Abstract:Given an n-vector p of processing times of jobs, the single machine scheduling polytope C arises as the convex hull of completion times of jobs when these are scheduled without idle time on a single machine. Given a point x ∈ C, Carathéodory's theorem implies that x can be written as convex combination of at most n vertices of C. We show that this convex combination can be computed from x and p in time O(n 2), which is linear in the naive encoding of the output. We obtain this result using essentially two ingr… Show more
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.