## Abstract

In the online capacitated interval coloring problem, a sequence of requests arrive online. Each request is an interval I_{j} ⊆ {1, 2, ⋯, n} with bandwidth b_{j}. We are initially given a vector of capacities (c_{1}, c_{2}, ⋯, c_{n}). Each color can support a set of requests such that the total bandwidth of intervals containing i is at most c_{i}. The goal is to color the requests using a minimum number of colors. We present a constant competitive algorithm for the case where the maximum bandwidth b_{max} = max_{j} b_{j} is at most the minimum capacity c_{min} = min_{i} c _{i}. For the case b_{max} > c_{min}, we give an algorithm with competitive ratio O(log b_{max}/c_{min}) and, using resource augmentation, a constant competitive algorithm. We also give a lower bound showing that a constant competitive ratio cannot be achieved in the general case without resource augmentation.

Original language | English |
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Pages (from-to) | 822-841 |

Number of pages | 20 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 23 |

Issue number | 2 |

DOIs | |

State | Published - 2009 |

## Keywords

- Competitive analysis
- Interval coloring with bandwidth
- Lower bound

## ASJC Scopus subject areas

- General Mathematics