Algorithms in Java, Third Edition, Part 5: Graph Algorithms

Chapter Twenty-One. Shortest Paths

Every path in a weighted digraph has an associated path weight, the value of which is the sum of the weights of that path’s edges. This essential measure allows us to formulate such problems as “find the lowest-weight path between two given vertices.” These shortest-paths problems are the topic of this chapter. Not only are shortest-paths problems intuitive for many direct applications, but they also take us into a powerful and general realm where we seek efficient algorithms to solve general problems that can encompass a broad variety of specific applications.

Several of the algorithms that we consider in this chapter relate directly to various algorithms that we examined in Chapters 17 through 20. Our basic ...