By Russell Schwartz
A practice-oriented survey of options for computational modeling and simulation appropriate for a wide 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)
A graph property is called inheritable if, when given a graph possessing the property, removing any node or edge leaves us with a graph possessing the property. A property is considered nontrivial if there are an inﬁnite number of graphs that have the property and an inﬁnite number that do not. An example of a nontrivial, inheritable property is bipartiteness. Recall that a bipartite graph is deﬁned by the fact that nodes can be partitioned into two groups (parts) with no edges between any two nodes in the same group.
A subsequence is an ordered subset of the characters of a sequence in which the characters have the same order as in the original sequence but need not be consecutive in the original sequence. The longest common subsequence problem can be formally stated as follows: Input Two sequences A and B Output A sequence C that is a subsequence of both A and B Metric jCj is maximized. For example, if we take the sequences A ¼ ABCABCABC and B ¼ CABBCCBB, then the sequence C ¼ ABBCB is a subsequence of both A and B.
This seems like a reasonable revision of our model, but it is useful only if we can still solve acceptably for it. It turns out that we can readily adapt our existing algorithms to this problem. Recall that in Kruskal’s algorithm, we sort the edges, then successively join together the pair of subtrees not already joined that have the minimum weight edge between them. The algorithm itself can make an arbitrary decision at that point, in that it may have multiple edges of equal weight to choose from.