Weizmann Logo
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style

All reports by Author Sumanta Ghosh:

TR22-063 | 30th April 2022
Vishwas Bhargava, Sumanta Ghosh, Zeyu Guo, Mrinal Kumar, Chris Umans

Fast Multivariate Multipoint Evaluation Over All Finite Fields

Multivariate multipoint evaluation is the problem of evaluating a multivariate polynomial, given as a coefficient vector, simultaneously at multiple evaluation points. In this work, we show that there exists a deterministic algorithm for multivariate multipoint evaluation over any finite field $\mathbb{F}$ that outputs the evaluations of an $m$-variate polynomial of ... more >>>

TR21-162 | 14th November 2021
Vishwas Bhargava, Sumanta Ghosh, Mrinal Kumar, Chandra Kanta Mohapatra

Fast, Algebraic Multivariate Multipoint Evaluation in Small Characteristic and Applications

Revisions: 3

Multipoint evaluation is the computational task of evaluating a polynomial given as a list of coefficients at a given set of inputs. Besides being a natural and fundamental question in computer algebra on its own, fast algorithms for this problem is also closely related to fast algorithms for other natural ... more >>>

TR21-121 | 21st August 2021
Sumanta Ghosh, Rohit Gurjar

Matroid Intersection: A pseudo-deterministic parallel reduction from search to weighted-decision

We study the matroid intersection problem from the parallel complexity perspective. Given
two matroids over the same ground set, the problem asks to decide whether they have a common base and its search version asks to find a common base, if one exists. Another widely studied variant is the weighted ... more >>>

TR21-062 | 29th April 2021
Vishwas Bhargava, Sumanta Ghosh

Improved Hitting Set for Orbit of ROABPs

Revisions: 2

The orbit of an $n$-variate polynomial $f(\mathbf{x})$ over a field $\mathbb{F}$ is the set $\{f(A \mathbf{x} + b)\,\mid\, A\in \mathrm{GL}({n,\mathbb{F}})\mbox{ and }\mathbf{b} \in \mathbb{F}^n\}$, and the orbit of a polynomial class is the union of orbits of all the polynomials in it. In this paper, we give improved constructions of ... more >>>

TR18-036 | 21st February 2018
Michael Forbes, Sumanta Ghosh, Nitin Saxena

Towards blackbox identity testing of log-variate circuits

Derandomization of blackbox identity testing reduces to extremely special circuit models. After a line of work, it is known that focusing on circuits with constant-depth and constantly many variables is enough (Agrawal,Ghosh,Saxena, STOC'18) to get to general hitting-sets and circuit lower bounds. This inspires us to study circuits with few ... more >>>

TR18-035 | 21st February 2018
Manindra Agrawal, Sumanta Ghosh, Nitin Saxena

Bootstrapping variables in algebraic circuits

We show that for the blackbox polynomial identity testing (PIT) problem it suffices to study circuits that depend only on the first extremely few variables. One only need to consider size-$s$ degree-$s$ circuits that depend on the first $\log^{\circ c} s$ variables (where $c$ is a constant and we are ... more >>>

TR17-035 | 23rd February 2017
Manindra Agrawal, Michael Forbes, Sumanta Ghosh, Nitin Saxena

Small hitting-sets for tiny arithmetic circuits or: How to turn bad designs into good

Research in the last decade has shown that to prove lower bounds or to derandomize polynomial identity testing (PIT) for general arithmetic circuits it suffices to solve these questions for restricted circuits. In this work, we study the smallest possibly restricted class of circuits, in particular depth-$4$ circuits, which would ... more >>>

ISSN 1433-8092 | Imprint