Linear time algorithms for the ring loading problem with demand splitting

Optimal online ring routing

“…Myung et al [9] gave an algorithm to solve the relaxed RLP that runs in O(nk) time, improving upon previous algorithms given by Dell'Amico et al [3] and Schrijver et al [11]. Myung and Kim [8] and Wang [12] later gave improved algorithms with running times O(min{nk, n 2 }) and O(k) when k ≥ n for some > 0, respectively. Lee and Chang [6], Myung [7], and Wang [12] have provided increasingly efficient algorithms for the relaxed RLP with Integer Demand Splitting.…”

“…Research in the area of bidirectional SONET Rings has focused on the Ring Loading Problem (RLP) [2][3][4][5][6][7][8][9][10][11][12], introduced by Cosares and Saniee [2]. Here, the concern is to set the initial capacity of the ring based on forecasted traffic demands d st from each source s to each destination t. In the original RLP, the entire demand between two given nodes must be routed in one of the two possible directions, and the objective is to minimize the maximum load on the cycle, where the load between two adjacent nodes is the sum of the demands routed over the edges connecting them in both directions.…”

“…Also, we handle each flow request separately rather than combining all flows between s and t into a single demand. The more general relaxed RLP [8,9,12] allows demands to be split arbitrarily in two directions. The relaxed RLP with Integer Demand Splitting [6,7,12] also allows demands to be split, but the amount of demand assigned to each direction must be an integer.…”

The Price of Anarchy for Selfish Ring Routing is Two

“…Indeed, considerable research has already gone into studying rings, in particular in the context of designing approximation algorithms for combinatorial optimization problems [Anshelevich and Zhang 2008;Blum et al 2001;Cheng 2004;Schrijver et al 1998;Wang 2005].…”

Stability vs. optimality in selfish ring routing

“…Secondly, rings have been a fundamental topology frequently encountered in communication networks, and attract considerable attention and efforts from the research community [3,5,6,8,24,25], especially in design of approximation algorithms for combinatorial optimization problems. Our study of selfish routing on the ring topology attempts not only to provide a good starting point for evaluating the PoA and PoS in asymmetric network congestion games, but also to enhance the diversity of network topologies amenable to the minimax criterion.…”