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# Circular-arc Graph Coloring and Unrolling

1 A3 - Advanced analysis to code optimization
UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France
Abstract : 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.
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https://hal.inria.fr/inria-00073353
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Submitted on : Wednesday, May 24, 2006 - 12:36:17 PM
Last modification on : Thursday, February 3, 2022 - 3:37:20 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:43:36 PM

### Identifiers

• HAL Id : inria-00073353, version 1

### Citation

Christine Eisenbeis, Sylvain Lelait, Bruno Marmol. Circular-arc Graph Coloring and Unrolling. RR-3336, INRIA. 1998. ⟨inria-00073353⟩

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