## Abstract

We consider online coloring of intervals with bandwidth in a setting where colors have variable capacities. Whenever the algorithm opens a new color, it must choose the capacity for that color and cannot change it later. A set of intervals can be assigned the same color a of capacity C _{a} if the sum of bandwidths of intervals at each point does not exceed C _{a}. The goal is to minimize the total capacity of all the colors used. We consider the bounded model, where all capacities must be chosen in the range (0,1], and the unbounded model, where the algorithm may use colors of any positive capacity. For the absolute competitive ratio, we give an upper bound of 14 and a lower bound of 4.59 for the bounded model, and an upper bound of 4 and a matching lower bound of 4 for the unbounded model. We also consider the offline version of these problems and show that whereas the unbounded model is polynomially solvable, the bounded model is NP-hard in the strong sense and admits a 3.6-approximation algorithm.

Original language | English |
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Pages (from-to) | 385-401 |

Number of pages | 17 |

Journal | Algorithmica |

Volume | 53 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2009 |

## Keywords

- Approximation algorithm
- Competitive analysis
- Interval coloring
- Lower bound

## ASJC Scopus subject areas

- General Computer Science
- Computer Science Applications
- Applied Mathematics