Abstract
Online OVSF code assignment has an important application to wireless communications. Recently, this problem was formally modeled as an online problem, and performances of online algorithms have been analyzed by the competitive analysis. The previous best upper and lower bounds on the competitive ratio were 10 and 5/3, respectively. In this paper, we improve them to 7 and 2, respectively. We also show that our analysis for the upper bound is tight by giving an input sequence for which the competitive ratio of our algorithm is 7 ― ε for an arbitrary constant ε > 0.
Highlights
Universal Mobile Telecommunication System (UMTS) [1, 2] is one of the third generation (3G) technologies, which is a mobile communication standard
We further show that our upper bound analysis is tight by giving a sequence of requests for which the competitive ratio of E XTENDED -L AZY is 7 − ε for an arbitrary constant ε > 0
For the online OVSF code assignment problem, there have been some resource augmentation models, namely, online algorithms are allowed to use more bandwidth than an optimal offline algorithm: Erlebach et al [4] developed a 4-competitive algorithm in which an online algorithm can use a double-sized OVSF code tree
Summary
Universal Mobile Telecommunication System (UMTS) [1, 2] is one of the third generation (3G) technologies, which is a mobile communication standard. Conditions (iii), (iv), and (v) remain satisfied for the levels which did not belong to tank[b, t] because no code was released from nor assigned to these levels. Case (4): By executing FreeTail(`(c)), receiving code c0 , and executing AppendRich(`(c), c), only tank[`(c0 ), `(c)] is removed but the statuses of all vertices remain the same.
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