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Finding Paths in Graphs
Finding Paths in GraphsRobert SedgewickPrinceton UniversityIntroductionMotivating exampleGrid graphsSearch methodsSmall world graphsConclusionSubtext: the scientific methodis necessary in algorithm design and implementationScientific method create a model describing natural world use model to develop hypotheses run experiments to validate hypotheses refine model and repeatAlgorithm designer who does not run experimentsrisks becoming lost in abstractionSoftware developer who ignores resource consumptionrisks catastrophic consequences Isolated theory or experiment can be of value when clearly identifiedmodelhypothesisexperimentIntro ductionIntroductionMotivating exampleGrid graphsSearch methodsSmall world graphsConclusionWarmup: random number generationProblem: write a program to generate random numbersmodel: classical probability and statisticshypothesis: frequency values should be uniform weak experiment: generate random numbers check for uniform frequenciesbetter experiment: generate random numbers use x2 test to check frequencyvalues against uniform distribution better hypotheses/experiments still needed many documented disasters active area of scientific research applications: simulation, cryptography connects to core issues in theory of computationV = 10random?
Finding Paths in Graphs Robert Sedgewick Princeton University. Introduction Motivating example Grid graphs Search methods Small world graphs Conclusion Subtext: the scientific method is necessary in algorithm design and implementation ... • augment flow along path (may create or delete edges)
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