Optimal online ring routing

Abstract

We study how to route online splittable flows in bidirectional ring networks to minimize maximum load. We show that the competitive ratio of any deterministic online algorithm for this problem is at least 2 − 2/n, where n is the size of the ring, and that the online algorithm that splits each flow inversely proportionally to the length of the flow's shortest path achieves this competitive ratio for all integers n ≥ 2.

Online algorithms for the mixed ring loading problem with two nodes

“…Motivated by [5,11], we consider the mixed ring loading problem with two nodes as described in Fig. 1c, where each link a ∈ {e, a 0 , a 1 } has a weight w(a) representing the cost of unit demand routed through this link.…”

“…2. When the demands are splittable, the optimal solution is to send 5 3 units of flow f 1 ( f 2 , respectively) on the directed link a 0 (a 1 , respectively), as shown in Fig. 2a.…”

“…For any i = 0, 1, let T i be the total demand of the flows of type i. When the demand is splittable, the MRL problem is similar to the online ring routing problem studied in [5]. If the ring contains four directed links as in Fig.…”

“…Due to the extensive applications in metropolitan area networks [5] and fiber-opticbased telecommunication networks [14], Cosares and Saniee [3] introduced the ring loading problem, which has been extensively studied in the literature [4][5][6][7][8][9][10][11][12][13][14]. Three kinds of models have been considered in previous studies of the ring loading problem: (1) demands may be sent either in the front or back route with demand splitting; (2) demands are allowed to be split into two parts but restricted to be integrally split; and (3) each demand must be routed entirely in either of the two directions without demand splitting.…”

“…Li et al [8] studied the ring loading problem with penalty cost which is N P-hard, and designed a 1.58-approximation algorithm. Havill and Hutson [5] When the demands are integer splittable, Myung et al [10] provided an O(nk) time optimal algorithm. Myung et al [9] improved the result by offering an O(min{nk, n 2 }) time optimal algorithm.…”