TY - GEN
T1 - Tight bounds for clairvoyant dynamic bin packing
AU - Azar, Yossi
AU - Vainstein, Danny
N1 - Publisher Copyright:
© 2017 Copyright held by the owner/author(s).
PY - 2017/7/24
Y1 - 2017/7/24
N2 - In this paper we focus on the Clairvoyant Dynamic Bin Packing (DBP) problem, which extends the classical online bin packing problem in that items arrive and depart over time and the departure time of an item is known upon its arrival. The problem naturally arises when handling cloud-based networks. We focus specifically on the MinUsageTime cost function which aims to minimize the overall usage time of all bins that are opened during the packing process. Earlierwork has shown a O( log μ/log log μ) upper bound where μ is defined as the ratio between the maximal and minimal durations of all items. We improve the upper bound by giving an O( p log μ)- competitive algorithm. We then provide a matching lower bound of Ω( √log μ) on the competitive ratio of any online algorithm, thus closing the gap with regards to this problem. We then focus on what we call the class of aligned inputs and give a O(log log μ)- competitive algorithm for this case, beating the lower bound of the general case by an exponential factor. Surprisingly enough, the analysis of our algorithm that we present, is closely related to various properties of binary strings.
AB - In this paper we focus on the Clairvoyant Dynamic Bin Packing (DBP) problem, which extends the classical online bin packing problem in that items arrive and depart over time and the departure time of an item is known upon its arrival. The problem naturally arises when handling cloud-based networks. We focus specifically on the MinUsageTime cost function which aims to minimize the overall usage time of all bins that are opened during the packing process. Earlierwork has shown a O( log μ/log log μ) upper bound where μ is defined as the ratio between the maximal and minimal durations of all items. We improve the upper bound by giving an O( p log μ)- competitive algorithm. We then provide a matching lower bound of Ω( √log μ) on the competitive ratio of any online algorithm, thus closing the gap with regards to this problem. We then focus on what we call the class of aligned inputs and give a O(log log μ)- competitive algorithm for this case, beating the lower bound of the general case by an exponential factor. Surprisingly enough, the analysis of our algorithm that we present, is closely related to various properties of binary strings.
KW - Analysis of algorithms
KW - Clairvoyant Setting
KW - Competitive ratio
KW - Dynamic bin packing
KW - Online algorithms
UR - http://www.scopus.com/inward/record.url?scp=85027864915&partnerID=8YFLogxK
U2 - 10.1145/3087556.3087570
DO - 10.1145/3087556.3087570
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AN - SCOPUS:85027864915
T3 - Annual ACM Symposium on Parallelism in Algorithms and Architectures
SP - 77
EP - 86
BT - SPAA 2017 - Proceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures
PB - Association for Computing Machinery
T2 - 29th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2017
Y2 - 24 July 2017 through 26 July 2017
ER -