Chapter 10. Shortest Paths

Chapter 10: Shortest Paths. 3 sections.

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Chapter 10. Shortest Paths

Programming › Algorithm Cookbook › Chapter 10. Shortest Paths ›

10.1 Finding Shortest Paths in Unweighted Graphs with Breadth-First Search

Breadth-first search (BFS) is the simplest shortest path algorithm.
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10.2 Finding Shortest Paths with BFS

Use BFS when every edge has the same cost.
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10.3 Solving Nonnegative Weighted Shortest Paths with Dijkstra's Algorithm

Breadth-first search works because every edge contributes the same cost.
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10.4 Implementing Dijkstra with Priority Queue Variants

The previous recipe used Dijkstra’s algorithm with a binary heap and lazy deletion.
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10.5 Detecting Negative Edges with Bellman-Ford

Dijkstra's algorithm depends on a crucial assumption: edge weights must be nonnegative.
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Programming › Algorithm Cookbook › Chapter 10. Shortest Paths ›

10.6 Detecting Negative Cycles with Bellman-Ford

In the previous recipe, Bellman-Ford was used to compute shortest paths in graphs that contain negative edge weights.
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Programming › Algorithm Cookbook › Chapter 10. Shortest Paths ›

10.7 Computing All-Pairs Shortest Paths with Floyd-Warshall

The algorithms covered so far solve the single-source shortest path problem.
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10.8 Finding Shortest Paths in Directed Acyclic Graphs

Many shortest-path algorithms are designed to handle arbitrary graphs.
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Programming › Algorithm Cookbook › Chapter 10. Shortest Paths ›

10.9 Computing Multi-Source Shortest Paths

Most shortest-path problems begin with a single source vertex.
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10.10 Solving 0-1 Shortest Path Problems with 0-1 BFS

Between ordinary BFS and Dijkstra lies an interesting class of shortest-path problems.
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Programming › Algorithm Cookbook › Chapter 10. Shortest Paths ›

10.11 Accelerating Search with A

Dijkstra's algorithm finds shortest paths by expanding vertices in order of increasing distance from the source.
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Programming › Algorithm Cookbook › Chapter 10. Shortest Paths ›

10.12 Accelerating Searches with Bidirectional Search

Many shortest-path algorithms begin at the source and gradually expand outward until the target is reached.
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Programming › Algorithm Cookbook › Chapter 10. Shortest Paths ›

10.13 Reconstructing Shortest Paths

Most shortest-path algorithms compute distances.
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10.14 Using Distance Labels and Relaxation Correctly

Every shortest-path algorithm in this chapter appears different on the surface.
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Programming › Algorithm Cookbook › Chapter 10. Shortest Paths ›

10.15 Using Potentials to Reweight Graphs

Negative edge weights complicate shortest-path algorithms.
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10.16 Solving Sparse All-Pairs Shortest Paths with Johnson's Algorithm

The shortest-path algorithms studied so far naturally divide into two groups.
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10.17 Finding K Shortest Paths

Most shortest-path algorithms answer a single question: > What is the shortest path from the source to the destination?
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10.18 Solving Shortest Paths on Grids

Many shortest-path problems are not given as explicit graph structures.
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Programming › Algorithm Cookbook › Chapter 10. Shortest Paths ›

10.19 Modeling State-Space Problems as Shortest Paths

One of the most powerful ideas in algorithm design is that many problems that do not look like graph problems can be transformed into shortest-path problems.
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Programming › Algorithm Cookbook › Chapter 10. Shortest Paths ›

10.20 Choosing the Right Shortest-Path Algorithm

This chapter introduced a substantial collection of shortest-path algorithms.
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Programming › Algorithm Cookbook › Chapter 10. Shortest Paths ›

10.21 Proving Correctness of Shortest-Path Algorithms

Shortest-path algorithms are easy to implement incorrectly.
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10.22 Analyzing Complexity of Shortest-Path Algorithms

Shortest-path algorithms are often chosen by correctness first, then by complexity.
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Programming › Algorithm Cookbook › Chapter 10. Shortest Paths ›

10.23 Common Shortest-Path Patterns and Interview Problems

Learning shortest-path algorithms is only the first step.
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10.24 Testing Shortest-Path Implementations

Shortest-path implementations are prone to subtle errors.
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10.25 Debugging and Optimizing Shortest-Path Code

Shortest-path code usually fails in predictable ways.
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