Abstract:We consider the problem of partitioning a line segment into two subsets, so that n finite measures all has the same ratio of values for the subsets. Letting α ∈ [0, 1] denote the desired ratio, this generalises the PPA-complete consensushalving problem, in which α = 1 2 . It is known that for any α, there exists a solution using 2n cuts of the segment. Here we show that if α is irrational, that upper bound is almost optimal. We also obtain bounds that are nearly exact for a large subset of rational values α. O… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.