All reports by Author Vinodchandran Variyam:

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TR19-091
| 7th July 2019
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Ryo Ashida, Tatsuya Imai, Kotaro Nakagawa, A. Pavan, Vinodchandran Variyam, Osamu Watanabe#### A Sublinear-space and Polynomial-time Separator Algorithm for Planar Graphs

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TR14-035
| 13th March 2014
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Diptarka Chakraborty, A. Pavan, Raghunath Tewari, Vinodchandran Variyam, Lin Yang#### New Time-Space Upperbounds for Directed Reachability in High-genus and $H$-minor-free Graphs.

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TR14-008
| 20th January 2014
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Vinodchandran Variyam#### Space Complexity of the Directed Reachability Problem over Surface-Embedded Graphs.

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TR11-060
| 15th April 2011
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Brady Garvin, Derrick Stolee, Raghunath Tewari, Vinodchandran Variyam#### ReachFewL = ReachUL

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TR10-154
| 8th October 2010
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Derrick Stolee, Vinodchandran Variyam#### Space-Efficient Algorithms for Reachability in Surface-Embedded Graphs

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TR10-151
| 30th September 2010
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Raghunath Tewari, Vinodchandran Variyam#### Green’s Theorem and Isolation in Planar Graphs

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TR10-079
| 28th April 2010
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Samir Datta, Raghav Kulkarni, Raghunath Tewari, Vinodchandran Variyam#### Space Complexity of Perfect Matching in Bounded Genus Bipartite Graphs

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TR10-009
| 13th January 2010
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A. Pavan, Raghunath Tewari, Vinodchandran Variyam#### On the Power of Unambiguity in Logspace

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TR09-071
| 1st September 2009
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John Hitchcock, A. Pavan, Vinodchandran Variyam#### Kolmogorov Complexity in Randomness Extraction

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TR09-049
| 5th May 2009
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Derrick Stolee, Chris Bourke, Vinodchandran Variyam#### A log-space algorithm for reachability in planar DAGs with few sources

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TR05-105
| 24th September 2005
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Lance Fortnow, John Hitchcock, A. Pavan, Vinodchandran Variyam, Fengming Wang#### Extracting Kolmogorov Complexity with Applications to Dimension Zero-One Laws

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TR05-062
| 17th June 2005
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A. Pavan, Vinodchandran Variyam#### 2-Local Random Reductions to 3-Valued Functions

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TR04-056
| 1st July 2004
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Vinodchandran Variyam#### A note on the circuit complexity of PP

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TR04-053
| 17th June 2004
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A. Pavan, Vinodchandran Variyam#### Polylogarithmic Round Arthur-Merlin Games and Random-Self-Reducibility

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TR04-025
| 24th January 2004
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John Hitchcock, A. Pavan, Vinodchandran Variyam#### Partial Bi-Immunity and NP-Completeness

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TR98-078
| 1st December 1998
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Vikraman Arvind, K.V. Subrahmanyam, Vinodchandran Variyam#### The Query Complexity of Program Checking by Constant-Depth Circuits

Ryo Ashida, Tatsuya Imai, Kotaro Nakagawa, A. Pavan, Vinodchandran Variyam, Osamu Watanabe

In [12] (CCC 2013), the authors presented an algorithm for the reachability problem over directed planar graphs that runs in polynomial-time and uses $O(n^{1/2+\epsilon})$ space. A critical ingredient of their algorithm is a polynomial-time, $\tldO(\sqrt{n})$-space algorithm to compute a separator of a planar graph. The conference version provided a sketch ... more >>>

Diptarka Chakraborty, A. Pavan, Raghunath Tewari, Vinodchandran Variyam, Lin Yang

We obtain the following new simultaneous time-space upper bounds for the directed reachability problem.

(1) A polynomial-time,

$\tilde{O}(n^{2/3}g^{1/3})$-space algorithm for directed graphs embedded on orientable surfaces of genus $g$. (2) A polynomial-time, $\tilde{O}(n^{2/3})$-space algorithm for all $H$-minor-free graphs given the tree decomposition, and (3) for $K_{3, 3}$-free and ...
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Vinodchandran Variyam

The graph reachability problem, the computational task of deciding whether there is a path between two given nodes in a graph is the canonical problem for studying space bounded computations. Three central open questions regarding the space complexity of the reachability problem over directed graphs are: (1) improving Savitch's $O(\log^2 ... more >>>

Brady Garvin, Derrick Stolee, Raghunath Tewari, Vinodchandran Variyam

We show that two complexity classes introduced about two decades ago are equal. ReachUL is the class of problems decided by nondeterministic log-space machines which on every input have at most one computation path from the start configuration to any other configuration. ReachFewL, a natural generalization of ReachUL, is the ... more >>>

Derrick Stolee, Vinodchandran Variyam

We consider the reachability problem for a certain class of directed acyclic graphs embedded on surfaces. Let ${\cal G}(m,g)$ be the class of directed acyclic graphs with $m = m(n)$ source vertices embedded on a surface (orientable or non-orientable) of genus $g = g(n)$. We give a log-space reduction that ... more >>>

Raghunath Tewari, Vinodchandran Variyam

We show a simple application of Green’s theorem from multivariable calculus to the isolation problem in planar graphs. In particular, we construct a skew-symmetric, polynomially bounded, edge weight function for a directed planar graph in logspace such that the weight of any simple cycle in the graph is non-zero with ... more >>>

Samir Datta, Raghav Kulkarni, Raghunath Tewari, Vinodchandran Variyam

We investigate the space complexity of certain perfect matching

problems over bipartite graphs embedded on surfaces of constant genus

(orientable or non-orientable). We show that the problems of deciding

whether such graphs have (1) a perfect matching or not and (2) a

unique perfect matching or not, are in the ...
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A. Pavan, Raghunath Tewari, Vinodchandran Variyam

We report progress on the \NL\ vs \UL\ problem.

\begin{itemize}

\item[-] We show unconditionally that the complexity class $\ReachFewL\subseteq\UL$. This improves on the earlier known upper bound $\ReachFewL \subseteq \FewL$.

\item[-] We investigate the complexity of min-uniqueness - a central

notion in studying the \NL\ vs \UL\ problem.

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John Hitchcock, A. Pavan, Vinodchandran Variyam

We clarify the role of Kolmogorov complexity in the area of randomness extraction. We show that a computable function is an almost randomness extractor if and only if it is a Kolmogorov complexity

extractor, thus establishing a fundamental equivalence between two forms of extraction studied in the literature: Kolmogorov extraction

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Derrick Stolee, Chris Bourke, Vinodchandran Variyam

Designing algorithms that use logarithmic space for graph reachability problems is fundamental to complexity theory. It is well known that for general directed graphs this problem is equivalent to the NL vs L problem. For planar graphs, the question is not settled. Showing that the planar reachability problem is NL-complete ... more >>>

Lance Fortnow, John Hitchcock, A. Pavan, Vinodchandran Variyam, Fengming Wang

We apply recent results on extracting randomness from independent

sources to ``extract'' Kolmogorov complexity. For any $\alpha,

\epsilon > 0$, given a string $x$ with $K(x) > \alpha|x|$, we show

how to use a constant number of advice bits to efficiently

compute another string $y$, $|y|=\Omega(|x|)$, with $K(y) >

(1-\epsilon)|y|$. ...
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A. Pavan, Vinodchandran Variyam

Yao (in a lecture at DIMACS Workshop on structural complexity and

cryptography) showed that if a language L is 2-locally-random

reducible to a Boolean functio, then L is in PSPACE/poly.

Fortnow and Szegedy quantitatively improved Yao's result to show that

such languages are in fact in NP/poly (Information Processing Letters, ...
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Vinodchandran Variyam

In this short note we show that for any integer k, there are

languages in the complexity class PP that do not have Boolean

circuits of size $n^k$.

A. Pavan, Vinodchandran Variyam

We consider Arthur-Merlin proof systems where (a) Arthur is a probabilistic quasi-polynomial time Turing machine

and (AMQ)(b) Arthur is a probabilistic exponential time Turing machine (AME). We prove two new results related to these classes.

John Hitchcock, A. Pavan, Vinodchandran Variyam

The Turing and many-one completeness notions for $\NP$ have been

previously separated under {\em measure}, {\em genericity}, and {\em

bi-immunity} hypotheses on NP. The proofs of all these results rely

on the existence of a language in NP with almost everywhere hardness.

In this paper we separate the same NP-completeness ... more >>>

Vikraman Arvind, K.V. Subrahmanyam, Vinodchandran Variyam

In this paper we study program checking (in the

sense of Blum and Kannan) using constant-depth circuits as

checkers. Our focus is on the number of queries made by the

checker to the program being checked and we term this as the

query complexity of the checker for the given ...
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