tailieunhanh - Skiena - The Algorithm Design Manual [Springer-Verlag 1997] Episode 3

Tham khảo tài liệu 'skiena - the algorithm design manual [springer-verlag 1997] episode 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Modeling Graph Problems Next I Up Previous Contents Index I CD Home I Lecture Notes Algorithms Repository Next Minimum Spanning Trees Up Graph Algorithms Previous Articulation Vertices Modeling Graph Problems Proper modeling is the key to making effective use of graph algorithms. We have seen a variety of definitions of graph properties and algorithms for computing them. All told about two dozen different graph problems are presented in the catalog mostly in Sections I I and I I. These problems provide a framework for modeling most applications. The applications below demonstrate the power of proper modeling. Each of them arose in a real-world application as stated and each can be modeled as a graph problem. Some of the modelings are quite clever but they illustrate the versatility of graphs in representing relationships. As you read the problem try to devise an appropriate graph representation before peeking to see how we did it. I m looking for an algorithm to design natural routes for video-game characters to follow through an obstacle-filled room. How should I do it Presumably the route that is wanted is the path that looks most like the one that an intelligent being would choose. Since intelligent beings are either lazy or efficient this should be modeled as some kind of shortest path problem. But what is the graph One approach would be to lay a grid of points in the room and have a vertex for each point that is a valid place for the character to stand . so it does not lie within an obstacle. There will be an edge between any pair of nearby vertices weighted according to the distance between them. The shortest path between two vertices will be close to the shortest path between the points. Although direct geometric methods are known for shortest paths see Section id it is easier to model this discretely as a graph. In DNA sequencing we are given experimental data consisting of small fragments. For each fragment f we have certain other fragments that are .

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