By Allan Borodin (auth.), Siu-Wing Cheng, Chung Keung Poon (eds.)
This booklet constitutes the refereed complaints of the second one foreign convention on Algorithmic points in details and administration, AAIM 2006, held in Hong Kong, China in June 2006.
The 34 revised complete papers provided including abstracts of two invited talks have been conscientiously reviewed and chosen from 263 submissions. The papers conceal themes from components equivalent to on-line scheduling, online game and finance, facts buildings and algorithms, computational geometry, optimization, graph, and string.
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Additional info for Algorithmic Aspects in Information and Management: Second International Conference, AAIM 2006, Hong Kong, China, June 20-22, 2006. Proceedings
After the deletion of the last job, it is still a counterexample. It is a contradiction. So the last job have deadline Ck,max + 2. If Lk = lk , then we have Ck,min > Ck,max . Therefore bk ≤ 4 and Lk ≤ 12 (fk + 2); If Lk ≤ lk − 12 , then we have bk ≤ 5 and thus prove Lk ≤ 12 (fk + 2). 42 J. Ding and G. Zhang Case 4. If ak = 3, then the last job must have deadline Ck,min + 3. Otherwise if we schedule the last three jobs at Ck,min using EDF , then the last job is not a critical job. After the deletion of the last job, it is still a counterexample.
Jawor, J. Sagll, T. Tichy. Online schedulig of equal-length jobs: randomization and restarts help. In Proc. 31st International Colloquium on Automata, Languages, and Programming (ICALP), LNCS 3142, pages 358-370, 2004. 3. H. Goldwasser. Patience is a virtue: the eﬀect of slack on competitiveness for admission control. In Proc. 10th ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 396-405, 1999. 4. H. Goldwasser and B. Kerbikov. Admission control with immediate notiﬁcation. Journal of Scheduling 6: 269-285, 2003.
Moreover all our results are still valid under the assumption of immediate notiﬁcation. 2 Lower Bounds for m ≥ 2 Machines Theorem 1. For on-line scheduling of unit-length jobs on m machines to maximize the number of jobs completed, the competitive ratio of any deterministic online algorithm is not smaller than ⎧ if m = 2 ⎪ ⎪ 3/2 ⎨ 6/5 + 1/(5k) if m = 3k R= , k ≥ 1. (6k + 2)/(5k + 1) if m = 3k + 1 ⎪ ⎪ ⎩ (6k + 3)/(5k + 2) if m = 3k + 2 Proof. We only prove the lower bound for m = 2. At time 0, a job with deadline 5 comes.
Algorithmic Aspects in Information and Management: Second International Conference, AAIM 2006, Hong Kong, China, June 20-22, 2006. Proceedings by Allan Borodin (auth.), Siu-Wing Cheng, Chung Keung Poon (eds.)