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Documents authored by Matias, Pedro

Document
DOI: 10.4230/LIPIcs.STACS.2022.4
Mapping Networks via Parallel kth-Hop Traceroute Queries

Authors: Ramtin Afshar, Michael T. Goodrich, Pedro Matias, and Martha C. Osegueda

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

Abstract
For a source node, v, and target node, w, the traceroute command iteratively issues "kth-hop" queries, for k = 1, 2, … , δ(v,w), which return the name of the kth vertex on a shortest path from v to w, where δ(v,w) is the distance between v and w, that is, the number of edges in a shortest-path from v to w. The traceroute command is often used for network mapping applications, the study of the connectivity of networks, and it has been studied theoretically with respect to biases it introduces for network mapping when only a subset of nodes in the network can be the source of traceroute queries. In this paper, we provide efficient network mapping algorithms, that are based on kth-hop traceroute queries. Our results include an algorithm that runs in a constant number of parallel rounds with a subquadratic number of queries under reasonable assumptions about the sampling coverage of the nodes that may issue kth-hop traceroute queries. In addition, we introduce a number of new algorithmic techniques, including a high-probability parametric parallelization of a graph clustering technique of Thorup and Zwick, which may be of independent interest.
Cite as

Ramtin Afshar, Michael T. Goodrich, Pedro Matias, and Martha C. Osegueda. Mapping Networks via Parallel kth-Hop Traceroute Queries. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 4:1-4:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{afshar_et_al:LIPIcs.STACS.2022.4,
  author =	{Afshar, Ramtin and Goodrich, Michael T. and Matias, Pedro and Osegueda, Martha C.},
  title =	{{Mapping Networks via Parallel kth-Hop Traceroute Queries}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{4:1--4:21},
  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.2022.4},
  URN =		{urn:nbn:de:0030-drops-158142},
  doi =		{10.4230/LIPIcs.STACS.2022.4},
  annote =	{Keywords: Network mapping, graph algorithms, parallel algorithms, distributed computing, query complexity, kth-hop queries}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.3
Reconstructing Biological and Digital Phylogenetic Trees in Parallel

Authors: Ramtin Afshar, Michael T. Goodrich, Pedro Matias, and Martha C. Osegueda

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

Abstract
In this paper, we study the parallel query complexity of reconstructing biological and digital phylogenetic trees from simple queries involving their nodes. This is motivated from computational biology, data protection, and computer security settings, which can be abstracted in terms of two parties, a responder, Alice, who must correctly answer queries of a given type regarding a degree-d tree, T, and a querier, Bob, who issues batches of queries, with each query in a batch being independent of the others, so as to eventually infer the structure of T. We show that a querier can efficiently reconstruct an n-node degree-d tree, T, with a logarithmic number of rounds and quasilinear number of queries, with high probability, for various types of queries, including relative-distance queries and path queries. Our results are all asymptotically optimal and improve the asymptotic (sequential) query complexity for one of the problems we study. Moreover, through an experimental analysis using both real-world and synthetic data, we provide empirical evidence that our algorithms provide significant parallel speedups while also improving the total query complexities for the problems we study.
Cite as

Ramtin Afshar, Michael T. Goodrich, Pedro Matias, and Martha C. Osegueda. Reconstructing Biological and Digital Phylogenetic Trees in Parallel. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 3:1-3:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{afshar_et_al:LIPIcs.ESA.2020.3,
  author =	{Afshar, Ramtin and Goodrich, Michael T. and Matias, Pedro and Osegueda, Martha C.},
  title =	{{Reconstructing Biological and Digital Phylogenetic Trees in Parallel}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{3:1--3:24},
  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.2020.3},
  URN =		{urn:nbn:de:0030-drops-128696},
  doi =		{10.4230/LIPIcs.ESA.2020.3},
  annote =	{Keywords: Tree Reconstruction, Parallel Algorithms, Privacy, Phylogenetic Trees, Data Structures, Hierarchical Clustering}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2019.51
New Applications of Nearest-Neighbor Chains: Euclidean TSP and Motorcycle Graphs

Authors: Nil Mamano, Alon Efrat, David Eppstein, Daniel Frishberg, Michael T. Goodrich, Stephen Kobourov, Pedro Matias, and Valentin Polishchuk

Published in: LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Abstract
We show new applications of the nearest-neighbor chain algorithm, a technique that originated in agglomerative hierarchical clustering. We use it to construct the greedy multi-fragment tour for Euclidean TSP in O(n log n) time in any fixed dimension and for Steiner TSP in planar graphs in O(n sqrt(n)log n) time; we compute motorcycle graphs, a central step in straight skeleton algorithms, in O(n^(4/3+epsilon)) time for any epsilon>0.
Cite as

Nil Mamano, Alon Efrat, David Eppstein, Daniel Frishberg, Michael T. Goodrich, Stephen Kobourov, Pedro Matias, and Valentin Polishchuk. New Applications of Nearest-Neighbor Chains: Euclidean TSP and Motorcycle Graphs. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 51:1-51:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{mamano_et_al:LIPIcs.ISAAC.2019.51,
  author =	{Mamano, Nil and Efrat, Alon and Eppstein, David and Frishberg, Daniel and Goodrich, Michael T. and Kobourov, Stephen and Matias, Pedro and Polishchuk, Valentin},
  title =	{{New Applications of Nearest-Neighbor Chains: Euclidean TSP and Motorcycle Graphs}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{51:1--51:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Lu, Pinyan and Zhang, Guochuan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.51},
  URN =		{urn:nbn:de:0030-drops-115477},
  doi =		{10.4230/LIPIcs.ISAAC.2019.51},
  annote =	{Keywords: Nearest-neighbors, Nearest-neighbor chain, motorcycle graph, straight skeleton, multi-fragment algorithm, Euclidean TSP, Steiner TSP}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2019.54
Tracking Paths in Planar Graphs

Authors: David Eppstein, Michael T. Goodrich, James A. Liu, and Pedro Matias

Published in: LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Abstract
We consider the NP-complete problem of tracking paths in a graph, first introduced by Banik et al. [Banik et al., 2017]. Given an undirected graph with a source s and a destination t, find the smallest subset of vertices whose intersection with any s-t path results in a unique sequence. In this paper, we show that this problem remains NP-complete when the graph is planar and we give a 4-approximation algorithm in this setting. We also show, via Courcelle’s theorem, that it can be solved in linear time for graphs of bounded-clique width, when its clique decomposition is given in advance.
Cite as

David Eppstein, Michael T. Goodrich, James A. Liu, and Pedro Matias. Tracking Paths in Planar Graphs. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 54:1-54:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{eppstein_et_al:LIPIcs.ISAAC.2019.54,
  author =	{Eppstein, David and Goodrich, Michael T. and Liu, James A. and Matias, Pedro},
  title =	{{Tracking Paths in Planar Graphs}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{54:1--54:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Lu, Pinyan and Zhang, Guochuan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.54},
  URN =		{urn:nbn:de:0030-drops-115500},
  doi =		{10.4230/LIPIcs.ISAAC.2019.54},
  annote =	{Keywords: Approximation Algorithm, Courcelle’s Theorem, Clique-Width, Planar, 3-SAT, Graph Algorithms, NP-Hardness}
}
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