## 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 θ(minflog k;mg) on the competitive ratio for this problem, where k is the total number of nodes to be connected and m is the total number of different bursts. In directed graphs of bounded edge asymmetry α , we provide a competitive ratio for this problem with a gap of O(min{α;m}) factor between the lower bound and the upper bound. We also show that a tight bound of (minflog k;mg) 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.

Original language | English (US) |
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Pages (from-to) | 869-887 |

Number of pages | 19 |

Journal | International Journal of Foundations of Computer Science |

Volume | 28 |

Issue number | 7 |

DOIs | |

State | Published - Nov 1 2017 |

Externally published | Yes |

## Keywords

- Approximation
- Online execution
- Steiner tree
- Terminal bursts
- Terminal steiner tree

## ASJC Scopus subject areas

- Computer Science (miscellaneous)