State-of-the-art solvers for Constraint Satisfaction Problems (CSP), Mixed Integer Programs (MIP), and satisfiability problems (SAT) are usually based on a branch-and-bound algorithm. The question how to split a problem into subproblems (branching) is in the core of any branch-and-bound algorithm. Branching on individual variables is very common in CSP, MIP, and SAT. The rules, however, which v...

This paper introduces interdiction branching, a new branching method for binary integer programs that is designed to overcome the difficulties encountered in solving problems for which branching on variables is inherently weak. Unlike traditional methods, selection of the disjunction in interdiction branching takes into account the best feasible solution found so far. In particular, the method ...

The study of branching processes began in the 1840s with Irénée-Jules Bienaymé, a probabilist and statistician, and was advanced in the 1870s with the work of Reverend Henry William Watson, a clergyman and mathematician, and Francis Galton, a biometrician. In 1873, Galton sent a problem to the Educational Times regarding the survival of family names. When he did not receive a satisfactory answe...

There are many examples of branching networks in nature, such as tree crowns, river systems, arteries and lungs. These networks have often been described as being self-similar, or following scale-invariant branching rules, and this property has been used to derive several scaling laws. In this paper we model root systems of Douglas-fir (Pseudotsuga menziesii var. glauca (Beissn.) Franco) as bra...

Neuron branching patterns can characterize neural cell types and act as markers for neurodegenerative disease and neural development. We develop a hybrid Markovian model for neural branching that extends previously published models by (i) using a discretized gamma model to account for underdispersion in primary branching, (ii) incorporating both bifurcation and trifurcation branching events to ...

The topology of self-assembled surfactant solutions includes varying degrees of micellar branching, ranging from linear wormlike micelles to a micellar network. Micellar branching acts as an effective attraction between micelles such that network condensation can lead to phase separation. Unlike chemical branching in polymers, micellar branches are labile. Movement of branches along a micelle c...

Most CSP algorithms are based on refinements and extensions of backtracking, and employ one of two simple “branching schemes”: 2-way branching or d-way branching, for domain size d. The schemes are not equivalent, but little is known about their relative power. Here we compare them in terms of how efficiently they can refute an unsatisfiable instance with optimal branching choices, by studying ...