We design the first efficient sensitivity oracles and dynamic algorithms for a variety of
parameterized problems. Our main approach is to modify the algebraic coding technique …

We study the following problem and its applications: given a homogeneous degree-d
polynomial g as an arithmetic circuit C, and ad× d matrix X whose entries are homogeneous …

Matroids, particularly linear ones, have been a powerful tool in parameterized complexity for
algorithms and kernelization. They have sped up or replaced dynamic programming. Delta …

We give a simplified account of the recent algebraic methods obtained for the longest path
problem of Brand, Dell and Husfeldt (STOC'18) and Brand (ESA'19). To this end, we …

The linear–algebraic notions of matrix rank and expansion in graphs are ubiquitous
throughout computer science, with applications to algebraic complexity theory …

In this paper we prove an analogue of the classic Bollobás lemma for approximate counting.
In fact, we match an analogous result of Fomin et al.[JACM 2016] for decision. This …

We extend the algebraic techniques of Brand and Pratt (ICALP'21) for deterministic detection
of k-multilinear monomials in a given polynomial with non-negative coefficients to the more …

The k-path problem asks whether a given graph contains a simple path of length k. Along
with other prominent parameterized problems, it reduces to the problem of detecting …

This dissertation is concerned with new results in the area of parameterized algorithms and
complexity. We develop a new technique for hard graph problems that generalizes and …

In this paper we prove an analogue of the classic Bollobás lemma for approximate counting.
In fact, we match an analogous result of Fomin et al.[JACM 2016] for decision. This …