Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
Tests for Gene Clusters Satisfying the Generalized Adjacency Criterion
BSB '08 Proceedings of the 3rd Brazilian symposium on Bioinformatics: Advances in Bioinformatics and Computational Biology
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We present a parametrized definition of gene clusters thatallows us to control the emphasis placed on conserved order within acluster. Though motivated by biological rather than mathematical considerations,this parameter turns out to be closely related to the maximumbandwidth parameter of a graph. Our focus will be on how thisparameter affects the characteristics of clusters: how numerous they are,how large they are, how rearranged they are and to what extent theyare preserved from ancestor to descendant in a phylogenetic tree. Weinfer the latter property by dynamic programming optimization of thepresence of individual edges at the ancestral nodes of the phylogeny. Weapply our analysis to a set of genomes drawn from the Yeast Gene OrderBrowser.