All reports by Author Sumanta Ghosh:

__
TR23-075
| 17th May 2023
__

Abhranil Chatterjee, Sumanta Ghosh, Rohit Gurjar, Roshan Raj#### Border Complexity of Symbolic Determinant under Rank One Restriction

__
TR23-033
| 24th March 2023
__

Sumanta Ghosh, Prahladh Harsha, Simao Herdade, Mrinal Kumar, Ramprasad Saptharishi#### Fast Numerical Multivariate Multipoint Evaluation

Revisions: 1

__
TR22-063
| 30th April 2022
__

Vishwas Bhargava, Sumanta Ghosh, Zeyu Guo, Mrinal Kumar, Chris Umans#### Fast Multivariate Multipoint Evaluation Over All Finite Fields

__
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

__
TR21-121
| 21st August 2021
__

Sumanta Ghosh, Rohit Gurjar#### Matroid Intersection: A pseudo-deterministic parallel reduction from search to weighted-decision

__
TR21-062
| 29th April 2021
__

Vishwas Bhargava, Sumanta Ghosh#### Improved Hitting Set for Orbit of ROABPs

Revisions: 2

__
TR18-036
| 21st February 2018
__

Michael Forbes, Sumanta Ghosh, Nitin Saxena#### Towards blackbox identity testing of log-variate circuits

__
TR18-035
| 21st February 2018
__

Manindra Agrawal, Sumanta Ghosh, Nitin Saxena#### Bootstrapping variables in algebraic circuits

__
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

Abhranil Chatterjee, Sumanta Ghosh, Rohit Gurjar, Roshan Raj

VBP is the class of polynomial families that can be computed by the determinant of a symbolic matrix of the form $A_0 + \sum_{i=1}^n A_ix_i$ where the size of each $A_i$ is polynomial in the number of variables (equivalently, computable by polynomial-sized algebraic branching programs (ABP)). A major open problem ... more >>>

Sumanta Ghosh, Prahladh Harsha, Simao Herdade, Mrinal Kumar, Ramprasad Saptharishi

We design nearly-linear time numerical algorithms for the problem of multivariate multipoint evaluation over the fields of rational, real and complex numbers. We consider both \emph{exact} and \emph{approximate} versions of the algorithm. The input to the algorithms are (1) coefficients of an $m$-variate polynomial $f$ with degree $d$ in each ... more >>>

Vishwas Bhargava, Sumanta Ghosh, Zeyu Guo, Mrinal Kumar, Chris Umans

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 >>>

Vishwas Bhargava, Sumanta Ghosh, Mrinal Kumar, Chandra Kanta Mohapatra

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 >>>

Sumanta Ghosh, Rohit Gurjar

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 >>>

Vishwas Bhargava, Sumanta Ghosh

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 >>>

Michael Forbes, Sumanta Ghosh, Nitin Saxena

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 >>>

Manindra Agrawal, Sumanta Ghosh, Nitin Saxena

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 >>>

Manindra Agrawal, Michael Forbes, Sumanta Ghosh, Nitin Saxena

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 >>>