All reports by Author Karthik C. S.:

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TR19-125
| 27th August 2019
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Elazar Goldenberg, Karthik C. S.#### Hardness Amplification of Optimization Problems

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TR19-115
| 4th September 2019
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Arnab Bhattacharyya, Édouard Bonnet, László Egri, Suprovat Ghoshal, Karthik C. S., Bingkai Lin, Pasin Manurangsi, Dániel Marx#### Parameterized Intractability of Even Set and Shortest Vector Problem

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TR18-210
| 30th November 2018
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Karthik C. S., Pasin Manurangsi#### On Closest Pair in Euclidean Metric: Monochromatic is as Hard as Bichromatic

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TR18-057
| 26th March 2018
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Arnab Bhattacharyya, Suprovat Ghoshal, Karthik C. S., Pasin Manurangsi#### Parameterized Intractability of Even Set and Shortest Vector Problem from Gap-ETH

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TR17-186
| 29th November 2017
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Karthik C. S., Bundit Laekhanukit, Pasin Manurangsi#### On the Parameterized Complexity of Approximating Dominating Set

Revisions: 1

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TR17-061
| 3rd April 2017
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Anat Ganor, Karthik C. S.#### Communication Complexity of Correlated Equilibrium in Two-Player Games

Elazar Goldenberg, Karthik C. S.

In this paper, we prove a general hardness amplification scheme for optimization problems based on the technique of direct products.

We say that an optimization problem $\Pi$ is direct product feasible if it is possible to efficiently aggregate any $k$ instances of $\Pi$ and form one large instance ...
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Arnab Bhattacharyya, Édouard Bonnet, László Egri, Suprovat Ghoshal, Karthik C. S., Bingkai Lin, Pasin Manurangsi, Dániel Marx

The k-Even Set problem is a parameterized variant of the Minimum Distance Problem of linear codes over $\mathbb{F}_2$, which can be stated as follows: given a generator matrix A and an integer k, determine whether the code generated by A has distance at most k, or in other words, whether ... more >>>

Karthik C. S., Pasin Manurangsi

Given a set of $n$ points in $\mathbb R^d$, the (monochromatic) Closest Pair problem asks to find a pair of distinct points in the set that are closest in the $\ell_p$-metric. Closest Pair is a fundamental problem in Computational Geometry and understanding its fine-grained complexity in the Euclidean metric when ... more >>>

Arnab Bhattacharyya, Suprovat Ghoshal, Karthik C. S., Pasin Manurangsi

The $k$-Even Set problem is a parameterized variant of the Minimum Distance Problem of linear codes over $\mathbb F_2$, which can be stated as follows: given a generator matrix $\mathbf A$ and an integer $k$, determine whether the code generated by $\mathbf A$ has distance at most $k$. Here, $k$ ... more >>>

Karthik C. S., Bundit Laekhanukit, Pasin Manurangsi

We study the parameterized complexity of approximating the $k$-Dominating Set (domset) problem where an integer $k$ and a graph $G$ on $n$ vertices are given as input, and the goal is to find a dominating set of size at most $F(k) \cdot k$ whenever the graph $G$ has a dominating ... more >>>

Anat Ganor, Karthik C. S.

We show a communication complexity lower bound for finding a correlated equilibrium of a two-player game. More precisely, we define a two-player $N \times N$ game called the 2-cycle game and show that the randomized communication complexity of finding a 1/poly($N$)-approximate correlated equilibrium of the 2-cycle game is $\Omega(N)$. For ... more >>>