In the Shortest Common Superstring problem (SCS), one is given a finite set of strings and is asked to find a shortest string containing every input string as a substring. Its best known approximation ratio is $2.466$, whereas the currently strongest upper bound on the approximation guarantee of the maximum-overlap ... more >>>

Matching Vector families (MVFs) are defined by two ordered lists of vectors in $\mathbb{Z}_m^n$ whose inner products satisfy specific residue patterns modulo an integer $m$. Most famously, restricted MVFs are used to construct the best-known constant-query Locally Decodable codes (LDCs).

We prove an upper bound of $2^{O\left(\sqrt{n\log n \log ... more >>>

We prove an exponential separation between zero-sided-error randomized and two-sided-error pseudodeterministic communication complexities of partial boolean functions. This qualitatively improves and simplifies the proof of the separation by Göös, Harms, Riazanov, Sofronova, Sokolov, and Yuan (STOC 2026), which had a two-sided-error randomized upper bound. Then, we generalize our technique to ... more >>>