An O(qn) algorithm to q-color a proper family of circular arcs
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, \textit{J. B. Orlin}, \textit{M. A. Bonuccelli} and \textit{D. P. Bovel} [SIAM J. Algebraic Discrete Methods 2, 88-93 (1981; Zbl 0496.68047)] 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.
scientific article; zbMATH DE number 3905862
scientific article