A simple on-line bin-packing algorithm
Journal of the ACM (JACM)
Bin packing with divisible item sizes
Journal of Complexity
Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
General Schedulers for the Pinwheel Problem Based on Double-Integer Reduction
IEEE Transactions on Computers
On the asymptotic worst case behavior of harmonic fit
Journal of Algorithms
Metropolitan area video-on-demand service using pyramid broadcasting
Multimedia Systems
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
Scheduling Algorithms for Multiprogramming in a Hard-Real-Time Environment
Journal of the ACM (JACM)
SIAM Journal on Discrete Mathematics
Harmonic broadcasting is optimal
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the online bin packing problem
Journal of the ACM (JACM)
An Efficient Periodic Broadcast Technique for Digital VideoLibraries
Multimedia Tools and Applications
Scheduling techniques for media-on-demand
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Minimizing Service and Operation Costs of Periodic Scheduling
Mathematics of Operations Research
Windows Scheduling Problems for Broadcast Systems
SIAM Journal on Computing
Pushing dependent data in clients-providers-servers systems
Wireless Networks
Dynamic bin packing of unit fractions items
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On-line windows scheduling of temporary items
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
A general buffer scheme for the windows scheduling problem
Journal of Experimental Algorithmics (JEA)
Dynamic bin packing of unit fractions items
Theoretical Computer Science
Periodic scheduling with obligatory vacations
Theoretical Computer Science
The gardener's problem for web information monitoring
Proceedings of the 18th ACM conference on Information and knowledge management
Dynamic bin packing with unit fraction items revisited
Information Processing Letters
Windows scheduling of arbitrary-length jobs on multiple machines
Journal of Scheduling
SIGACT news online algorithms column 20: the power of harmony
ACM SIGACT News
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Given is a sequence of n positive integers w1,w2,…,wn that are associated with the items 1,2,…n, respectively. In the windows scheduling problem, the goal is to schedule all the items (equal-length information pages) on broadcasting channels such that the gap between two consecutive appearances of page i on any of the channels is at most wi slots (a slot is the transmission time of one page). In the unit-fractions bin packing problem, the goal is to pack all the items in bins of unit size where the size (width) of item i is 1/wi. The optimization objective is to minimize the number of channels or bins. In the offline setting, the sequence is known in advance, whereas in the online setting, the items arrive in order and assignment decisions are irrevocable. Since a page requires at least 1/wi of a channel's bandwidth, it follows that windows scheduling without migration (i.e., all broadcasts of a page must be from the same channel) is a restricted version of unit-fractions bin packing. Let H = ⌈&sumi=1n(1/wi) be the bandwidth lower bound on the required number of bins (channels). The best-known offline algorithm for the windows scheduling problem used H + O(ln H) channels. This article presents an offline algorithm for the unit-fractions bin packing problem with at most H + 1 bins. In the online setting, this article presents algorithms for both problems with H + O(&sqrt;H) channels or bins, where the one for the unit-fractions bin packing problem is simpler. On the other hand, this article shows that already for the unit-fractions bin packing problem, any online algorithm must use at least H+&Omega(ln H) bins. For instances in which the window sizes form a divisible sequence, an optimal online algorithm is presented. Finally, this article includes a new NP-hardness proof for the windows scheduling problem.