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  About site: http://cgm.cs.mcgill.ca/~godfried/teaching/algorithms-web.html

Title: Algorithms - Web Data Structures and Algorithms Lecture notes and links for a course by Godfried Toussaint.
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Web Data Structures and Algorithms"Computer science is no more about computers than astronomy isabout telescopes."E. W. DijkstraUseful General Links251B- Godfried Toussaint's Course Topics on the Web251-MikeHallet's web pageVirtualLibrary of Algorithms and Data StructuresAlgorithmsand Data Structures Research & Reference MaterialAlgorithmsCourses on the WEBGraphTheory LessonsDavidEppstein's course on algorithmsAlgorithmsCourse at the University of AberdeenSpecific Course Material: 308-251BChapter Index:The Complexityof AlgorithmsThe Correctnessof AlgorithmsLinearData StructuresGraphsTreesSearching AlgorithmsPlane-Sweep AlgorithmsGreedy AlgorithmsDivide-and-ConquerAlgorithmsOn-Line AlgorithmsReal-Time AlgorithmsEliminationAlgorithmsDistributiveAlgorithmsPrune-and-SearchMethodsLinear ProgrammingProbabilisticAlgorithmsApproximationAlgorithmsParallel AlgorithmsNumerical AlgorithmsGeometric AlgorithmsSequence Comparison1. The Complexityof Algorithms:

Models of Computation (Old and New)

(1) Knotted Strings, the Abacus andother Models of Computation

Gravity as a Computer:Computingthe Centroid of a Polygon with a PlumblineCentersof Gravity of PolygonsTheKnotted String ComputerPythagoras' Theorem:Pythagoras'Theorem (An award winning proof and interactive Java applet demo)AnimatedProof of the Pythagoream Theorem by M. D. MeyersonAHinged Dissection Proof of the Pythagorean TheoremOtherDissection Proofs (with interactive Java applets)Morethan forty other proofs of the Pythagorean theoremTheConverse of Pythagoras' TheoremTheAbacusTheAbacus in various number systemsNapier'sBones in Various BasesTheVirtual Museum of ComputingLinksto History of Computing

(2) The Straight Edge and Compass

FrancoisLabelle's Tutorial on the Complexity of Ruler and Compass Constructions(with interactive Java applet)GRACE(A graphical ruler and compass editor)The straight-edge andcompassConstructivegeometry of the GreeksGeometricconstructionsGeometrographyand the Lemoine simplicity of geometric constructionsEuclid'sElementsSecondProposition (Java applet)Euclidof AlexandriaMoreEuclid on the WebRelative computing power of models of computation:TheCollapsing CompassA New Look at Euclid's Second Proposition (PostScript)(PDF)TheCompass without straight edge (Mohr-Mascheroni)Heron'sShortest Path via a Line (with interactive Java applet)Moreon Heron's problem and other constrained shortest path problems (withinteractive Java applets)Moreabout Heron of AlexandriaTheLunes of HippocratesMoreabout Hippocrates of ChiosWondersof Ancient Greek Geometry

(3) Modern Models of Computation

Introductionto Turing machinesFantasticTuring machine applet!TheTuring Machine and Random Access Machine (Luc Devroye's class notes)Moreabout Alan TuringCeilingand Floor FunctionsLogarithmicfunctionsTheharmonic seriesBig"Oh" Notation (Luc Devroye's class notes)Basicanalysis tools (Goodrich & Tamassia text)Computability theoryWhatcomputers can't do (Turing and the Halting Problem)(4) The Complexity of Algorithmsand Problems:Recursion(Luc Devroye's class notes)Algorithmsfor computing the Fibonacci function (David Eppstein)Fibonaccinumbers (mathematical properties)Fibonaccinumbers and natureFibonacciHome PageBiographyof Leonardo Fibonacci from PisaFibonaccinumbers and domino tilingsVibonaccinumbersRecursionsolving appletProofsof Binet's formulaLowerBounds (Luc Devroye's class notes)2. The Correctness of Algorithms (Proof Techniques):Noteson methods of proofNotes on how to do proofsMoreon proof methodsClassicfallaciesConstructive Proofs:3-coloringall the points in the planeProofs by Contradiction:Euclid'sProof of the infinitude of prime numbersInduction Proofs:TheTechnique of Proof by InductionMoreon inductionInduction Algorithm Design:Polynomial evaluationMany niceexamples of different types of proofsOnProofs in MathematicsHowto read proofsWritingDown ProofsTheNuts and Bolts of ProofsLogicalsystemsCommonerrors in mathematicsProofsand proof strategies3. Linear Data Structures:LinearData Structures (Luc Devroye's class notes)Universityof Aberdeen NotesStackQueueArrayLinkedlistPriorityQueueDequeDataStructure Animations4. Graphs:InteractiveIntroduction to Graph TheoryGraphTheory Tutorials (Euler and Hamilton circuits, Coloring, Spanning and SteinerTrees)AppliedGraph Theory CourseIntroductionto Graphs (Luc Devroye's Notes)GraphisomorphismGraphplanarityGraph data structures:AdjacencylistsAdjacencymatricesDoubly-Connected-Edge-List(DCEL)GraphAlgorithm AnimationsGraphTheory Web TutorialsIntroductionto graph theoryEulerand Hamiltonian circuitsGraphtheoryGraphTheory and EnumerationPathsand CircuitsAlgorithmfor Constructing an Eulerian CircuitEulerTours: Fleury's AlgorithmAppletfor Euler toursMore on Fleury's algorithm(postscript)Greattutorial on Euler tours and Fleury's algorithmGraphGlossaryProximity graphs:Minimalspanning trees (Luc Devroye's class notes)DavidEppstein's class notesJava appletof Euclidean minimal spanning treeThe Relative NeighborhoodGraphHamiltonian Tours:Hamiltonianpaths in tournamentsHamiltonian cycles in dense graphs:Ore's TheoremBackward induction proofDirac'sTheoremPosa'sproof of Dirac's theorem by contradictionTheHamiltonian PageGreattutorial on Hamilton circuitsSufficientconditions for Hamiltonian cyclesHamiltoniancircuits of point sets with specific properties (polygonizations)Minimum Spanning Trees:Minimumspanning trees (Luc Devroye's class notes)Minimumspanning tree algorithms: Kruskal, Prim & Baruvka (David Eppstein'sclass notes)MinimumSpanning Trees (Steve Skiena)Kruskal'sAlgorithm with appletLeastCost Networks: Kruskal's AlgorithmAnotherapplet for Kruskal's algorithmPrim'salgorithm with pointers and appletPrim'salgorithm with adjacency matrices and appletBaruvka'sAlgorithm (David Mount's notes) PostScript file17Proofs of Euler's TheoremGraph and Map Coloring:Graphand map coloringDualGraphsGraphColoringMapcoloring WEB tutorialThescheduling problemTwo-ColorableMapsApplicationsof graph coloringThefour-color theoremHistoryof the problemAnew proof of the 4-color theoremTheGraph Coloring PageDavidEppstein's Coloring PageTheFive-Color Theorem for planar graphsTheKonigsberg Bridge ProblemPlanarity and the TorusTherotating-caliper graphThe Travelling Salesman Problem:An introductionto the TSP problemApictorial history of the TSP problemAnelastic-band approach to the TSP problem (JAVA applet)ThePolygon Counting AppletThe TravellingSalesman Home PageDifferentheuristics for the TSP problemApproximateTSP algorithm via MST yields twice optimal tourGraphdrawing5. Trees:Introduction to Trees:LucDevroye's class notes with tree traversal (applet)Treetraversals (preorder, inorder and postorder)Introductionto trees (Goodrich & Tamassia text)TreeAlgorithm AnimationsBinarytrees.Moreinformation on binary trees.LogarithmsBinarysearch trees (Luc Devroye's class notes)Quad treesBalanced trees:Tutorialon 2-4 trees2-4Trees (also AVL and Red-Black trees)Heaps:Tutorialon heaps with appletHeaps(Luc Devroye's class notes)Huffman trees and data compression:DatacompressionIntroductionto Data CompressionFundamentalConceptsShannon-FanoCodingMore about ClaudeShannonTheSignificance of Claude Shannon's WorkPicturesof ShannonMore about Robert FanoHuffmancodingOptimalityof Huffman codesHuffmantrees and applications (Luc Devroye's course notes)Huffmancoding appletHuffmancoding tutorial and another appletMore About DavidHuffmanDavidHuffman dies at 74Geometric paperfoldingLempel-ZivCompression (Luc Devroye's notes)Lempel-ZivData Compression SchemesMoreabout Abraham LempelAnimationof Welch variant of Lempel-Ziv compressionTextcompression (Steve Skiena)Morse CodeMorseCode basicsTheInternational Morse CodeMoreabout Samuel MorseIntroduction to probability and information theoryEntropyMarkov models of natural language (monkeys and typewriters)The ShannonizerSpelling correction programs.Spellcheckers are wonderful but .....Decision treesGame trees:Play Checkers with Chinook(The World Champion)Play Othello with Keyanoand other programsPlay Chess with TheTurkGame treesOtherGames, Toys and PuzzlesClevergames for clever peopleTetris6. SearchingAlgorithms:Sequential searchBinary search:CreatingBinary Search Trees (Java applet)Searchingin a Binary Search Tree (Java applet demo)TheNumber-Guessing GameMaze searching:Depth-firstsearch (Luc Devroye's class notes)DFSappletAMaze Game (interactive Java applet)3D Mazes in JavaThe mathematicsof mazesTheseusand the MinotaurTheMinotaur LegendThemad maze of Theseus and the MinotaurTHEMYTH OF THE MINOTAURBreadth-firstsearch (Luc Devroye's class notes)BSFappletBSFand DFS (David Eppstein's class notes)Graphtraversal (Goodrich & Tamassia text)Interpolation searchOrthogonalrange searchingNearest Neighbor Search:ProjectionmethodsAccessTreesVoronoi diagram methodsClosest-pair searching in the planeTutorialwith appletsAnimationapplet of divide-and-conquer algorithm!Closestpairs (Goodrich & Tamassia text)Branch-and-boundThe A* algorithm7. Plane-Sweep Algorithms:Closest pair problemLine segment intersections8. GreedyAlgorithms:GreedyalgorithmsComplexity, convexity and unimodalityHill climbing algorithmsQuick sortQuick hull9. Divide & Conquer Algorithms:SortingFinding closest pairConvex hulls10. On-LineAlgorithms:Convex hulls of polygonsConvex hulls of points11. Real-Time Algorithms:Convex hulls of polygonsConvex hulls of points12. EliminationMethods:Convex hulls of point sets13. Distributive Methods:Distributive sortingBucketing methodsBucket sortRadix sort14. Prune & Search Methods:Thegeometric seriesEar-cuttingand polygon triangulationLineartime median finding and selection (Luc Devroye's course notes)Lineartime median finding and selection (David Eppstein's course notes)Convex hulls15. LinearProgramming:Introductionto Linear Programming and the Simplex AlgorithmMegiddo's linear time algorithmLinearprogramming and optimization problems (with Java applet)16. Probabilistic Algorithms:RandomizationMonte-Carlo AlgorithmsLas-Vegas AlgorithmsRandomized convex hullProbabilityand Random Number GenerationVisualizingrandomnessMoreon generating random numbersMonte Carlo Simulation:Simulatingrandom knots in a latticeSelf-avoidingwalks in polymer physics and molecular biologyPolymerJava appletProteinfoldingBouncingballsBuffon'sNeedleRollingDice17. Approximation Algorithms:ApproximationalgorithmsThevertex-cover problemApproximationalgorithmThe bin-packingproblemThetravelling salesman problem18. Parallel Algorithms:ParallelAlgorithm AnimationsRealand ArtificialNeuronsThresholdlogic units.Dr.Gurney's course on neural networks.Perceptrons& neural networks (learning machines).Sharpening, the Laplacianand lateral inhibition in neural networks (PostScript)19. NumericalAlgorithms:

19.1 Numbers

Whatis a Number?Moreon irrational numbersTwoproofs of the irrationality of the diagonal of the unit cubeElementarynumber theoryNumbers:Real, rational, integer and binary numbers (bits and bytes)FloatingPoint NumbersNewton's Method:Introductionto Newton's methodComputingapproximate square roots with Newton's MethodTheEuclidean factorization algorithmPrime Numbers:Primenumbers (FAQ's)Historicalintroduction to primesThe Prime NumberHome PageEuclid'sProof of the Infinitude of PrimesPrimeNumber GeneratorPrimeCurios!19.2 Sorting AlgorithmsSorting Numbers:SortingAlgorithm AnimationsSelectionsort tutorialBubblesort tutorialHeapsort tutorialMergesort tutorial (Divide and Conquer)Bucket-Sorting and Floor Functions(PostScript file), (PDFfile)Quicksortwith nice applet! (in place version and comparison to heapsort)Expectedanalysis of randomized quicksortRandombinary search trees and QuicksortSelectionand order statisticsMoreSorting Algorithm Animations (Applets also sort your own set of numbers!)SortingCode20. GeometricAlgorithms:Polygon Triangulation:Historyof Triangulation AlgorithmsEars and Mouths of Polygons:Ian Garton'sTutorial on cutting ears and stuffing mouths (with interactive Javaapplets)Simplepolygons have earsand mouthsMeisters' Two-EarsTheoremMore aboutGary MeistersThe one-mouth theorem:Ian Garton's TutorialPostScript fileDiagonal insertionPrune-and-Search:Finding an ear in lineartime (PostScript)Finding an earin linear time (HTML)The Graham Scantriangulates simple polygons (PostScript)FastPolygon Triangulation in Practice:Efficient polygontriangulation algorithms. Includes counter-examplesto many published algorithms. (PostScript)TheArt-Gallery Theorem (with interactive applet)The MinimalSpanning Tree appletGeometricAlgorithm AnimationsPolygons: crossing, simple and convex.PolygonizingSets of Points:Uniquenessof orthogonal connect-the-dotsThe area of a polygon.Determiningif a point is inside a polygon.Smoothingpolygons and polygonal waveforms.Convex Hulls:Rosenberg& Landgridge algorithm (extreme edges)Convexhulls, segment intersections and closest pairs (Goodrich & Tamassiatext)Convexhulls in 2 and 3 dimensions (interactive Java demos)TheGift-Wrapping Algorithm (Jarvis' March)TheQuick-Hull Algorithm (stretching an elastic band)Divide& Conquer (nice tutorial) and other methodsDivide& Conquer (applet)TheGraham Scan Algorithm3-CoinsAlgorithm Tutorial (Greg Aloupis and Bohdan Kaluzny)Moreconvex hull animationsVoronoi Diagrams:Introductionto Voronoi diagramsGreatVoronoi diagram applet21. Sequence Comparison:Editdistance with dynamic programming (with applet)TeachingActivitiesHomepage 
 

Lecture

notes

and

links

for

a

course

by

Godfried

Toussaint.

http://cgm.cs.mcgill.ca/~godfried/teaching/algorithms-web.html

Web Data Structures and Algorithms 2008 July

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Lecture notes and links for a course by Godfried Toussaint.

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