Algorithmica (2018) 80:1556–1574 https://doi.org/10.1007/s00453-018-0420-y Towards Flexible Demands in Online Leasing Problems Shouwei Li 1 · Christine Markarian 1 · Friedhelm Meyer auf der Heide 1 Received: 25 October 2015 / Accepted: 16 February 2018 / Published online: 20 February 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 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 in which 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 any time between its arrival a i and its deadline a i +d i by a leased resource. The objective is to meet all dead- lines while minimizing the total leasing costs. This model is a natural generalization of Meyerson’s ParkingPermitProblem (in: Proceedings of the 46th annual IEEE symposium on foundations of computer science, FOCS ’05, IEEE Computer Society, Washington, pp 274–284, 2005) in which d i = 0 for all i . We propose an online algorithm that is Θ( K + 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 SetCoverLeas- ing and FacilityLeasing to their respective variants in which deadlines are added. For the former, we give an O  log(m · ( K + d max l min )) log l max  -competitive randomized algorithm, where m represents the number of subsets and l max represents the largest available lease length. This improves on existing solutions for the original SetCov- The results presented in this paper are based on the conference paper [28]. This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Center ‘On-The-Fly Computing’ (SFB 901). B Christine Markarian christine.markarian@uni-paderborn.de Shouwei Li shouwei.li@uni-paderborn.de Friedhelm Meyer auf der Heide fmadh@uni-paderborn.de 1 Computer Science Department, Heinz Nixdorf Institute, University of Paderborn, Fürstenallee 11, 33102 Paderborn, Germany 123