexander Hill, Linda Kleist, Irina Kostitsyna, Dominik Krupke, Roel Lambers, and Martijn Struijs. Minimum Scan Cover and Variants - Theory and Experiments. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{buchin_et_al:LIPIcs.SEA.2021.4,
  author =	{Buchin, Kevin and Fekete, S\'{a}ndor P. and Hill, Alexander and Kleist, Linda and Kostitsyna, Irina and Krupke, Dominik and Lambers, Roel and Struijs, Martijn},
  title =	{{Minimum Scan Cover and Variants - Theory and Experiments}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{4:1--4:16},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.4},
  URN =		{urn:nbn:de:0030-drops-137765},
  doi =		{10.4230/LIPIcs.SEA.2021.4},
  annote =	{Keywords: Graph scanning, angular metric, makespan, energy, bottleneck, complexity, approximation, algorithm engineering, mixed-integer programming, constraint programming}
}
Document
DOI: 10.4230/LIPIcs.SEA.2021.5
Three Is Enough for Steiner Trees

Authors: Emmanuel Arrighi and Mateus de Oliveira Oliveira

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

Abstract
In the Steiner tree problem, the input consists of an edge-weighted graph G together with a set S of terminal vertices. The goal is to find a minimum weight tree in G that spans all terminals. This fundamental NP-hard problem has direct applications in many subfields of combinatorial optimization, such as planning, scheduling, etc. In this work we introduce a new heuristic for the Steiner tree problem, based on a simple routine for improving the cost of sub-optimal Steiner trees: first, the sub-optimal tree is split into three connected components, and then these components are reconnected by using an algorithm that computes an optimal Steiner tree with 3-terminals (the roots of the three components). We have implemented our heuristic into a solver and compared it with several state-of-the-art solvers on well-known data sets. Our solver performs very well across all the data sets, and outperforms most of the other benchmarked solvers on very large graphs, which have been either obtained from real-world applications or from randomly generated data sets.
Cite as

Emmanuel Arrighi and Mateus de Oliveira Oliveira. Three Is Enough for Steiner Trees. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{arrighi_et_al:LIPIcs.SEA.2021.5,
  author =	{Arrighi, Emmanuel and de Oliveira Oliveira, Mateus},
  title =	{{Three Is Enough for Steiner Trees}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{5:1--5:15},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.5},
  URN =		{urn:nbn:de:0030-drops-137775},
  doi =		{10.4230/LIPIcs.SEA.2021.5},
  annote =	{Keywords: Steiner Tree, Heuristics, 3TST}
}
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