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arXiv · 1704.08835

Relaxing the Irrevocability Requirement for Online Graph Algorithms

Joan Boyar·Lene M. Favrholdt·Kim S. Larsen·Michal Kotrbčík
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Abstract

Online graph problems are considered in models where the irrevocability requirement is relaxed. Motivated by practical examples where, for example, there is a cost associated with building a facility and no extra cost associated with doing it later, we consider the Late Accept model, where a request can be accepted at a later point, but any acceptance is irrevocable. Similarly, we also consider a Late Reject model, where an accepted request can later be rejected, but any rejection is irrevocable (this is sometimes called preemption). Finally, we consider the Late Accept/Reject model, where late accepts and rejects are both allowed, but any late reject is irrevocable. For Independent Set, the Late Accept/Reject model is necessary to obtain a constant competitive ratio, but for Vertex Cover the Late Accept model is sufficient and for Minimum Spanning Forest the Late Reject model is sufficient. The Matching problem has a competitive ratio of 2, but in the Late Accept/Reject model, its competitive ratio is 3/2.

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Joan Boyar, Lene M. Favrholdt, Kim S. Larsen, Michal Kotrbčík. 2017-04-28. Relaxing the Irrevocability Requirement for Online Graph Algorithms. https://arxiv.org/abs/1704.08835

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