# lec17 - Introduction to Algorithms 6.006 Lecture 17 Prof...

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Introduction to Algorithms 6.006 Lecture 17 Prof. Piotr Indyk

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Menu Last two weeks – Bellman-Ford • O(VE) time • general weights – Dijkstra • O( (V+E)logV ) time • non-negative weights Today: applications – Obstacle course for robots – Scheduling with constraints
Obstacle course for robots Obstacles: disjoint triangles T 1 …T n Robot: a point at position A Goal: the shortest route from A to B A B

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Path planning algorithm Let V be the set consisting of triangle vertices, A and B – Note that V=O(n) Observation: the shortest path consists of line segments between points in V Approach: – For each pair u,v in V such that the segment u-v is “free”, create an edge u-v (weight = segment length). This is called visibility graph G – Compute the shortest path from A to B in G A B
Computing visibility graph For each segment u-v , check whether there is any triangle T i such that one of its sides (say, s ) intersects u-v – The test whether s intersects u-v can

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lec17 - Introduction to Algorithms 6.006 Lecture 17 Prof...

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