TY - JOUR

T1 - Non-additive two-option ski rental

AU - Levi, Amir

AU - Patt-Shamir, Boaz

N1 - Publisher Copyright:
© 2015 Elsevier B.V.

PY - 2015/6/13

Y1 - 2015/6/13

N2 - We consider the following generalization of the classical problem of ski rental. There is a game that ends at an unknown time, and the algorithm needs to decide how to pay for the time until the game ends. In our generalization, there are two "payment plans" called "options," such that each option i (for i=1, 2) consists of two kinds of costs: bi is the (one time) cost to start using Option i, and ai is the (ongoing) usage cost per unit of time for Option i. We assume w.l.o.g. that a1>a2 and b12. Additionally, we assume the existence of a transition cost c, which is incurred if we switch from Option 1 to Option 2. (In the classical version, b1=0, a2=0 and c=b2.)We give deterministic and randomized algorithms for this general setting and analyze their competitive ratio. We also prove that the competitive ratios of our algorithms are the best possible by presenting matching lower bounds for both the deterministic and the randomized cases.

AB - We consider the following generalization of the classical problem of ski rental. There is a game that ends at an unknown time, and the algorithm needs to decide how to pay for the time until the game ends. In our generalization, there are two "payment plans" called "options," such that each option i (for i=1, 2) consists of two kinds of costs: bi is the (one time) cost to start using Option i, and ai is the (ongoing) usage cost per unit of time for Option i. We assume w.l.o.g. that a1>a2 and b12. Additionally, we assume the existence of a transition cost c, which is incurred if we switch from Option 1 to Option 2. (In the classical version, b1=0, a2=0 and c=b2.)We give deterministic and randomized algorithms for this general setting and analyze their competitive ratio. We also prove that the competitive ratios of our algorithms are the best possible by presenting matching lower bounds for both the deterministic and the randomized cases.

KW - Buy or rent

KW - Competitive analysis

KW - Duration prediction

KW - Randomized algorithms

KW - Ski rental

UR - http://www.scopus.com/inward/record.url?scp=84951769249&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2015.01.038

DO - 10.1016/j.tcs.2015.01.038

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84951769249

SN - 0304-3975

VL - 584

SP - 42

EP - 52

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -