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

Abstract

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.