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Electronic Colloquium on Computational Complexity

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All reports by Author Siddharth Bhandari:

TR22-075 | 21st May 2022
Siddharth Bhandari, Prahladh Harsha, Ramprasad Saptharishi, Srikanth Srinivasan

Vanishing Spaces of Random Sets and Applications to Reed-Muller Codes

Revisions: 1

We study the following natural question on random sets of points in $\mathbb{F}_2^m$:

Given a random set of $k$ points $Z=\{z_1, z_2, \dots, z_k\} \subseteq \mathbb{F}_2^m$, what is the dimension of the space of degree at most $r$ multilinear polynomials that vanish on all points in $Z$?

We ... more >>>

TR21-163 | 19th November 2021
Siddharth Bhandari, Prahladh Harsha, Mrinal Kumar, A. Shankar

Algorithmizing the Multiplicity Schwartz-Zippel Lemma

Revisions: 1

The multiplicity Schwartz-Zippel lemma asserts that over a field, a low-degree polynomial cannot vanish with high multiplicity very often on a sufficiently large product set. Since its discovery in a work of Dvir, Kopparty, Saraf and Sudan [DKSS13], the lemma has found nu- merous applications in both math and computer ... more >>>

TR19-164 | 6th November 2019
Siddharth Bhandari, Sayantan Chakraborty

Improved bounds for perfect sampling of $k$-colorings in graphs

Revisions: 1

We present a randomized algorithm that takes as input an undirected $n$-vertex graph $G$ with maximum degree $\Delta$ and an integer $k > 3\Delta$, and returns a random proper $k$-coloring of $G$. The
distribution of the coloring is perfectly uniform over the set of all proper $k$-colorings; ... more >>>

TR18-207 | 5th December 2018
Siddharth Bhandari, Prahladh Harsha, Tulasimohan Molli, Srikanth Srinivasan

On the Probabilistic Degree of OR over the Reals

We study the probabilistic degree over reals of the OR function on $n$ variables. For an error parameter $\epsilon$ in (0,1/3), the $\epsilon$-error probabilistic degree of any Boolean function $f$ over reals is the smallest non-negative integer $d$ such that the following holds: there exists a distribution $D$ of polynomials ... more >>>

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