Biological Modeling and Simulation: A Survey of Practical by Russell Schwartz

By Russell Schwartz

A practice-oriented survey of recommendations for computational modeling and simulation appropriate for a extensive variety of organic problems.

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Additional resources for Biological Modeling and Simulation: A Survey of Practical Models, Algorithms, and Numerical Methods (Computational Molecular Biology)

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Note that a maximal matching only means that we cannot add any additional edges without the set’s no longer being a matching.

We want to give the patient as few drugs as possible. If we define S to be our set of bacteria and each ci A C to be the subset of bacteria a¤ected by antibiotic i, then a minimum cover would give us the smallest possible set of antibiotics that a¤ects every bacterium. The vertex cover problem we saw earlier in the chapter can be thought of as a special case of set cover in which we have a set for each edge containing the two endpoints of the edge. 4 Hardness Reductions Our main goal in studying the preceding problems is to recognize when we have developed a model that leads to a hard optimization problem.

Though we will not cover the proof here, we can intuitively understand why this is so by noting that the minimum cut is the tightest bottleneck through which a flow must pass, and is therefore the limiting factor on the maximum flow. 1. Because of the relationship between max flow and min cut, they are generally solved simultaneously by the same algorithm. The standard method is the Edmonds– Karp algorithm, an instance of the more general Ford–Fulkerson method. 1 Graph Problems 23 Fulkerson constructs a maximum flow iteratively by repeatedly finding a single path from s to t in which all edges have excess capacity, known as an augmenting path.

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