Journal of Discrete Algorithms
On the multimessage capacity region for undirected ring networks
IEEE Transactions on Information Theory
Approximation algorithms for the ring loading problem with penalty cost
Information Processing Letters
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The following problem arose in the planning of optical communications networks which use bidirectional SONET rings. Traffic demands di,j are given for each pair of nodes in an $n$-node ring; each demand must be routed one of the two possible ways around the ring. The object is to minimize the maximum load on the cycle, where the load of an edge is the sum of the demands routed through that edge.We provide a fast, simple algorithm which achieves a load that is guaranteed to exceed the optimum by at most 3/2 times the maximum demand, and that performs even better in practice. En route we prove the following curious lemma: for any $x_1, \dots, x_n \in [0,1]$ there exist $y_1, \dots, y_n$ such that for each $k$, $|y_k|=x_k$ and $$ \left| \sum_{i=1}^k y_i - \sum_{i=k+1}^n y_i \right| \le 2. $$ [This article is reprinted here (with updates) from SIAM J. Discrete Math., 11 (1998), pp. 1--14. New developments include a $1+\varepsilon$ approximation algorithm and a variation of ring loading in the setting of wavelength division multiplexing; remarks added for this printing, about these and other issues, are enclosed in brackets.]