DROPS

Document

Scalable Data Structures (Dagstuhl Seminar 23211)

Authors: Gerth Stølting Brodal, John Iacono, László Kozma, Vijaya Ramachandran, and Justin Dallant

Published in: Dagstuhl Reports, Volume 13, Issue 5 (2023)

Abstract

This report documents the program and the outcomes of Dagstuhl Seminar 23211 "Scalable Data Structures". Data structures enable the organization, storage and retrieval of data across a variety of applications. As they are deployed at unprecedented scales, data structures can profoundly affect the efficiency of almost all computational tasks. The study of data structures thus continues to be an important and active area of research with an interplay between data structure design and analysis, developments in computer hardware, and the needs of modern applications. The extended abstracts included in this report give a snapshot of the current state of research on scalable data structures and establish directions for future developments in the field.

Cite as

Gerth Stølting Brodal, John Iacono, László Kozma, Vijaya Ramachandran, and Justin Dallant. Scalable Data Structures (Dagstuhl Seminar 23211). In Dagstuhl Reports, Volume 13, Issue 5, pp. 114-135, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@Article{brodal_et_al:DagRep.13.5.114,
  author =	{Brodal, Gerth St{\o}lting and Iacono, John and Kozma, L\'{a}szl\'{o} and Ramachandran, Vijaya and Dallant, Justin},
  title =	{{Scalable Data Structures (Dagstuhl Seminar 23211)}},
  pages =	{114--135},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{13},
  number =	{5},
  editor =	{Brodal, Gerth St{\o}lting and Iacono, John and Kozma, L\'{a}szl\'{o} and Ramachandran, Vijaya and Dallant, Justin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.5.114},
  URN =		{urn:nbn:de:0030-drops-193676},
  doi =		{10.4230/DagRep.13.5.114},
  annote =	{Keywords: algorithms, big data, computational models, data structures, GPU computing, parallel computation}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2023.39

Dynamic Planar Embedding Is in DynFO

Authors: Samir Datta, Asif Khan, and Anish Mukherjee

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract

Planar Embedding is a drawing of a graph on the plane such that the edges do not intersect each other except at the vertices. We know that testing the planarity of a graph and computing its embedding (if it exists), can efficiently be computed, both sequentially [John E. Hopcroft and Robert Endre Tarjan, 1974] and in parallel [Vijaya Ramachandran and John H. Reif, 1994], when the entire graph is presented as input. In the dynamic setting, the input graph changes one edge at a time through insertion and deletions and planarity testing/embedding has to be updated after every change. By storing auxilliary information we can improve the complexity of dynamic planarity testing/embedding over the obvious recomputation from scratch. In the sequential dynamic setting, there has been a series of works [David Eppstein et al., 1996; Giuseppe F. Italiano et al., 1993; Jacob Holm et al., 2018; Jacob Holm and Eva Rotenberg, 2020], culminating in the breakthrough result of polylog(n) sequential time (amortized) planarity testing algorithm of Holm and Rotenberg [Jacob Holm and Eva Rotenberg, 2020]. In this paper we study planar embedding through the lens of DynFO, a parallel dynamic complexity class introduced by Patnaik et al [Sushant Patnaik and Neil Immerman, 1997] (also [Guozhu Dong et al., 1995]). We show that it is possible to dynamically maintain whether an edge can be inserted to a planar graph without causing non-planarity in DynFO. We extend this to show how to maintain an embedding of a planar graph under both edge insertions and deletions, while rejecting edge insertions that violate planarity. Our main idea is to maintain embeddings of only the triconnected components and a special two-colouring of separating pairs that enables us to side-step cascading flips when embedding of a biconnected planar graph changes, a major issue for sequential dynamic algorithms [Jacob Holm and Eva Rotenberg, 2020; Jacob Holm and Eva Rotenberg, 2020].

Cite as

Samir Datta, Asif Khan, and Anish Mukherjee. Dynamic Planar Embedding Is in DynFO. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 39:1-39:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{datta_et_al:LIPIcs.MFCS.2023.39,
  author =	{Datta, Samir and Khan, Asif and Mukherjee, Anish},
  title =	{{Dynamic Planar Embedding Is in DynFO}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{39:1--39:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.39},
  URN =		{urn:nbn:de:0030-drops-185736},
  doi =		{10.4230/LIPIcs.MFCS.2023.39},
  annote =	{Keywords: Dynamic Complexity, Planar graphs, Planar embedding}
}

Document

DOI: 10.4230/DagRep.11.1.1

Scalable Data Structures (Dagstuhl Seminar 21071)

Authors: Gerth Stølting Brodal, John Iacono, Markus E. Nebel, and Vijaya Ramachandran

Published in: Dagstuhl Reports, Volume 11, Issue 1 (2021)

Abstract

This report documents the program and the outcomes of Dagstuhl Seminar 21071 "Scalable Data Structure". Even if the field of data structures is quite mature, new trends and limitations in computer hardware together with the ever-increasing amounts of data that need to be processed raise new questions with respect to efficiency and continuously challenge the existing models of computation. Thermal and electrical power constraints have caused technology to reach "the power wall" with stagnating single processor performance, meaning that all nontrivial applications need to address scalability with multiple processors, a memory hierarchy and other communication challenges. Scalable data structures are pivotal to this process since they form the backbone of the algorithms driving these applications. The extended abstracts included in this report contain both recent state of the art advances and lay the foundation for new directions within data structures research.

Cite as

Gerth Stølting Brodal, John Iacono, Markus E. Nebel, and Vijaya Ramachandran. Scalable Data Structures (Dagstuhl Seminar 21071). In Dagstuhl Reports, Volume 11, Issue 1, pp. 1-23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@Article{brodal_et_al:DagRep.11.1.1,
  author =	{Brodal, Gerth St{\o}lting and Iacono, John and Nebel, Markus E. and Ramachandran, Vijaya},
  title =	{{Scalable Data Structures (Dagstuhl Seminar 21071)}},
  pages =	{1--23},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2021},
  volume =	{11},
  number =	{1},
  editor =	{Brodal, Gerth St{\o}lting and Iacono, John and Nebel, Markus E. and Ramachandran, Vijaya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.11.1.1},
  URN =		{urn:nbn:de:0030-drops-143481},
  doi =		{10.4230/DagRep.11.1.1},
  annote =	{Keywords: algorithms, big data, data structures, GPU computing, large data sets, models of computation, parallel algorithms}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2016.8

Finding k Simple Shortest Paths and Cycles

Authors: Udit Agarwal and Vijaya Ramachandran

Published in: LIPIcs, Volume 64, 27th International Symposium on Algorithms and Computation (ISAAC 2016)

Abstract

We present algorithms and techniques for several problems related to finding multiple simple shortest paths and cycles in a graph. Our main result is a new algorithm for finding k simple shortest paths for all pairs of vertices in a weighted directed graph G = (V, E). For k = 2 our algorithm runs in O(mn + n^2 log n) time where m and n are the number of edges and vertices in G. For k = 3 our algorithm runs in O(mn^2 + n^3 log n) time, which is almost a factor of n faster than the best previous algorithm. Our approach is based on forming suitable path extensions to find simple shortest paths; this method is different from the 'detour finding' technique used in most of the prior work on simple shortest paths, replacement paths, and distance sensitivity oracles. We present new algorithms for generating simple cycles and simple paths in G in non-decreasing order of their weight. The algorithm for generating simple paths is much faster,and uses another variant of path extensions.

Cite as

Udit Agarwal and Vijaya Ramachandran. Finding k Simple Shortest Paths and Cycles. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 8:1-8:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{agarwal_et_al:LIPIcs.ISAAC.2016.8,
  author =	{Agarwal, Udit and Ramachandran, Vijaya},
  title =	{{Finding k Simple Shortest Paths and Cycles}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{8:1--8:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Hong, Seok-Hee},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.8},
  URN =		{urn:nbn:de:0030-drops-67830},
  doi =		{10.4230/LIPIcs.ISAAC.2016.8},
  annote =	{Keywords: Graph Algorithms, Shortest Paths, k Simple Shortest Paths, Enumerat- ing Simple Cycles, Enumerating Simple Paths}
}

4 Search Results for "Ramachandran, Vijaya"

Scalable Data Structures (Dagstuhl Seminar 23211)

Abstract

Cite as

Dynamic Planar Embedding Is in DynFO

Abstract

Cite as

Scalable Data Structures (Dagstuhl Seminar 21071)

Abstract

Cite as

Finding k Simple Shortest Paths and Cycles

Abstract

Cite as

Thanks for your feedback!

Could not send message