All reports by Author Karthik C. S.:

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TR24-007
| 25th December 2023
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Karthik C. S., Pasin Manurangsi#### On Inapproximability of Reconfiguration Problems: PSPACE-Hardness and some Tight NP-Hardness Results

Revisions: 1

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TR21-177
| 22nd November 2021
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Vincent Cohen-Addad, Karthik C. S., Euiwoong Lee#### Johnson Coverage Hypothesis: Inapproximability of k-means and k-median in $\ell_p$-metrics

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TR21-156
| 10th November 2021
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Boris Bukh, Karthik C. S., Bhargav Narayanan#### Applications of Random Algebraic Constructions to Hardness of Approximation

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TR20-086
| 5th June 2020
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Andreas Feldmann, Karthik C. S., Euiwoong Lee, Pasin Manurangsi#### A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms

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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

Karthik C. S., Pasin Manurangsi

The field of combinatorial reconfiguration studies search problems with a focus on transforming one feasible solution into another.

Recently, Ohsaka [STACS'23] put forth the Reconfiguration Inapproximability Hypothesis (RIH), which roughly asserts that there is some $\varepsilon>0$ such that given as input a $k$-CSP instance (for some constant $k$) over ... more >>>

Vincent Cohen-Addad, Karthik C. S., Euiwoong Lee

k-median and k-means are the two most popular objectives for clustering algorithms. Despite intensive effort, a good understanding of the approximability of these objectives, particularly in $\ell_p$-metrics, remains a major open problem. In this paper, we significantly improve upon the hardness of approximation factors known in literature for these objectives ... more >>>

Boris Bukh, Karthik C. S., Bhargav Narayanan

In this paper, we show how one may (efficiently) construct two types of extremal combinatorial objects whose existence was previously conjectural.

(*) Panchromatic Graphs: For fixed integer k, a k-panchromatic graph is, roughly speaking, a balanced bipartite graph with one partition class equipartitioned into k colour classes in ...
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Andreas Feldmann, Karthik C. S., Euiwoong Lee, Pasin Manurangsi

Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and hardness perspectives, with emphasis on new techniques and potential future research directions.

more >>>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 >>>