Energy bounds for minimum cut and maximum matching

Establish almost matching energy-complexity upper and lower bounds for distributed minimum cut and maximum matching in the SLEEPING-CONGEST model.

Background

The paper develops an information-theoretic framework for proving polynomial energy lower bounds in the SLEEPING-CONGEST model and applies it to several graph problems, including triangle enumeration, APSP, diameter computation, minimum weight cycle, maximum independent set, minimum dominating set, and minimum vertex cover. For these problems, the derived energy lower bounds nearly match the corresponding round-complexity lower bounds, up to logarithmic factors.

The conclusion identifies minimum cut and maximum matching as remaining problems for which the paper does not provide almost matching energy bounds. Thus, determining such bounds is explicitly left as an unresolved direction for future research.