An Algorithmic View on OVSF Code Assignment

Orthogonal Variable Spreading Factor (OVSF) codes are used in UMTS to share the radio spectrum among several connections of possibly different bandwidth requirements. The combinatorial core of the OVSF code assignment problem is to assign some nodes of a complete binary tree of height h (the code tree) to n simultaneous connections, such that no two assigned nodes (codes) are on the same root-to-leaf path. A connection that uses a 2-d fraction of the total bandwidth requires some code at depth d in the tree, but this code assignment is allowed to change over time. Requests for connections that would exceed the total available bandwidth are rejected. We consider the one-step code assignment problem: Given an assignment, move the minimum number of codes to serve a new request. Minn and Siu propose the so-called DCA algorithm to solve the problem optimally. In contrast, we show that DCA does not always return an optimal solution, and that the problem is NP-hard. We give an exact nO(h)-time algorithm, and a polynomial-time greedy algorithm that achieves approximation ratio Θ(h). A more practically relevant version is the online code assignment problem, where future requests are not known in advance. Our objective is to minimize the overall number of code reassignments. We present a Θ(h)-competitive online algorithm, and show that no deterministic online algorithm can achieve a competitive ratio better than 1.5. We show that the greedy strategy (minimizing the number of reassignments in every step) is not better than Ω(h) competitive. We give a 2-resource augmented online algorithm that achieves an amortized constant number of (re-)assignments. Finally, we show that the problem is fixed-parameter tractabl

Applied Metaheuristic Computing

For decades, Applied Metaheuristic Computing (AMC) has been a prevailing optimization technique for tackling perplexing engineering and business problems, such as scheduling, routing, ordering, bin packing, assignment, facility layout planning, among others. This is partly because the classic exact methods are constrained with prior assumptions, and partly due to the heuristics being problem-dependent and lacking generalization. AMC, on the contrary, guides the course of low-level heuristics to search beyond the local optimality, which impairs the capability of traditional computation methods. This topic series has collected quality papers proposing cutting-edge methodology and innovative applications which drive the advances of AMC

Online OVSF code assignment with resource augmentation

Orthogonal Variable Spreading Factor (OVSF) code assignment is a fundamental problem in Wideband Code-Division Multiple-Access (W-CDMA) systems, which play an important role in third generation mobile communications. In the OVSF problem, codes must be assigned to incoming code requests, with different data rate requirements, in such a way that they are mutually orthogonal with respect to an OVSF code tree. An OVSF code tree is a complete binary tree in which each node represents a code associated with the combined bandwidths of its two children. To be mutually orthogonal, each leaf-to-root path must contain at most one assigned code. In this paper, we focus on the online version of the OVSF code assignment problem, in the often-studied context of the single cell as well as in the more general context of the whole multi-cell cellular network (for which there are no known results). With the help of 1/8 and 11/8 extra bandwidth resources, we are able to give a 5-competitive algorithm in the single cell and the multicell context respectively, which means that the competitive ratio is a constant and not a function of the height of the OVSF tree and thereby improving upon past results. © Springer-Verlag Berlin Heidelberg 2007.link_to_subscribed_fulltex

Online OVSF code assignment with resource augmentation

Orthogonal Variable Spreading Factor (OVSF) code assignment is a fundamental problem in Wideband Code-Division Multiple-Access (W-CDMA) systems, which play an important role in third generation mobile communications. In the OVSF problem, codes must be assigned to incoming code requests, with different data rate requirements, in such a way that they are mutually orthogonal with respect to an OVSF code tree. An OVSF code tree is a complete binary tree in which each node represents a code associated with the combined bandwidths of its two children. To be mutually orthogonal, each leaf-to-root path must contain at most one assigned code. In this paper, we focus on the online version of the OVSF code assignment problem, in the often-studied context of the single cell as well as in the more general context of the whole multi-cell cellular network (for which there are no known results). With the help of 1/8 and 11/8 extra bandwidth resources, we are able to give a 5-competitive algorithm in the single cell and the multicell context respectively, which means that the competitive ratio is a constant and not a function of the height of the OVSF tree and thereby improving upon past results. © Springer-Verlag Berlin Heidelberg 2007.link_to_subscribed_fulltex

Applied Methuerstic computing

For decades, Applied Metaheuristic Computing (AMC) has been a prevailing optimization technique for tackling perplexing engineering and business problems, such as scheduling, routing, ordering, bin packing, assignment, facility layout planning, among others. This is partly because the classic exact methods are constrained with prior assumptions, and partly due to the heuristics being problem-dependent and lacking generalization. AMC, on the contrary, guides the course of low-level heuristics to search beyond the local optimality, which impairs the capability of traditional computation methods. This topic series has collected quality papers proposing cutting-edge methodology and innovative applications which drive the advances of AMC

(1+ε)-competitive algorithm for online OVSF code assignment with resource augmentation

This paper studies the online Orthogonal Variable Spreading Factor (OVSF) code assignment problem with resource augmentation introduced by Erlebach et al. (in STACS 2004. LNCS, vol. 2996, pp. 270–281, 2004). We propose a (1+1/α)-competitive algorithm with help of (1+⌈α⌉)lg∗ h trees for the height h of the OVSF code tree and any α≥1. In other words, it is a (1+ε)-competitive algorithm with help of (1+⌈1/ε⌉)lg∗ h trees for any constant 0<ε≤1. In the case of α=1 (or ε=1), we obtain a 2-competitive algorithm with 2lg∗ h trees, which substantially improves the previous resource of 3h/8+2 trees shown by Chan et al. (COCOON 2009. LNCS, vol. 5609, pp. 358–367, 2009). In another aspect, if it is not necessary to bound the incurred cost for individual requests to a constant, an amortized (4/3+δ)-competitive algorithm with (11/4+4/(3δ)) trees for any 0<δ≤4/3 is also designed in Chan et al. (COCOON 2009. LNCS, vol. 5609, pp. 358–367, 2009). The algorithm in this paper gives us a new trade-off between the competitive ratio and the resource augmentation when α≥3 (or ε≤1/3), although the incurred cost for individual requests is bounded to a constant