The Bursty Steiner Tree Problem

Abstract

We introduce and study a new Steiner tree problem variation called the bursty Steiner tree problem where new nodes arrive into bursts. This is an online problem which becomes the well-known online Steiner tree problem if the number of nodes in each burst is exactly one and becomes the classic Steiner tree problem if all the nodes appear in a single burst. In undirected graphs, we provide a tight bound of [Formula: see text] on the competitive ratio for this problem, where [Formula: see text] is the total number of nodes to be connected and [Formula: see text] is the total number of different bursts. In directed graphs of bounded edge asymmetry [Formula: see text], we provide a competitive ratio for this problem with a gap of [Formula: see text] factor between the lower bound and the upper bound. We also show that a tight bound of [Formula: see text] on the competitive ratio can be obtained for a bursty variation of the terminal Steiner tree problem. These are the first results that provide clear performance trade-offs for a novel Steiner tree problem variation that subsumes both of its online and classic versions.