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Electronic Colloquium on Computational Complexity

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All reports by Author Santhoshini Velusamy:

TR22-068 | 5th May 2022
Chi-Ning Chou, Alexander Golovnev, Amirbehshad Shahrasbi, Madhu Sudan, Santhoshini Velusamy

Sketching Approximability of (Weak) Monarchy Predicates

We analyze the sketching approximability of constraint satisfaction problems on Boolean domains, where the constraints are balanced linear threshold functions applied to literals. In particular, we explore the approximability of monarchy-like functions where the value of the function is determined by a weighted combination of the vote of the first ... more >>>

TR21-086 | 22nd June 2021
Chi-Ning Chou, Alexander Golovnev, Madhu Sudan, Ameya Velingker, Santhoshini Velusamy

Linear Space Streaming Lower Bounds for Approximating CSPs

Revisions: 1

We consider the approximability of constraint satisfaction problems in the streaming setting. For every constraint satisfaction problem (CSP) on $n$ variables taking values in $\{0,\ldots,q-1\}$, we prove that improving over the trivial approximability by a factor of $q$ requires $\Omega(n)$ space even on instances with $O(n)$ constraints. We also identify ... more >>>

TR21-064 | 5th May 2021
Noah Singer, Madhu Sudan, Santhoshini Velusamy

Streaming approximation resistance of every ordering CSP

Revisions: 2

An ordering constraint satisfaction problem (OCSP) is given by a positive integer $k$ and a constraint predicate $\Pi$ mapping permutations on $\{1,\ldots,k\}$ to $\{0,1\}$. Given an instance of OCSP$(\Pi)$ on $n$ variables and $m$ constraints, the goal is to find an ordering of the $n$ variables that maximizes the number ... more >>>

TR21-063 | 3rd May 2021
Chi-Ning Chou, Alexander Golovnev, Madhu Sudan, Santhoshini Velusamy

Approximability of all finite CSPs in the dynamic streaming setting

Revisions: 3

A constraint satisfaction problem (CSP), Max-CSP$({\cal F})$, is specified by a finite set of constraints ${\cal F} \subseteq \{[q]^k \to \{0,1\}\}$ for positive integers $q$ and $k$. An instance of the problem on $n$ variables is given by $m$ applications of constraints from ${\cal F}$ to subsequences of the $n$ ... more >>>

TR21-011 | 13th February 2021
Chi-Ning Chou, Alexander Golovnev, Madhu Sudan, Santhoshini Velusamy

Classification of the streaming approximability of Boolean CSPs

Revisions: 4 , Comments: 1

A Boolean constraint satisfaction problem (CSP), Max-CSP$(f)$, is a maximization problem specified by a constraint $f:\{-1,1\}^k\to\{0,1\}$. An instance of the problem consists of $m$ constraint applications on $n$ Boolean variables, where each constraint application applies the constraint to $k$ literals chosen from the $n$ variables and their negations. The goal ... more >>>

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