By Allan Borodin (auth.), Siu-Wing Cheng, Chung Keung Poon (eds.)
This publication constitutes the refereed court cases 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 offered including abstracts of two invited talks have been rigorously reviewed and chosen from 263 submissions. The papers hide issues from parts equivalent to on-line scheduling, online game and finance, facts buildings and algorithms, computational geometry, optimization, graph, and string.
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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
Otherwise, if d1 > Ck,max + 1, then we consider the job j2 that is started at time Ck,max − 1. By the algorithm d2 < Ck,min + 1. If not, then α > 0 and d2 ≥ Ck,min + 1. Job j2 should not have been started at Ck,max − 1. 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.
An instance of the basic ODARPTW in the metric space M consists of a sequence R = (r1 , r2 , · · · , rm ) of requests. Each request is a quadruple ri = (ti , zi , ai , bi ) ∈ R × N × X × X with the following meaning: ti ∈ R is the time that request ri is released and zi ∈ N is the quantity of goods that needs to be transported by the server; ai ∈ X and bi ∈ X are the source and destination, respectively, between which the goods corresponding to request ri is to be transported. The capacity of the server is ﬁnite, denoted by constant Z.
Other than the single machine case in which a greedy algorithm can achieve the best ratio of two, the case that m ≥ 2 becomes much more complex. It is easy to have an online algorithm with competitive ratio of two. To improve the bound we design a non-trivial optimal 3/2-competitive online algorithm for m = 2. Our algorithms satisfy the assumption of immediate notiﬁcation. An obvious question is to improve the Simple Algorithm LS for the general case of m machines. Before closing the paper we propose a stronger property than immediate notiﬁcation, called immediate decision.