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Documents authored by Roy, Sambuddha

Document
DOI: 10.4230/LIPIcs.FSTTCS.2013.249
Distributed and Parallel Algorithms for Set Cover Problems with Small Neighborhood Covers

Authors: Archita Agarwal, Venkatesan T. Chakaravarthy, Anamitra Roy Choudhury, Sambuddha Roy, and Yogish Sabharwal

Published in: LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)

Abstract
In this paper, we study a class of set cover problems that satisfy a special property which we call the small neighborhood cover property. This class encompasses several well-studied problems including vertex cover, interval cover, bag interval cover and tree cover. We design unified distributed and parallel algorithms that can handle any set cover problem falling under the above framework and yield constant factor approximations. These algorithms run in polylogarithmic communication rounds in the distributed setting and are in NC, in the parallel setting.
Cite as

Archita Agarwal, Venkatesan T. Chakaravarthy, Anamitra Roy Choudhury, Sambuddha Roy, and Yogish Sabharwal. Distributed and Parallel Algorithms for Set Cover Problems with Small Neighborhood Covers. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 249-261, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{agarwal_et_al:LIPIcs.FSTTCS.2013.249,
  author =	{Agarwal, Archita and Chakaravarthy, Venkatesan T. and Choudhury, Anamitra Roy and Roy, Sambuddha and Sabharwal, Yogish},
  title =	{{Distributed and Parallel Algorithms for Set Cover Problems with Small Neighborhood Covers}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
  pages =	{249--261},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-64-4},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{24},
  editor =	{Seth, Anil and Vishnoi, Nisheeth K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.249},
  URN =		{urn:nbn:de:0030-drops-43775},
  doi =		{10.4230/LIPIcs.FSTTCS.2013.249},
  annote =	{Keywords: approximation algorithms, set cover problem, tree cover}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2013.275
Knapsack Cover Subject to a Matroid Constraint

Authors: Venkatesan T. Chakaravarthy, Anamitra Roy Choudhury, Sivaramakrishnan R. Natarajan, and Sambuddha Roy

Published in: LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)

Abstract
We consider the Knapsack Covering problem subject to a matroid constraint. In this problem, we are given an universe U of n items where item i has attributes: a cost c(i) and a size s(i). We also have a demand D. We are also given a matroid M = (U, I) on the set U. A feasible solution S to the problem is one such that (i) the cumulative size of the items chosen is at least D, and (ii) the set S is independent in the matroid M (i.e. S is in I). The objective is to minimize the total cost of the items selected, sum_{i in S}c(i). Our main result proves a 2-factor approximation for this problem. The problem described above falls in the realm of mixed packing covering problems. We also consider packing extensions of certain other covering problems and prove that in such cases it is not possible to derive any constant factor pproximations.
Cite as

Venkatesan T. Chakaravarthy, Anamitra Roy Choudhury, Sivaramakrishnan R. Natarajan, and Sambuddha Roy. Knapsack Cover Subject to a Matroid Constraint. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 275-286, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{chakaravarthy_et_al:LIPIcs.FSTTCS.2013.275,
  author =	{Chakaravarthy, Venkatesan T. and Choudhury, Anamitra Roy and Natarajan, Sivaramakrishnan R. and Roy, Sambuddha},
  title =	{{Knapsack Cover Subject to a Matroid Constraint}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
  pages =	{275--286},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-64-4},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{24},
  editor =	{Seth, Anil and Vishnoi, Nisheeth K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.275},
  URN =		{urn:nbn:de:0030-drops-43795},
  doi =		{10.4230/LIPIcs.FSTTCS.2013.275},
  annote =	{Keywords: Approximation Algorithms, LP rounding, Matroid Constraints, Knapsack problems}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2012.199
Scheduling Resources for Executing a Partial Set of Jobs

Authors: Venkatesan T. Chakaravarthy, Arindam Pal, Sambuddha Roy, and Yogish Sabharwal

Published in: LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

Abstract
In this paper, we consider the problem of choosing a minimum cost set of resources for executing a specified set of jobs. Each input job is an interval, determined by its start-time and end-time. Each resource is also an interval determined by its start-time and end-time; moreover, every resource has a capacity and a cost associated with it. We consider two versions of this problem. In the partial covering version, we are also given as input a number k, specifying the number of jobs that must be performed. The goal is to choose $k$ jobs and find a minimum cost set of resources to perform the chosen k jobs (at any point of time the capacity of the chosen set of resources should be sufficient to execute the jobs active at that time). We present an O(log n)-factor approximation algorithm for this problem. We also consider the prize collecting version, wherein every job also has a penalty associated with it. The feasible solution consists of a subset of the jobs, and a set of resources, to perform the chosen subset of jobs. The goal is to find a feasible solution that minimizes the sum of the costs of the selected resources and the penalties of the jobs that are not selected. We present a constant factor approximation algorithm for this problem.
Cite as

Venkatesan T. Chakaravarthy, Arindam Pal, Sambuddha Roy, and Yogish Sabharwal. Scheduling Resources for Executing a Partial Set of Jobs. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 199-210, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{chakaravarthy_et_al:LIPIcs.FSTTCS.2012.199,
  author =	{Chakaravarthy, Venkatesan T. and Pal, Arindam and Roy, Sambuddha and Sabharwal, Yogish},
  title =	{{Scheduling Resources for Executing a Partial Set of Jobs}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)},
  pages =	{199--210},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.199},
  URN =		{urn:nbn:de:0030-drops-38598},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.199},
  annote =	{Keywords: Approximation Algorithms, Partial Covering, Interval Graphs}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2012.236
Density Functions subject to a Co-Matroid Constraint

Authors: Venkatesan T. Chakaravarthy, Natwar Modani, Sivaramakrishnan R. Natarajan, Sambuddha Roy, and Yogish Sabharwal

Published in: LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

Abstract
In this paper we consider the problem of finding the densest subset subject to co-matroid constraints. We are given a monotone supermodular set function f defined over a universe U, and the density of a subset S is defined to be f(S)/|S|. This generalizes the concept of graph density. Co-matroid constraints are the following: given matroid M a set S is feasible, iff the complement of S is independent in the matroid. Under such constraints, the problem becomes NP-hard. The specific case of graph density has been considered in literature under specific co-matroid constraints, for example, the cardinality matroid and the partition matroid. We show a 2-approximation for finding the densest subset subject to co-matroid constraints. Thereby we improve the approximation guarantees for the result for partition matroids in the literature.
Cite as

Venkatesan T. Chakaravarthy, Natwar Modani, Sivaramakrishnan R. Natarajan, Sambuddha Roy, and Yogish Sabharwal. Density Functions subject to a Co-Matroid Constraint. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 236-248, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{chakaravarthy_et_al:LIPIcs.FSTTCS.2012.236,
  author =	{Chakaravarthy, Venkatesan T. and Modani, Natwar and Natarajan, Sivaramakrishnan R. and Roy, Sambuddha and Sabharwal, Yogish},
  title =	{{Density Functions subject to a Co-Matroid Constraint}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)},
  pages =	{236--248},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.236},
  URN =		{urn:nbn:de:0030-drops-38627},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.236},
  annote =	{Keywords: Approximation Algorithms, Submodular Functions, Graph Density}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2010.251
Finding Independent Sets in Unions of Perfect Graphs

Authors: Venkatesan T. Chakaravarthy, Vinayaka Pandit, Sambuddha Roy, and Yogish Sabharwal

Published in: LIPIcs, Volume 8, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)

Abstract
The maximum independent set problem (MaxIS) on general graphs is known to be NP-hard to approximate within a factor of $n^{1-epsilon}$, for any $epsilon > 0$. However, there are many ``easy" classes of graphs on which the problem can be solved in polynomial time. In this context, an interesting question is that of computing the maximum independent set in a graph that can be expressed as the union of a small number of graphs from an easy class. The MaxIS problem has been studied on unions of interval graphs and chordal graphs. We study the MaxIS problem on unions of perfect graphs (which generalize the above two classes). We present an $O(sqrt{n})$-approximation algorithm when the input graph is the union of two perfect graphs. We also show that the MaxIS problem on unions of two comparability graphs (a subclass of perfect graphs) cannot be approximated within any constant factor.
Cite as

Venkatesan T. Chakaravarthy, Vinayaka Pandit, Sambuddha Roy, and Yogish Sabharwal. Finding Independent Sets in Unions of Perfect Graphs. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 251-259, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{chakaravarthy_et_al:LIPIcs.FSTTCS.2010.251,
  author =	{Chakaravarthy, Venkatesan T. and Pandit, Vinayaka and Roy, Sambuddha and Sabharwal, Yogish},
  title =	{{Finding Independent Sets in Unions of Perfect Graphs}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)},
  pages =	{251--259},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-23-1},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{8},
  editor =	{Lodaya, Kamal and Mahajan, Meena},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2010.251},
  URN =		{urn:nbn:de:0030-drops-28683},
  doi =		{10.4230/LIPIcs.FSTTCS.2010.251},
  annote =	{Keywords: Approximation Algorithms; Comparability Graphs; Hardness of approximation}
}
Document
DOI: 10.4230/LIPIcs.STACS.2008.1342
Finding Irrefutable Certificates for S_2^p via Arthur and Merlin

Authors: Venkatesan T. Chakaravarthy and Sambuddha Roy

Published in: LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008)

Abstract
We show that $S_2^psubseteq P^{prAM}$, where $S_2^p$ is the symmetric alternation class and $prAM$ refers to the promise version of the Arthur-Merlin class $AM$. This is derived as a consequence of our main result that presents an $FP^{prAM}$ algorithm for finding a small set of ``collectively irrefutable certificates'' of a given $S_2$-type matrix. The main result also yields some new consequences of the hypothesis that $NP$ has polynomial size circuits. It is known that the above hypothesis implies a collapse of the polynomial time hierarchy ($PH$) to $S_2^psubseteq ZPP^{NP}$ (Cai 2007, K"obler and Watanabe 1998). Under the same hypothesis, we show that $PH$ collapses to $P^{prMA}$. We also describe an $FP^{prMA}$ algorithm for learning polynomial size circuits for $SAT$, assuming such circuits exist. For the same problem, the previously best known result was a $ZPP^{NP}$ algorithm (Bshouty et al. 1996).
Cite as

Venkatesan T. Chakaravarthy and Sambuddha Roy. Finding Irrefutable Certificates for S_2^p via Arthur and Merlin. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 157-168, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{chakaravarthy_et_al:LIPIcs.STACS.2008.1342,
  author =	{Chakaravarthy, Venkatesan T. and Roy, Sambuddha},
  title =	{{Finding Irrefutable Certificates for S\underline2^p via Arthur and Merlin}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{157--168},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Albers, Susanne and Weil, Pascal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1342},
  URN =		{urn:nbn:de:0030-drops-13421},
  doi =		{10.4230/LIPIcs.STACS.2008.1342},
  annote =	{Keywords: Symmetric alternation, promise-AM, Karp--Lipton theorem, learning circuits}
}
Document
DOI: 10.4230/LIPIcs.STACS.2008.1346
Deterministically Isolating a Perfect Matching in Bipartite Planar Graphs

Authors: Samir Datta, Raghav Kulkarni, and Sambuddha Roy

Published in: LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008)

Abstract
We present a deterministic way of assigning small (log bit) weights to the edges of a bipartite planar graph so that the minimum weight perfect matching becomes unique. The isolation lemma as described in (Mulmuley et al. 1987) achieves the same for general graphs using a randomized weighting scheme, whereas we can do it deterministically when restricted to bipartite planar graphs. As a consequence, we reduce both decision and construction versions of the matching problem to testing whether a matrix is singular, under the promise that its determinant is $0$ or $1$, thus obtaining a highly parallel SPL algorithm for bipartite planar graphs. This improves the earlier known bounds of non-uniform SPL by (Allender et al. 1999) and $NC^2$ by (Miller and Naor 1995, Mahajan and Varadarajan 2000). It also rekindles the hope of obtaining a deterministic parallel algorithm for constructing a perfect matching in non-bipartite planar graphs, which has been open for a long time. Our techniques are elementary and simple.
Cite as

Samir Datta, Raghav Kulkarni, and Sambuddha Roy. Deterministically Isolating a Perfect Matching in Bipartite Planar Graphs. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 229-240, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{datta_et_al:LIPIcs.STACS.2008.1346,
  author =	{Datta, Samir and Kulkarni, Raghav and Roy, Sambuddha},
  title =	{{Deterministically Isolating a Perfect Matching in Bipartite Planar Graphs}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{229--240},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Albers, Susanne and Weil, Pascal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1346},
  URN =		{urn:nbn:de:0030-drops-13465},
  doi =		{10.4230/LIPIcs.STACS.2008.1346},
  annote =	{Keywords: }
}
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