Information complexity is one of the most powerful tools to prove information-theoretical lower bounds, with broad applications in communication complexity and streaming algorithms. A core notion in information complexity analysis is the Shannon entropy. Though it has some convenient properties, such as chain rules, Shannon entropy still has inherent limitations. ... more >>>

Relaxations for the constraint satisfaction problem (CSP) include bounded width, linear program (LP), semidefinite program (SDP), afinfe integer program (AIP), and the combined LP+AIP of Brakensiek, Guruswami, Wrochna, and Živný (SICOMP 2020). Tightening relaxations systematically leads to hierarchies and stronger algorithms. For the LP+AIP hierarchy, a constant level lower bound ... more >>>

Estimating quantiles is one of the foundational problems of data sketching. Given $n$ elements $x_1, x_2, \dots, x_n$ from some universe of size $U$ arriving in a data stream, a quantile sketch estimates the rank of any element with additive error at most $\varepsilon n$. A low-space algorithm solving this ... more >>>