4 Search Results for "Rao, S. Srinivasa"

Document
DOI: 10.4230/LIPIcs.SEA.2021.10
Practical Implementation of Encoding Range Top-2 Queries

Authors: Seungbum Jo, Wooyoung Park, and Srinivasa Rao Satti

Published in: LIPIcs, Volume 190, 19th International Symposium on Experimental Algorithms (SEA 2021)

Abstract
We design a practical variant of an encoding for range Top-2 queries (RT2Q), and evaluate its performance. Given an array A[1,n] of n elements from a total order, the range Top-2 encoding problem is to construct a data structure that can answer RT2Q queries, which return the positions of the first and the second largest elements within a given query range of A, without accessing the array A at query time. Davoodi et al. [Phil. Trans. Royal Soc. A, 2016] proposed a (3.272n + o(n))-bit encoding, which answers RT2Q queries in O(1) time, while Gawrychowski and Nicholson [ICALP, 2015] gave an optimal (2.755n + (n))-bit encoding which doesn't support efficient queries. In this paper, we propose the first practical implementation of the encoding data structure for answering RT2Q. Our implementation is based on an alternative representation of Davoodi et al.’s data structure. The experimental results show that our implementation is efficient in practice, and gives improved time-space trade-offs compared to the indexing data structures (which keep the original array A as part of the data structure) for range maximum queries.
Cite as

Seungbum Jo, Wooyoung Park, and Srinivasa Rao Satti. Practical Implementation of Encoding Range Top-2 Queries. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{jo_et_al:LIPIcs.SEA.2021.10,
  author =	{Jo, Seungbum and Park, Wooyoung and Satti, Srinivasa Rao},
  title =	{{Practical Implementation of Encoding Range Top-2 Queries}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{10:1--10:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-185-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{190},
  editor =	{Coudert, David and Natale, Emanuele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.10},
  URN =		{urn:nbn:de:0030-drops-137827},
  doi =		{10.4230/LIPIcs.SEA.2021.10},
  annote =	{Keywords: Range top-2 query, Range minimum query, Cartesian tree, Succinct encoding}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.13
A Framework for In-place Graph Algorithms

Authors: Sankardeep Chakraborty, Anish Mukherjee, Venkatesh Raman, and Srinivasa Rao Satti

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract
Read-only memory (ROM) model is a classical model of computation to study time-space tradeoffs of algorithms. A classical result on the ROM model is that any algorithm to sort n numbers using O(s) words of extra space requires Omega (n^2/s) comparisons for lg n <= s <= n/lg n and the bound has also been recently matched by an algorithm. However, if we relax the model, we do have sorting algorithms (say Heapsort) that can sort using O(n lg n) comparisons using O(lg n) bits of extra space, even keeping a permutation of the given input sequence at anytime during the algorithm. We address similar relaxations for graph algorithms. We show that a simple natural relaxation of ROM model allows us to implement fundamental graph search methods like BFS and DFS more space efficiently than in ROM. By simply allowing elements in the adjacency list of a vertex to be permuted, we show that, on an undirected or directed connected graph G having n vertices and m edges, the vertices of G can be output in a DFS or BFS order using O(lg n) bits of extra space and O(n^3 lg n) time. Thus we obtain similar bounds for reachability and shortest path distance (both for undirected and directed graphs). With a little more (but still polynomial) time, we can also output vertices in the lex-DFS order. As reachability in directed graphs (even in DAGs) and shortest path distance (even in undirected graphs) are NL-complete, and lex-DFS is P-complete, our results show that our model is more powerful than ROM if L != P. En route, we also introduce and develop algorithms for another relaxation of ROM where the adjacency lists of the vertices are circular lists and we can modify only the heads of the lists. Here we first show a linear time DFS implementation using n + O(lg n) bits of extra space. Improving the extra space exponentially to only O(lg n) bits, we also obtain BFS and DFS albeit with a slightly slower running time. Both the models we propose maintain the graph structure throughout the algorithm, only the order of vertices in the adjacency list changes. In sharp contrast, for BFS and DFS, to the best of our knowledge, there are no algorithms in ROM that use even O(n^{1-epsilon}) bits of extra space; in fact, implementing DFS using cn bits for c<1 has been mentioned as an open problem. Furthermore, DFS (BFS, respectively) algorithms using n+o(n) (o(n), respectively) bits of extra use Reingold's [JACM, 2008] or Barnes et al's reachability algorithm [SICOMP, 1998] and hence have high runtime. Our results can be contrasted with the recent result of Buhrman et al. [STOC, 2014] which gives an algorithm for directed st-reachability on catalytic Turing machines using O(lg n) bits with catalytic space O(n^2 lg n) and time O(n^9).
Cite as

Sankardeep Chakraborty, Anish Mukherjee, Venkatesh Raman, and Srinivasa Rao Satti. A Framework for In-place Graph Algorithms. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chakraborty_et_al:LIPIcs.ESA.2018.13,
  author =	{Chakraborty, Sankardeep and Mukherjee, Anish and Raman, Venkatesh and Satti, Srinivasa Rao},
  title =	{{A Framework for In-place Graph Algorithms}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{13:1--13:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.13},
  URN =		{urn:nbn:de:0030-drops-94760},
  doi =		{10.4230/LIPIcs.ESA.2018.13},
  annote =	{Keywords: DFS, BFS, in-place algorithm, space-efficient graph algorithms, logspace}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2014.291
Asymptotically Optimal Encodings for Range Selection

Authors: Gonzalo Navarro, Rajeev Raman, and Srinivasa Rao Satti

Published in: LIPIcs, Volume 29, 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)

Abstract
We consider the problem of preprocessing an array A[1..n] to answer range selection and range top-k queries. Given a query interval [i..j] and a value k, the former query asks for the position of the k-th largest value in A[i..j], whereas the latter asks for the positions of all the k largest values in A[i..j]. We consider the encoding} version of the problem, where A is not available at query time, and an upper bound kappa on k, the rank that is to be selected, is given at construction time. We obtain data structures with asymptotically optimal size and query time on a RAM model with word size Theta(lg(n)): our structures use O(n*lg(kappa)) bits and answer range selection queries in time O(1+lg(k) / lg(lg(n))) and range top-k queries in time O(k), for any k <= kappa.
Cite as

Gonzalo Navarro, Rajeev Raman, and Srinivasa Rao Satti. Asymptotically Optimal Encodings for Range Selection. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 291-301, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{navarro_et_al:LIPIcs.FSTTCS.2014.291,
  author =	{Navarro, Gonzalo and Raman, Rajeev and Satti, Srinivasa Rao},
  title =	{{Asymptotically Optimal Encodings for Range Selection}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{291--301},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-77-4},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{29},
  editor =	{Raman, Venkatesh and Suresh, S. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.291},
  URN =		{urn:nbn:de:0030-drops-48502},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.291},
  annote =	{Keywords: Data Structures, Order Statistics, Succinct Data Structures, Space-efficient Data Structures}
}
Document
DOI: 10.4230/LIPIcs.STACS.2009.1847
More Haste, Less Waste: Lowering the Redundancy in Fully Indexable Dictionaries

Authors: Roberto Grossi, Alessio Orlandi, Rajeev Raman, and S. Srinivasa Rao

Published in: LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009)

Abstract
We consider the problem of representing, in a compressed format, a bit-vector~$S$ of $m$ bits with $n$ $\mathbf{1}$s, supporting the following operations, where $b \in \{ \mathbf{0}, \mathbf{1} \}$: \begin{itemize} \item $\mathtt{rank}_b(S,i)$ returns the number of occurrences of bit $b$ in the prefix $S\left[1..i\right]$; \item $\mathtt{select}_b(S,i)$ returns the position of the $i$th occurrence of bit $b$ in $S$. \end{itemize} Such a data structure is called \emph{fully indexable dictionary (\textsc{fid})} [Raman, Raman, and Rao, 2007], and is at least as powerful as predecessor data structures. Viewing $S$ as a set $X = \{ x_1, x_2, \ldots, x_n \}$ of $n$ distinct integers drawn from a universe $[m] = \{1, \ldots, m\}$, the predecessor of integer $y \in [m]$ in $X$ is given by $\ensuremath{\mathtt{select}^{}_1}(S, \ensuremath{\mathtt{rank}_1}(S,y-1))$. {\textsc{fid}}s have many applications in succinct and compressed data structures, as they are often involved in the construction of succinct representation for a variety of abstract data types. Our focus is on space-efficient {\textsc{fid}}s on the \textsc{ram} model with word size $\Theta(\lg m)$ and constant time for all operations, so that the time cost is independent of the input size. Given the bitstring $S$ to be encoded, having length $m$ and containing $n$ ones, the minimal amount of information that needs to be stored is $B(n,m) = \lceil \log {{m}\choose{n}} \rceil$. The state of the art in building a \textsc{fid}\ for~$S$ is given in~\mbox{}[P\v{a}tra\c{s}cu, 2008] using $B(m,n)+O( m / ( (\log m/ t) ^t) ) + O(m^{3/4}) $ bits, to support the operations in $O(t)$ time. Here, we propose a parametric data structure exhibiting a time/space trade-off such that, for any real constants $0 < \delta \leq 1/2$, $0 < \varepsilon \leq 1$, and integer $s > 0$, it uses \[ B(n,m) + O\left(n^{1+\delta} + n \left(\frac{m}{n^s}\right)^\varepsilon\right) \] bits and performs all the operations in time $O(s\delta^{-1} + \varepsilon^{-1})$. The improvement is twofold: our redundancy can be lowered parametrically and, fixing $s = O(1)$, we get a constant-time \textsc{fid}\ whose space is $B(n,m) + O(m^\varepsilon/\mathrm{poly}(n))$ bits, for sufficiently large $m$. This is a significant improvement compared to the previous bounds for the general case.
Cite as

Roberto Grossi, Alessio Orlandi, Rajeev Raman, and S. Srinivasa Rao. More Haste, Less Waste: Lowering the Redundancy in Fully Indexable Dictionaries. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 517-528, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{grossi_et_al:LIPIcs.STACS.2009.1847,
  author =	{Grossi, Roberto and Orlandi, Alessio and Raman, Rajeev and Rao, S. Srinivasa},
  title =	{{More Haste, Less Waste: Lowering the Redundancy in Fully Indexable Dictionaries}},
  booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{517--528},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-09-5},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{3},
  editor =	{Albers, Susanne and Marion, Jean-Yves},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1847},
  URN =		{urn:nbn:de:0030-drops-18470},
  doi =		{10.4230/LIPIcs.STACS.2009.1847},
  annote =	{Keywords: }
}
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