Abstract
We consider online leasing problems in which demands arrive over time and need to be served by leasing resources. We introduce a new model for these problems such that a resource can be leased for K different durations each incurring a different cost (longer leases cost less per time unit). Each demand i can be served anytime between its arrival \(a_i\) and its deadline \(a_i + d_i\) by a leased resource. The objective is to meet all deadlines while minimizing the total leasing costs. This model is a natural generalization of Meyerson’s ParkingPermitProblem (FOCS 2005) in which \(d_i=0\) for all i. We propose an online algorithm that is \(\Theta (K + \frac{d_{max}}{l_{min}})\)-competitive where \(d_{max}\) and \(l_{min}\) denote the largest \(d_i\) and the shortest available lease length, respectively. We also extend the SetCoverLeasing problem by deadlines and give a competitive online algorithm which also improves on existing solutions for the original SetCoverLeasing problem.
This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Center ‘On-The-Fly Computing’ (SFB 901) and the International Graduate School ‘Dynamic Intelligent Systems’.
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Li, S., Mäcker, A., Markarian, C., Meyer auf der Heide, F., Riechers, S. (2015). Towards Flexible Demands in Online Leasing Problems. In: Xu, D., Du, D., Du, D. (eds) Computing and Combinatorics. COCOON 2015. Lecture Notes in Computer Science(), vol 9198. Springer, Cham. https://doi.org/10.1007/978-3-319-21398-9_22
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DOI: https://doi.org/10.1007/978-3-319-21398-9_22
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