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Documents authored by Serna, Maria

Document
DOI: 10.4230/LIPIcs.SEA.2022.7
Relating Real and Synthetic Social Networks Through Centrality Measures

Authors: Maria J. Blesa, Mihail Eduard Popa, and Maria Serna

Published in: LIPIcs, Volume 233, 20th International Symposium on Experimental Algorithms (SEA 2022)

Abstract
We perform here a comparative study on the behaviour of real and synthetic social networks with respect to a selection of nine centrality measures. Some of them are topology based (degree, closeness, betweenness), while others consider the relevance of the actors within the network (Katz, PageRank) or their ability to spread influence through it (Independent Cascade rank, Linear Threshold Rank). We run different experiments on synthetic social networks, with 1K, 10K, and 100K nodes, generated according to the Gaussian Random partition model, the stochastic block model, the LFR benchmark graph model and hyperbolic geometric graphs model. Some real social networks are also considered, with the aim of discovering how do they relate to the synthetic models in terms of centrality. Apart from usual statistical measures, we perform a correlation analysis between all the nine measures. Our results indicate that, in general, the correlation matrices of the different models scale nicely with size. Moreover, the correlation plots distinguish four categories that classify most of the real networks studied here. Those categories have a clear correspondence with particular configurations of the models for synthetic networks.
Cite as

Maria J. Blesa, Mihail Eduard Popa, and Maria Serna. Relating Real and Synthetic Social Networks Through Centrality Measures. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 7:1-7:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{blesa_et_al:LIPIcs.SEA.2022.7,
  author =	{Blesa, Maria J. and Popa, Mihail Eduard and Serna, Maria},
  title =	{{Relating Real and Synthetic Social Networks Through Centrality Measures}},
  booktitle =	{20th International Symposium on Experimental Algorithms (SEA 2022)},
  pages =	{7:1--7:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-251-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{233},
  editor =	{Schulz, Christian and U\c{c}ar, Bora},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2022.7},
  URN =		{urn:nbn:de:0030-drops-165410},
  doi =		{10.4230/LIPIcs.SEA.2022.7},
  annote =	{Keywords: centrality measures, influence spread models, synthetic social networks}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.20
Data-Compression for Parametrized Counting Problems on Sparse Graphs

Authors: Eun Jung Kim, Maria Serna, and Dimitrios M. Thilikos

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
We study the concept of compactor, which may be seen as a counting-analogue of kernelization in counting parameterized complexity. For a function F:Sigma^* -> N and a parameterization kappa: Sigma^* -> N, a compactor (P,M) consists of a polynomial-time computable function P, called condenser, and a computable function M, called extractor, such that F=M o P, and the condensing P(x) of x has length at most s(kappa(x)), for any input x in Sigma^*. If s is a polynomial function, then the compactor is said to be of polynomial-size. Although the study on counting-analogue of kernelization is not unprecedented, it has received little attention so far. We study a family of vertex-certified counting problems on graphs that are MSOL-expressible; that is, for an MSOL-formula phi with one free set variable to be interpreted as a vertex subset, we want to count all A subseteq V(G) where |A|=k and (G,A) models phi. In this paper, we prove that every vertex-certified counting problems on graphs that is MSOL-expressible and treewidth modulable, when parameterized by k, admits a polynomial-size compactor on H-topological-minor-free graphs with condensing time O(k^2n^2) and decoding time 2^{O(k)}. This implies the existence of an FPT-algorithm of running time O(n^2 k^2)+2^{O(k)}. All aforementioned complexities are under the Uniform Cost Measure (UCM) model where numbers can be stored in constant space and arithmetic operations can be done in constant time.
Cite as

Eun Jung Kim, Maria Serna, and Dimitrios M. Thilikos. Data-Compression for Parametrized Counting Problems on Sparse Graphs. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 20:1-20:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{kim_et_al:LIPIcs.ISAAC.2018.20,
  author =	{Kim, Eun Jung and Serna, Maria and Thilikos, Dimitrios M.},
  title =	{{Data-Compression for Parametrized Counting Problems on Sparse Graphs}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{20:1--20:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.20},
  URN =		{urn:nbn:de:0030-drops-99688},
  doi =		{10.4230/LIPIcs.ISAAC.2018.20},
  annote =	{Keywords: Parameterized counting, compactor, protrusion decomposition}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.630
Absorption Time of the Moran Process

Authors: Josep Díaz, Leslie Ann Goldberg, David Richerby, and Maria Serna

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

Abstract
The Moran process models the spread of mutations in populations on graphs. We investigate the absorption time of the process, which is the time taken for a mutation introduced at a randomly chosen vertex to either spread to the whole population, or to become extinct. It is known that the expected absorption time for an advantageous mutation is polynomial on an n-vertex undirected graph, which allows the behaviour of the process on undirected graphs to be analysed using the Markov chain Monte Carlo method. We show that this does not extend to directed graphs by exhibiting an infinite family of directed graphs for which the expected absorption time is exponential in the number of vertices. However, for regular directed graphs, we give the expected absorption time is blog n lower bound and an explicit quadratic upper bound. We exhibit families of graphs matching these bounds and give improved bounds for other families of graphs, based on isoperimetric number. Our results are obtained via stochastic dominations which we demonstrate by establishing a coupling in a related continuous-time model. The coupling also implies several natural domination results regarding the fixation probability of the original (discrete-time) process, resolving a conjecture of Shakarian, Roos and Johnson.
Cite as

Josep Díaz, Leslie Ann Goldberg, David Richerby, and Maria Serna. Absorption Time of the Moran Process. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 630-642, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{diaz_et_al:LIPIcs.APPROX-RANDOM.2014.630,
  author =	{D{\'\i}az, Josep and Goldberg, Leslie Ann and Richerby, David and Serna, Maria},
  title =	{{Absorption Time of the Moran Process}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{630--642},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.630},
  URN =		{urn:nbn:de:0030-drops-47279},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.630},
  annote =	{Keywords: Moran Process}
}
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