Mixed integer programs are commonly solved with linear programming based branch-and-bound algorithms. The success of the algorithm strongly depends on the strategy used to select the variable to branch on.We present a new generalization called reliability branching of today's state-of-the-art strong branching and pseudocost branching branching strategies for linear programming based branch-and-bound algorithms. After reviewing commonly used branching strategies and performing extensive computational studies we compare different parameter settings and show the superiority of our proposed new strategy.

In this paper, we present the implementation of a branch-and-cut algorithm for solving Steiner tree problems in graphs. Our algorithm is based on an integer programming formulation for directed graphs and comprises preprocessing, separation algorithms, and primal heuristics. We are able to solve nearly all problem instances discussed in the literature to optimality, including one problem that-to our knowledge-has not yet been solved. We also report on our computational experiences with some very large Steiner tree problems arising from the design of electronic circuits. All test problems are gathered in a newly introduced library called SteinLib that is accessible via the World Wide Web.

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Microbial populations stochastically generate variants with strikingly different properties, such as virulence or avirulence and antibiotic tolerance or sensitivity.Photorhabdus luminescensbacteria have a variable life history in which they alternate between pathogens to a wide variety of insects and mutualists to their specific host nematodes. Here, we show that theP. luminescenspathogenic variant (P form) switches to a smaller-cell variant (M form) to initiate mutualism in host nematode intestines. A stochastic promoter inversion causes the switch between the two distinct forms. M-form cells are much smaller (one-seventh the volume), slower growing, and less bioluminescent than P-form cells; they are also avirulent and produce fewer secondary metabolites. Observations of form switching by individual cells in nematodes revealed that the M form persisted in maternal nematode intestines, were the first cells to colonize infective juvenile (IJ) offspring, and then switched to P form in the IJ intestine, which armed these nematodes for the next cycle of insect infection.