Algorithmic Aspects in Information and Management: Second by Allan Borodin (auth.), Siu-Wing Cheng, Chung Keung Poon

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

This booklet constitutes the refereed lawsuits 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 rigorously reviewed and chosen from 263 submissions. The papers conceal themes from parts equivalent to on-line scheduling, video game and finance, information constructions and algorithms, computational geometry, optimization, graph, and string.

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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. The competitive ratio of algorithm M EDF is 32 . Proof. Now we consider the last period. By Lemma 7, we have Lk ≤ lk . It is easy to verify ak ≤ 3. Otherwise if we schedule the last ak jobs at Ck,min using EDF , then the last job is not a critical job.

An interesting extension of the problem considered in this paper may take into account the non-uniform time windows. That is, each of the requests has a different size of time window. ) to see if better bounds can be obtained. Other possible extension of the problem is to crew scheduling in which more than one server is used to serve the requests. All of these can be further investigated. 70525004). References 1. , and Marchetti-Spaccamela et al. Non-abusiveness helps: An o(1)-competitive algorithm for minimizing the maximum flow time in the online traveling salesman problem.

So we have d2 < Ck,min + 1. By the algorithm after the deletion of job j1 , it is still a counterexample. It is a contradiction. Thus d1 = Ck,max + 1. If Lk = lk , then Ck,min > Ck,max . We get bk ≤ 2 and Lk ≤ 12 (fk + 1); If Lk ≤ lk − 12 , then bk ≤ 3. 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.

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