By Russell Schwartz
A practice-oriented survey of options for computational modeling and simulation compatible for a large diversity of organic problems.
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Additional info for Biological Modeling and Simulation: A Survey of Practical Models, Algorithms, and Numerical Methods (Computational Molecular Biology)
The second general method is Prim’s algorithm, which builds the spanning tree outward from a single node, greedily adding in whichever node not in the current tree has the lowest-weight edge connecting it to the tree. 4 provides pseudocode for Prim’s algorithm. The runtime of Prim’s algorithm depends on the priority queue used to select the node with minimum key. Most standard priority queue algorithms will give OðjEj lgjV jÞ runtime, as with Kruskal’s algorithm, although Prim’s algorithm can be implemented with runtime OðjEj þ jV j lgjV jÞ by using a sophisticated kind of priority queue called a Fibonacci heap.
A su‰x tree implicitly encodes each su‰x of a given sequence or set of sequences. 10, directly encoding every possible su‰x of the string. What is surprising about su‰x trees, though, is that we can create a data structure that encodes this same information but requires only linear space and can be constructed in linear time. The construction is quite involved and would require a whole chapter to explain, so we omit it here. 10 Conceptual illustration of a su‰x tree encoding the string ABCCA. Each su‰x of the string is represented by a path from the root to a terminal node (/).
9 is an example of unweighted bipartite maximum matching. Though this variant may seem specialized, it is very useful in practice. It is also easy to solve, since it can be cast as a maximum ﬂow problem. To accomplish this, we divide the the graph into its two parts, V1 and V2 , and convert all edges into directed edges from V1 to V2 . We then add an additional source node s and sink node t. Next, we add edges ðs; v1 Þ for each v1 A V1 and ðv2 ; tÞ for each v2 A V2 . 9 Unweighted bipartite maximum matching.
Biological Modeling and Simulation: A Survey of Practical Models, Algorithms, and Numerical Methods (Computational Molecular Biology) by Russell Schwartz