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Documents authored by Osegueda, Martha C.

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-dev.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.FUN.2021.4
Taming the Knight’s Tour: Minimizing Turns and Crossings

Authors: Juan Jose Besa, Timothy Johnson, Nil Mamano, and Martha C. Osegueda

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
We introduce two new metrics of "simplicity" for knight’s tours: the number of turns and the number of crossings. We give a novel algorithm that produces tours with 9.5n+O(1) turns and 13n+O(1) crossings on a n× n board, and we show lower bounds of (6-ε)n and 4n-O(1) on the respective problems of minimizing these metrics. Hence, our algorithm achieves approximation ratios of 19/12+o(1) and 13/4+o(1). We generalize our techniques to rectangular boards, high-dimensional boards, symmetric tours, odd boards with a missing corner, and tours for (1,4)-leapers. In doing so, we show that these extensions also admit a constant approximation ratio on the minimum number of turns, and on the number of crossings in most cases.
Cite as

Juan Jose Besa, Timothy Johnson, Nil Mamano, and Martha C. Osegueda. Taming the Knight’s Tour: Minimizing Turns and Crossings. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{besa_et_al:LIPIcs.FUN.2021.4,
  author =	{Besa, Juan Jose and Johnson, Timothy and Mamano, Nil and Osegueda, Martha C.},
  title =	{{Taming the Knight’s Tour: Minimizing Turns and Crossings}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{4:1--4:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.4},
  URN =		{urn:nbn:de:0030-drops-127654},
  doi =		{10.4230/LIPIcs.FUN.2021.4},
  annote =	{Keywords: Graph Drawing, Chess, Hamiltonian Cycle, Approximation Algorithms}
}
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-dev.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}
}
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