Chloroplasts were once free-living cyanobacteria that became endosymbionts, but the genomes of contemporary plastids encode only Ϸ5-10% as many genes as those of their free-living cousins, indicating that many genes were either lost from plastids or transferred to the nucleus during the course of plant evolution. Previous estimates have suggested that between 800 and perhaps as many as 2,000 genes in the Arabidopsis genome might come from cyanobacteria, but genome-wide phylogenetic surveys that could provide direct estimates of this number are lacking. We compared 24,990 proteins encoded in the Arabidopsis genome to the proteins from three cyanobacterial genomes, 16 other prokaryotic reference genomes, and yeast. Of 9,368 Arabidopsis proteins sufficiently conserved for primary sequence comparison, 866 detected homologues only among cyanobacteria and 834 other branched with cyanobacterial homologues in phylogenetic trees. Extrapolating from these conserved proteins to the whole genome, the data suggest that Ϸ4,500 of Arabidopsis protein-coding genes (Ϸ18% of the total) were acquired from the cyanobacterial ancestor of plastids. These proteins encompass all functional classes, and the majority of them are targeted to cell compartments other than the chloroplast. Analysis of 15 sequenced chloroplast genomes revealed 117 nuclear-encoded proteins that are also still present in at least one chloroplast genome. A phylogeny of chloroplast genomes inferred from 41 proteins and 8,303 amino acids sites indicates that at least two independent secondary endosymbiotic events have occurred involving red algae and that amino acid composition bias in chloroplast proteins strongly affects plastid genome phylogeny.

√ log n) shown by Garg and Tamassia in 1996 could be improved. To answer this question, we show how to solve the uncapacitated min-cost flow problem on a planar bidirected graph with bounded costs and face sizes in O(n 3/2 ) time.

We are developing a social network tool that is powerful, comprehensive, and yet easy to use. The unique feature of our tool is the integration of network analysis and visualization. In a long-term interdisciplinary research collaboration, members of our group had implemented several prototypes to explore and demonstrate the feasibility of novel methods. These prototypes have been revised and combined into a stand-alone tool which will be extended regularly.

Abstract. Fan-planar graphs were recently introduced as a generalization of 1-planar graphs. A graph is fan-planar if it can be embedded in the plane, such that each edge that is crossed more than once, is crossed by a bundle of two or more edges incident to a common vertex. A graph is outer-fan-planar if it has a fan-planar embedding in which every vertex is on the outer face. If, in addition, the insertion of an edge destroys its outer-fan-planarity, then it is maximal outer-fan-planar. In this paper, we present a polynomial-time algorithm to test whether a given graph is maximal outerfan-planar. The algorithm can also be employed to produce an outer-fan-planar embedding, if one exists. On the negative side, we show that testing fan-planarity of a graph is NP-hard, for the case where the rotation system (i.e., the cyclic order of the edges around each vertex) is given.

Planar drawings of clustered graphs are considered. We introduce the notion of completely connected clustered graphs, i.e., hierarchically clustered graphs that have the property that not only every cluster but also each complement of a cluster induces a connected subgraph. As a main result, we prove that a completely connected clustered graph is c-planar if and only if the underlying graph is planar. Further, we investigate the influence of the root of the inclusion tree to the choice of the outer face of the underlying graph and vice versa.