IEEE Transactions on Parallel and Distributed Systems
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We present a polynomial-time algorithm for finding an almost optimal solution to the following combinatorial problem, which is motivated by the problem of balancing communication in networks having the structure of rings. {\it Input:} a circle and a multiset of $c$ chords, having $n$ distinct endpoints, representing desired point-to-point communications; $c''$ of the chords are distinct. {\it The task:} to map each chord to an arc having the same endpoints, in a way that minimizes the maximum number of arcs crossing any normal to the circle. Our algorithm operates in time $O(n^2c)$ and uses $O(n + c'')$ words of storage; it finds a mapping that is within $+ 1$ of optimal. \end{document}