Abstract
A family of arcs on a circle is proper if no arc is properly contained within another. While general minimal arc coloring is NP-complete, Orlin et al. recently obtained on O( n 2) algorithm for q-coloring a proper family of arcs by modeling proper arc coloring as a shortest path problem in an associated network (with negative edges). This paper simplifies Orlin's shortest-path network to obtain an O( qn) time algorithm.
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