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

By Russell Schwartz

A practice-oriented survey of strategies for computational modeling and simulation appropriate for a vast diversity of organic problems.

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Recall that the minimum cut problem is solvable in polynomial time. There are several other problems involving cut inference that are NP-hard. One simple one is maximum cut. Maximum cut is not quite the same as simply flipping the optimization criterion in minimum cut, since that would yield a trivial problem. Rather, in maximum cut, we seek to partition the graph into two sets so as to maximize the cost of the cut separating those sets. The decision variant of this problem can be formally stated as follows: Maximum Cut Input An undirected graph G ¼ ðV ; EÞ with weight function f : V Â V !

But that does not mean that if we come up with a model and it turns out to yield a hard problem, we should immediately give up on that model. It is certainly worth considering whether small changes to the model might make it tractable. But even if we cannot make our model tractable, we still have options. This section is an attempt to provide a nonexhaustive but useful guidebook to some of the options we can consider when confronted with a hard problem. There are other, more sophisticated options than those outlined below available, but this is a set that should be reasonably accessible to anyone who can follow the rest of this chapter.

One simple one is maximum cut. Maximum cut is not quite the same as simply flipping the optimization criterion in minimum cut, since that would yield a trivial problem. Rather, in maximum cut, we seek to partition the graph into two sets so as to maximize the cost of the cut separating those sets. The decision variant of this problem can be formally stated as follows: Maximum Cut Input An undirected graph G ¼ ðV ; EÞ with weight function f : V Â V ! R and a bound B A R Question Does there exist a partition of V , V ¼ V1 W V2 , such that P v1 AV1 ; v2 AV2 f ðv1 ; v2 Þ b B?

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