On the asymptotic worst case behavior of harmonic fit
Journal of Algorithms
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Recent advances in the modeling, scheduling and control of flexible automation
WSC '93 Proceedings of the 25th conference on Winter simulation
Disk load balancing for video-on-demand systems
Multimedia Systems
Design and implementation of scalable continuous media servers
Parallel Computing - Special issues on applications: parallel data servers and applications
Online computation and competitive analysis
Online computation and competitive analysis
New Algorithms for Bin Packing
Journal of the ACM (JACM)
Approximation algorithms for data placement on parallel disks
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Developments from a June 1996 seminar on Online algorithms: the state of the art
Developments from a June 1996 seminar on Online algorithms: the state of the art
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Worst-case analysis of memory allocation algorithms
STOC '72 Proceedings of the fourth annual ACM symposium on Theory of computing
Fast algorithms for bin packing
Journal of Computer and System Sciences
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We consider class constrained packing problems, in which we are given a set of bins, each having a capacity v and c compartments, and n items of M different classes and the same (unit) size. We need to fill the bins with items, subject to capacity constraints, such that items of different classes are placed in separate compartments; thus, each bin can contain items of at most c distinct classes. We consider two optimization goals. In the class-constrained bin-packing problem (CCBP), our goal is to pack all the items in a minimal number of bins; in the class-constrained multiple knapsack problem (CCMK), we wish to maximize the total number of items packed in m bins, for m 1. The CCBP and CCMK model fundamental resource allocation problems in computer and manufacturing systems. Both are known to be strongly NP-hard.In this paper we derive tight bounds for the online variants of these problems. We first present a lower bound of (1 + 驴) on the competitive ratio of any deterministic algorithm for the online CCBP, where 驴 驴 (0, 1] depends on v, c, M and n. We show that this ratio is achieved by the algorithm first-fit.We then consider the temporary CCBP, in which items may be packed for a bounded time interval (that is unknown in advance). We obtain a lower bound of v/c on the competitive ratio of any deterministic algorithm. We show that this ratio is achieved by all any-fit algorithms. Finally, tight bounds are derived for the online CCMK and the temporary CCMK problems.