2 Search Results for "Manghiuc, Bogdan-Adrian"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.103
Approximating Dasgupta Cost in Sublinear Time from a Few Random Seeds

Authors: Michael Kapralov, Akash Kumar, Silvio Lattanzi, Aida Mousavifar, and Weronika Wrzos-Kaminska

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Testing graph cluster structure has been a central object of study in property testing since the foundational work of Goldreich and Ron [STOC'96] on expansion testing, i.e. the problem of distinguishing between a single cluster (an expander) and a graph that is far from a single cluster. More generally, a (k, ε)-clusterable graph G is a graph whose vertex set admits a partition into k induced expanders, each with outer conductance bounded by ε. A recent line of work initiated by Czumaj, Peng and Sohler [STOC'15] has shown how to test whether a graph is close to (k, ε)-clusterable, and to locally determine which cluster a given vertex belongs to with misclassification rate ≈ ε, but no sublinear time algorithms for learning the structure of inter-cluster connections are known. As a simple example, can one locally distinguish between the "cluster graph" forming a line and a clique? In this paper, we consider the problem of testing the hierarchical cluster structure of (k, ε)-clusterable graphs in sublinear time. Our measure of hierarchical clusterability is the well-established Dasgupta cost, and our main result is an algorithm that approximates Dasgupta cost of a (k, ε)-clusterable graph in sublinear time, using a small number of randomly chosen seed vertices for which cluster labels are known. Our main result is an O(√{log k}) approximation to Dasgupta cost of G in ≈ n^{1/2+O(ε)} time using ≈ n^{1/3} seeds, effectively giving a sublinear time simulation of the algorithm of Charikar and Chatziafratis [SODA'17] on clusterable graphs. To the best of our knowledge, ours is the first result on approximating the hierarchical clustering properties of such graphs in sublinear time.
Cite as

Michael Kapralov, Akash Kumar, Silvio Lattanzi, Aida Mousavifar, and Weronika Wrzos-Kaminska. Approximating Dasgupta Cost in Sublinear Time from a Few Random Seeds. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 103:1-103:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kapralov_et_al:LIPIcs.ICALP.2025.103,
  author =	{Kapralov, Michael and Kumar, Akash and Lattanzi, Silvio and Mousavifar, Aida and Wrzos-Kaminska, Weronika},
  title =	{{Approximating Dasgupta Cost in Sublinear Time from a Few Random Seeds}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{103:1--103:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.103},
  URN =		{urn:nbn:de:0030-drops-234804},
  doi =		{10.4230/LIPIcs.ICALP.2025.103},
  annote =	{Keywords: Sublinear algorithms, Hierarchical Clustering, Dasgupta’s Cost}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.70
Augmenting the Algebraic Connectivity of Graphs

Authors: Bogdan-Adrian Manghiuc, Pan Peng, and He Sun

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
For any undirected graph G = (V,E) and a set E_W of candidate edges with E ∩ E_W = ∅, the (k,γ)-spectral augmentability problem is to find a set F of k edges from E_W with appropriate weighting, such that the algebraic connectivity of the resulting graph H = (V, E ∪ F) is least γ. Because of a tight connection between the algebraic connectivity and many other graph parameters, including the graph’s conductance and the mixing time of random walks in a graph, maximising the resulting graph’s algebraic connectivity by adding a small number of edges has been studied over the past 15 years, and has many practical applications in network optimisation. In this work we present an approximate and efficient algorithm for the (k,γ)-spectral augmentability problem, and our algorithm runs in almost-linear time under a wide regime of parameters. Our main algorithm is based on the following two novel techniques developed in the paper, which might have applications beyond the (k,γ)-spectral augmentability problem: - We present a fast algorithm for solving a feasibility version of an SDP for the algebraic connectivity maximisation problem from [Ghosh and Boyd, 2006]. Our algorithm is based on the classic primal-dual framework for solving SDP, which in turn uses the multiplicative weight update algorithm. We present a novel approach of unifying SDP constraints of different matrix and vector variables and give a good separation oracle accordingly. - We present an efficient algorithm for the subgraph sparsification problem, and for a wide range of parameters our algorithm runs in almost-linear time, in contrast to the previously best known algorithm running in at least Ω(n²mk) time [Kolla et al., 2010]. Our analysis shows how the randomised BSS framework can be generalised in the setting of subgraph sparsification, and how the potential functions can be applied to approximately keep track of different subspaces.
Cite as

Bogdan-Adrian Manghiuc, Pan Peng, and He Sun. Augmenting the Algebraic Connectivity of Graphs. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 70:1-70:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{manghiuc_et_al:LIPIcs.ESA.2020.70,
  author =	{Manghiuc, Bogdan-Adrian and Peng, Pan and Sun, He},
  title =	{{Augmenting the Algebraic Connectivity of Graphs}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{70:1--70:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.70},
  URN =		{urn:nbn:de:0030-drops-129367},
  doi =		{10.4230/LIPIcs.ESA.2020.70},
  annote =	{Keywords: Graph sparsification, Algebraic connectivity, Semidefinite programming}
}
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