Dynamic session management for static and mobile users: a competitive on-line algorithmic approach
DIALM '00 Proceedings of the 4th international workshop on Discrete algorithms and methods for mobile computing and communications
Dynamic TCP acknowledgement and other stories about e/(e-1)
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Theoretical Computer Science
On the Performance of Competitive Algorithms in Practice
Developments from a June 1996 seminar on Online algorithms: the state of the art
Online strategies for dynamic power management in systems with multiple power-saving states
ACM Transactions on Embedded Computing Systems (TECS)
Nearly optimal strategies for special cases of on-line capital investment
Theoretical Computer Science
SIAM Journal on Computing
Ski rental with two general options
Information Processing Letters
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The multislope ski-rental problem [11] is an extension of the classical ski-rental problem [10], where the player has several lease options in addition to the pure rent and buy options. In this problem an instance, which is the setting of the options, significantly affects the player's performance. There is an algorithm that for a given instance, computes the best possible strategy [1]. However, the output is given in numerical values and the relational nature between the instance and the best possible performance has not been known. In this paper we prove that even for the easiest instance, a competitive ratio smaller than e/(e−1)≈1.58 cannot be achieved. More precisely, according to the number of options, tight bounds are obtained in a closed form. Furthermore, we establish a matching upper and lower bound of the competitive ratio each for the 3-slope and 4-slope problems.