A Better bound of randomized algorithms for the multislope ski-rental problem

Hu, Maolin; Xu, Weijun

doi:10.1051/ita/2017009

Hu, Maolin ¹ ; Xu, Weijun ²

¹ School of Mathematical Science, Huaiyin Normal University, Huaian, Jiangsu 223300, P.R. China.
² School of Business Administration, South China University of Technology, Guangzhou 510641, P.R. China.

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 51 (2017) no. 2, pp. 91-98.

Résumé

The multislope ski-rental problem is an extension of the classical ski-rental problem, where the player has several lease options in addition to the pure rent and buy options. For the additive general model, Lotker, Patt-Shamir and Rawitz [in: SIAM J. Discr. Math. 26 (2012) 718–736] obtained a randomized algorithm with the competitive ratio bounded by $\frac{e - r_{k} / r_{0}}{e - 1}$ . However, obtaining a better bound on the competitive factor as a function of the slopes parameters remains an open problem in their paper. In this paper, we study randomized algorithm for the additive multislope ski rental problem, and extend the competitive ratio bound $\frac{e - r_{k} / r_{0}}{e - 1}$ proposed by Lotker et al. to $\frac{e}{e - 1 + r_{k} / r_{0}}$ .

Reçu le : 2017-04-11
Accepté le : 2017-09-11

MR Zbl

DOI : 10.1051/ita/2017009

Classification : 68W27, 91A80
Mots clés : Online algorithms, ski rental, randomized algorithms, competitive ratio

Affiliations des auteurs :

Hu, Maolin ¹ ; Xu, Weijun ²

@article{ITA_2017__51_2_91_0,
     author = {Hu, Maolin and Xu, Weijun},
     title = {A {Better} bound of randomized algorithms for the multislope ski-rental problem},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {91--98},
     publisher = {EDP-Sciences},
     volume = {51},
     number = {2},
     year = {2017},
     doi = {10.1051/ita/2017009},
     mrnumber = {3731539},
     zbl = {1383.68102},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita/2017009/}
}

TY  - JOUR
AU  - Hu, Maolin
AU  - Xu, Weijun
TI  - A Better bound of randomized algorithms for the multislope ski-rental problem
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2017
SP  - 91
EP  - 98
VL  - 51
IS  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ita/2017009/
DO  - 10.1051/ita/2017009
LA  - en
ID  - ITA_2017__51_2_91_0
ER  -

%0 Journal Article
%A Hu, Maolin
%A Xu, Weijun
%T A Better bound of randomized algorithms for the multislope ski-rental problem
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2017
%P 91-98
%V 51
%N 2
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ita/2017009/
%R 10.1051/ita/2017009
%G en
%F ITA_2017__51_2_91_0

Hu, Maolin; Xu, Weijun. A Better bound of randomized algorithms for the multislope ski-rental problem. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 51 (2017) no. 2, pp. 91-98. doi : 10.1051/ita/2017009. http://www.numdam.org/articles/10.1051/ita/2017009/

Bibliographie
Cité par

Y. Azar, Y. Bartal, E. Feuerstein, A. Fiat, S. Leonardi and A. Rosen, On capital investment. Algorithmica 25 (1999) 22–36. | DOI | Zbl

P. Damaschke, Nearly optimal strategies for special cases of on-line capital investment. Theoret. Comput. Sci. 302 (2003) 35–44. | DOI | Zbl

R. El-Yaniv, R. Kaniel and N. Linial, Competitive optimal online leasing. Algorithmica 25 (1999) 116–140. | DOI | Zbl

R. Fleischer, On the Bahncard problem. Theoret. Comput. Sci. 268 (2001) 161–174. | DOI | MR | Zbl

A.R. Karlin, M.S. Manasse, L.A. Mcgeoch and S.S. Owicki, Competitive randomized algorithms for nonuniform problems. Algorithmica 11 (1994) 542–571. | DOI | MR | Zbl

A.R. Karlin, M.S. Manasse, L. Rudolph and D.D. Sleator, Competitive snoopy caching. Algorithmica 3 (1988) 77–119. | DOI | MR | Zbl

R. Karp, On-line algorithms versus off-line algorithms: How much is it worth to know the future? Proc. of the IFIP 12th World Computer Congress 1 (1992) 416–429.

Z. Lotker, B. Patt-Shamir and D. Rawitz, Ski rental with two general options. Inf. Process Lett. 108 (2008) 339–422. | DOI | MR | Zbl

Z. Lotker, B. Patt-Shamir and D. Rawitz. Rent, lease or buy: Randomized algorithms for multislope ski rental. SIAM J. Discrete Math. 26 (2012) 718–736. | DOI | MR | Zbl

Cité par Sources :