A Constant-Competitive Algorithm for Online OVSF Code Assignment

Chin, F.; Ting, Hing-Fung; Zhang, Y.

doi:10.1007/s00453-008-9241-8

Cited by 6 publications

(13 citation statements)

References 12 publications

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“…Let us consider a call sequence σ1 = (8,1,6,10,8,4,8,19,6,8,13,11). To apply the algorithm Hybrid , we first partition the frequencies into the following sets: Proof.…”

Section: Upper Boundmentioning

confidence: 99%

Online frequency allocation in cellular networks

Chan

Chin

et al. 2007

Proceedings of the Nineteenth Annual ACM Symposium on Parallel Algorithms and Architectures

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Given a mobile telephone network, whose geographical coverage area is divided into cells, phone calls are serviced by assigning frequencies to them, so that no two calls emanating from the same or neighboring cells are assigned the same frequency. Assuming an online arrival of calls and the calls will not terminate, the problem is to minimize the span of frequencies used.By first considering χ-colorable networks, which is a generalization of (the 3-colorable) cellular networks, we present a (χ + 1)/2-competitive online algorithm. This algorithm, when applied to cellular networks, is effectively a positive solution to the open problem posed in [8]: Does a 2-competitive online algorithm exist for frequency allocation in cellular networks? We further prove a lower bound which shows that our 2-competitive algorithm is optimal.We discover that an interesting phenomenon occurs for the online frequency allocation problem when the number of calls considered becomes large: previously-derived optimal (lower and upper) bounds on competitive ratios no longer hold true. For cellular networks, we show new asymptotic lower and upper bounds of 1.5 and 1.9126, respectively, which breaks through the optimal bound of 2 shown previously.

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“…Let us consider a call sequence σ1 = (8,1,6,10,8,4,8,19,6,8,13,11). To apply the algorithm Hybrid , we first partition the frequencies into the following sets: Proof.…”

Section: Upper Boundmentioning

confidence: 99%

Online frequency allocation in cellular networks

Chan

Chin

et al. 2007

Proceedings of the Nineteenth Annual ACM Symposium on Parallel Algorithms and Architectures

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“…To serve a release request, we just need to mark a specified assigned node free. There are two constraints for the node assignments, which are (1) any node can be assigned to at most one unreleased assignment request, (without ambiguity, all assigned requests are assumed unreleased), and (2) there is at most one assigned node in every leaf-to-root path. Fig.…”

Section: Introductionmentioning

confidence: 99%

“…1 gives a valid tree node assignment. The tree node assignment problem can be considered as a general resource allocation problem, which can model the specific problems, such as the Orthogonal Variable Spreading Factor (OVSF) code assignment problem [2,3,7,12,13,14,15,16,17], the buddy memory allocation problem [1,5,10,11], and the hypercube subcube allocation problem [6]. The main difference between these problems is how the resource, the nodes at level i, for 0 ≤ i ≤ h, are interpreted.…”

Section: Introductionmentioning

confidence: 99%

“…Forisek et al [8] gave a constant-competitive algorithm, but without deriving the exact value of the constant. Chin, Ting and Zhang [2] gave a 10-competitive algorithm and, in addition, their algorithm guarantees that each request is served with at most 5 assignments/reassignments. They then improved the upper bound by proposing a 6-competitive algorithm [3].…”

Section: Introductionmentioning

confidence: 99%

“…They then improved the upper bound by proposing a 6-competitive algorithm [3]. They improved the lower bound of the competitive ratio to 5/3 ≈ 1.67 [2]. Very recently, Miyazaki and Okamoto [14] gave a 7-competitive algorithm and improved the lower bound of the competitive ratio to 2.…”

Section: Introductionmentioning

confidence: 99%

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Online tree node assignment with resource augmentation

et al. 2010

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Abstract. Given a complete binary tree of height h, the online tree node assignment problem is to serve a sequence of assignment/release requests, where an assignment request, with an integer parameter 0 ≤ i ≤ h, is served by assigning a (tree) node at level (or height) i and a release request is served by releasing a specified assigned node. The node assignments have to guarantee that no node is assigned to two assignment requests unreleased, and every leaf-to-root path of the tree contains at most one assigned node. With assigned node reassignments allowed, the target of the problem is to minimize the number of assignments/reassigments, i.e., the cost, to serve the whole sequence of requests. This online tree node assignment problem is fundamental to many applications, including OVSF code assignment in WCDMA networks, buddy memory allocation and hypercube subcube allocation.Most of the previous results focus on how to achieve good performance when the same amount of resource is given to both the online and the optimal offline algorithms, i.e., one tree. In this paper, we focus on resource augmentation, where the online algorithm is allowed to use more trees than the optimal offline algorithm. By using different approaches, we give (1) a 1-competitive online algorithm, which uses (h + 1)/2 trees, and is optimal because (h + 1)/2 trees are required by any online algorithm to match the cost of the optimal offline algorithm with one tree; (2) a 2-competitive algorithm with 3h/8 + 2 trees; (3) an amortized (4/3 + α)-competitive algorithm with (11/4 + 4/(3α)) trees, for any α where 0 < α ≤ 4/3.

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