Consider the following problem of learning an unknown linear order on $n$ items. In each round, the learner guesses a complete ordering of the items and receives either confirmation that the guess is correct or a counterexample:
a pair of items in the wrong order. The goal is to identify ... more >>>

We prove exponential lower bounds for $k$-DNF resolution on random $3$-CNF formulas throughout the range $k=O(\sqrt{\log n})$ at every constant clause density above the elementary first-moment bound for unsatisfiability. For random $3$-CNFs this improves Alekhnovich's range $k=O(\sqrt{\log n/\log\log n})$, and matches the $O(\sqrt{\log n})$ range obtained by Sofronova and Sokolov ... more >>>

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 >>>