Core algorithms deployed

To demonstrate the importance of algorithms (e.g. to students and professors who don't do theory or are even from entirely different fields) it is sometimes useful to have ready at hand a list of examples where core algorithms have been deployed in commercial, governmental, or widely-used software/hardware. I am looking for such examples that satisfy the following criteria: The software/hardware using the algorithm should be in wide use right now. The example should be specific. Please give a reference to a specific system and a specific algorithm. E.g., in "algorithm X is useful for image processing" the term "image processing" is not specific enough; in "Google search uses graph algorithms" the term "graph algorithms" is not specific enough. The algorithm should be taught in typical undergraduate or Ph.D. classes in algorithms or data structures. Ideally, the algorithm is covered in typical algorithms textbooks. E.g., "well-known system X uses little-known algorithm Y" is not good. Update: Thanks again for the great answers and links! Some people comment that it is hard to satisfy the criteria because core algorithms are so pervasive that it's hard to point to a specific use. I see the difficulty. But I think it is worthwhile to come up with specific examples because in my experience telling people: "Look, algorithms are important because they are just about everywhere!" does not work.