Understanding the power of space-bounded computation with access to catalytic space has been an important theme in complexity theory over the recent years. One of the key algorithmic results in this area is that bipartite maximum matching can be computed in catalytic logspace with a polynomial-time bound, Agarwala and Mertz ... more >>>

Locality-sensitive hashing (LSH) has found widespread use as a fundamental primitive, particularly to accelerate nearest neighbor search. An LSH scheme for a similarity function $S:\mathcal{X} \times \mathcal{X} \to [0,1]$ is a distribution over hash functions on $\mathcal{X}$ with the property that the probability of collision of any two elements $x,y\in ... more >>>

We prove superpolynomial length lower bounds for the semantic tree-like Frege refutation system with bounded line size. Concretely, for any function $n^{2-\varepsilon} \leq s(n) \leq \exp\bigl(n^{1-\varepsilon}\bigr)$ we exhibit an explicit family $\mathcal{A}$ of $n$-variate CNF formulas $A$, each of size $|A| \le s(n)^{1+\varepsilon}$, such that if $A$ is chosen uniformly ... more >>>