Optimal stopping for many connected components in a graph

Abstract

AbstractWe study a new optimal stopping problem: Let G be a fixed graph with n vertices which become active on‐line in time, one by another, in a random order. The active part of G is the subgraph induced by the active vertices. Find a stopping algorithm that maximizes the expected number of connected components of the active part of G. We prove that if G is a k‐tree, then there is no asymptotically better algorithm than “wait until fraction of vertices”. The maximum expected number of connected components is equal to urn:x-wiley:rsa:media:rsa21000:rsa21000-math-0002