Shortest Paths

Based on CLRS, Ch 24 and 25. Motivating example—want to drive from Austin to Berkeley. Given a road map, with distances between each pair of adjacent intersections, how to find the shortest route? • Enumerate all paths from Austin to Berkeley – cycles cause problems; huge number of paths; many should not be considered (e.g,, going via Cambridge) In this unit, we’ll address such problems using a graph representation, specifically all complexity results are relative to an adjacency list representation. Given a weighted directed graph G = (V,E), with weight function w : E 7→ (−∞,∞). • Define weight of a path p = 〈v0, v1, . . . , vk〉, its weight is defined to be sum of the weights of the edges on the path, i.e., w(p) = k