New PDF release: Algorithmic Aspects in Information and Management: Second

By Allan Borodin (auth.), Siu-Wing Cheng, Chung Keung Poon (eds.)

ISBN-10: 3540351574

ISBN-13: 9783540351573

This e-book constitutes the refereed complaints of the second one overseas convention on Algorithmic points in info 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 rigorously reviewed and chosen from 263 submissions. The papers conceal subject matters from parts comparable to on-line scheduling, video game and finance, info buildings and algorithms, computational geometry, optimization, graph, and string.

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Read Online or Download Algorithmic Aspects in Information and Management: Second International Conference, AAIM 2006, Hong Kong, China, June 20-22, 2006. Proceedings PDF

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Extra info for Algorithmic Aspects in Information and Management: Second International Conference, AAIM 2006, Hong Kong, China, June 20-22, 2006. Proceedings

Example text

It is a contradiction with the assumption of a minimum counterexample. Let j0 be the first job arranged in the schedule σ. Let [si , Ci,min ], i = 1, . . , k, be the i-th period during which both machines are busy in σ (see Figure 3). Let fi be the number of jobs starting before time Ci,min in σ. Denote by Ci,max the largest completion time among the jobs starting before time Ci,min . Let Ai , Bi denote the job sets in which all the jobs arrive before time Ci,min and are started at or after Ci,min in σ and in σ ∗ , respectively.

Hence Lk ≤ 12 (fk + 1). Case 3. If ak = 2, then the last job must have deadline Ck,max + 2. Otherwise if we schedule the last two 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. 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.

Online Scheduling with Hard Deadlines on Parallel Machines 41 ... j* s* j* Ci ,min Fig. 6. The case that s∗ < Ci,min − 1 s* Ci ,min Fig. 7. The case that s∗ = Ci,min − 1 We further give two lemmas below. The omitted proofs will be included in the full paper. Lemma 6. L1 ≤ l1 . Furthermore, if L1 = l1 , then C1,min > C1,max ; if L1 = l1 − 12 , then C1,max ≥ C1,max . Lemma 7. Li ≤ li for i = 1, . . , k. Furthermore, if Li = li , then Ci,min > Ci,max ; if Li = li − 12 , then Ci,max ≥ Ci,max . Theorem 3.

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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.)


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