Circular-arc Graph Coloring and Unrolling
Résumé
The register periodic allocation problem is viewed as unrolling and coloring the underlying structure of circular-arc graph. The problem is to find relations between the unrolling degree and the chromatic number. For this purpose we distinguish cyclic colorings that can be found by means of the {\em meeting graph} and non-cyclic ones for which we prove the asymptotic property: let $r$ be the width of the original interval family. Then the $u$-unrolled graph is $r$ or $r+1$-colorable for $u$ large enough.