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Documents authored by Ziccardi, Isabella

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.2024.28
Self-Stabilizing MIS Computation in the Beeping Model

Authors: George Giakkoupis, Volker Turau, and Isabella Ziccardi

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)

Abstract
We consider self-stabilizing algorithms to compute a Maximal Independent Set (MIS) in the extremely weak beeping communication model. The model consists of an anonymous network with synchronous rounds. In each round, each vertex can optionally transmit a signal to all its neighbors (beep). After the transmission of a signal, each vertex can only differentiate between no signal received, or at least one signal received. We also consider an extension of this model where vertices can transmit signals through two distinguishable beeping channels. We assume that vertices have some knowledge about the topology of the network. We revisit the not self-stabilizing algorithm proposed by Jeavons, Scott, and Xu (2013), which computes an MIS in the beeping model. We enhance this algorithm to be self-stabilizing, and explore three different variants, which differ in the knowledge about the topology available to the vertices and the number of beeping channels. In the first variant, every vertex knows an upper bound on the maximum degree Δ of the graph. For this case, we prove that the proposed self-stabilizing version maintains the same run-time as the original algorithm, i.e., it stabilizes after O(log n) rounds w.h.p. on any n-vertex graph. In the second variant, each vertex only knows an upper bound on its own degree. For this case, we prove that the algorithm stabilizes after O(log n⋅ log log n) rounds on any n-vertex graph, w.h.p. In the third variant, we consider the model with two beeping channels, where every vertex knows an upper bound of the maximum degree of the nodes in the 1-hop neighborhood. We prove that this variant stabilizes w.h.p. after O(log n) rounds.
Cite as

George Giakkoupis, Volker Turau, and Isabella Ziccardi. Self-Stabilizing MIS Computation in the Beeping Model. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 28:1-28:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{giakkoupis_et_al:LIPIcs.DISC.2024.28,
  author =	{Giakkoupis, George and Turau, Volker and Ziccardi, Isabella},
  title =	{{Self-Stabilizing MIS Computation in the Beeping Model}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{28:1--28:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.28},
  URN =		{urn:nbn:de:0030-drops-212540},
  doi =		{10.4230/LIPIcs.DISC.2024.28},
  annote =	{Keywords: Maximal Independent Set, Self-Stabilization, Beeping Model}
}
Document
DOI: 10.4230/LIPIcs.SAND.2023.3
Bond Percolation in Small-World Graphs with Power-Law Distribution

Authors: Luca Becchetti, Andrea Clementi, Francesco Pasquale, Luca Trevisan, and Isabella Ziccardi

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

Abstract
Full-bond percolation with parameter p is the process in which, given a graph, for every edge independently, we keep the edge with probability p and delete it with probability 1-p. Bond percolation is studied in parallel computing and network science to understand the resilience of distributed systems to random link failure and the spread of information in networks through unreliable links. Moreover, the full-bond percolation is equivalent to the Reed-Frost process, a network version of SIR epidemic spreading. We consider one-dimensional power-law small-world graphs with parameter α obtained as the union of a cycle with additional long-range random edges: each pair of nodes {u,v} at distance L on the cycle is connected by a long-range edge {u,v}, with probability proportional to 1/L^α. Our analysis determines three phases for the percolation subgraph G_p of the small-world graph, depending on the value of α. - If α < 1, there is a p < 1 such that, with high probability, there are Ω(n) nodes that are reachable in G_p from one another in 𝒪(log n) hops; - If 1 < α < 2, there is a p < 1 such that, with high probability, there are Ω(n) nodes that are reachable in G_p from one another in log^{𝒪(1)}(n) hops; - If α > 2, for every p < 1, with high probability all connected components of G_p have size 𝒪(log n).
Cite as

Luca Becchetti, Andrea Clementi, Francesco Pasquale, Luca Trevisan, and Isabella Ziccardi. Bond Percolation in Small-World Graphs with Power-Law Distribution. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 3:1-3:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{becchetti_et_al:LIPIcs.SAND.2023.3,
  author =	{Becchetti, Luca and Clementi, Andrea and Pasquale, Francesco and Trevisan, Luca and Ziccardi, Isabella},
  title =	{{Bond Percolation in Small-World Graphs with Power-Law Distribution}},
  booktitle =	{2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)},
  pages =	{3:1--3:22},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2023.3},
  URN =		{urn:nbn:de:0030-drops-179392},
  doi =		{10.4230/LIPIcs.SAND.2023.3},
  annote =	{Keywords: Information spreading, gossiping, epidemics, fault-tolerance, network self-organization and formation, complex systems, social and transportation networks}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.66
Resilient Level Ancestor, Bottleneck, and Lowest Common Ancestor Queries in Dynamic Trees

Authors: Luciano Gualà, Stefano Leucci, and Isabella Ziccardi

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
We study the problem of designing a resilient data structure maintaining a tree under the Faulty-RAM model [Finocchi and Italiano, STOC'04] in which up to δ memory words can be corrupted by an adversary. Our data structure stores a rooted dynamic tree that can be updated via the addition of new leaves, requires linear size, and supports resilient (weighted) level ancestor queries, lowest common ancestor queries, and bottleneck vertex queries in O(δ) worst-case time per operation.
Cite as

Luciano Gualà, Stefano Leucci, and Isabella Ziccardi. Resilient Level Ancestor, Bottleneck, and Lowest Common Ancestor Queries in Dynamic Trees. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 66:1-66:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{guala_et_al:LIPIcs.ISAAC.2021.66,
  author =	{Gual\`{a}, Luciano and Leucci, Stefano and Ziccardi, Isabella},
  title =	{{Resilient Level Ancestor, Bottleneck, and Lowest Common Ancestor Queries in Dynamic Trees}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{66:1--66:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.66},
  URN =		{urn:nbn:de:0030-drops-154998},
  doi =		{10.4230/LIPIcs.ISAAC.2021.66},
  annote =	{Keywords: level ancestor queries, lowest common ancestor queries, bottleneck vertex queries, resilient data structures, faulty-RAM model, dynamic trees}
}
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