6 problems

Let the finite $d$-dimensional grid be the wrapped-around grid graph with $n$ nodes. For a set $S$ of $j$ nodes, let $E(S)$ denote the set of incoming edges of $S$, and suppose…

Optimal spreading-time conjecture. With finer tuning of concentration-of-measure and coupling techniques, it may be possible to obtain

Logarithmic-gap conjecture. With finer tuning of the concentration-of-measure techniques, the current gap can be narrowed to

Exact spreading-time conjecture. The spreading time is conjectured to have exact order

Consider $k$-dissemination in an algebraic gossip network, and let $T$ denote the time required to disseminate a single message to all nodes. Haeupler's upper-bound conjecture. The…

Let $k$ be the dissemination parameter, let $D$ be the graph diameter, and consider uniform algebraic gossip using the EXCHANGE protocol in the asynchronous time model on graphs of…