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- Geir Agnarsson, Ágúst S. Egilsson, Magnús M. Halldórsson
- AGTIVE
- 2003

We consider vertex coloring of a simple acyclic digraph G in such a way that two vertices which have a common ancestor in G receive distinct colors. Such colorings arise in a natural way when clustering, indexing and bounding space for various genetic data for efficient analysis. We discuss the corresponding chromatic number and derive an upper bound as a… (More)

- Ágúst S. Egilsson, Hakon Gudbjartsson
- ArXiv
- 2003

We introduce indexing of tables referencing complex structures such as digraphs and spatial objects, appearing in genetics and other data intensive analysis. The indexing is achieved by extracting dimension schemas from the referenced structures. The schemas and their dimensionality are determined by proper coloring algorithms and the duality between all… (More)

- Geir Agnarsson, Ágúst S. Egilsson, Magnús M. Halldórsson
- Discrete Applied Mathematics
- 2008

We consider vertex coloring of an acyclic digraph G in such a way that two vertices which have a common ancestor in G receive distinct colors. Such colorings arise in a natural way when bounding space for various genetic data for efficient analysis. We discuss the corresponding down-chromatic number and derive an upper bound as a function of D(G), the… (More)

In this paper we first describe the geometry of the Newton polyhedra of polynomials invariant under certain linear Hamiltonian circle actions. From the geometry of the polyhedra, various Poisson structures on the orbit spaces of the actions are derived and Poisson embeddings into model spaces, for the orbit spaces, are constructed. The Poisson structures,… (More)

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