Algorithms Course Materials
compgeom.cs.uiuc.edu
compgeom.cs.uiuc.edu
Masterfully hidden from view are the edits, re-edits, discussions, Tex/Latex tutorials, file conversions, hand-written notes, lecture preps, student questions and a hundred other details that end in an 814 page treatise for humans to enjoy via that "other thing" they did at UIUC.
Well done Jeff Erickson, et.al.
Cute: By the time computing got powerful enough so that everyone could have TeX, LaTeX, and something to write the output to PDF to create Knuth's "beautiful books", computing also enabled the Internet and wide use of PDF so that the days of tree killer "books" are nearly over!
Reading through the book quickly and mostly just looking at the topics, he has a lot there. E.g., he includes some on the fast Fourier transform (FFT).
So, there is a question about selection of content: Of course the FFT is a darned cute, powerful, and valuable algorithm (actually, it is awash in closely related but still significantly different versions -- can find more than one whole book describing a collection of just some of the more popular versions). And to some extent can look at that algorithm as a source of how to do an algorithm and also as an application of some somewhat more general techniques in algorithms. But treating the FFT as mostly just an algorithm is a bit of a strain: Why? Because as soon as the original Cooley-Tukey paper came out in the 1960s (yes, with some ideas that to one extent or another had been published before going back decades or so), there was a big splash in military sonar, radar, and more. We're talking a huge splash. It bought me a nice high end Camaro!. I used to drive home going south on Route 29 just south of the JHU/APL in Howard County, Maryland and going up one particular hill try to get to 100 MPH in second gear in the Turbo 400 automatic transmission! Nice car!
So, with the FFT could do a wide range of digital filtering. It also got used in X-ray crystalography. At least for a while, Texas Instruments was going to make a 'radio' receiver that would have no local oscillator circuit and, instead, would feed the antenna signal directly to a very sensitive, very fast, high resolution analog-digital converter and then run that digital output through the FFT as the means of 'tuning' to particular frequencies. Then, of course, could 'listen' to several different frequencies at once, do spread spectrum tricks, etc. Big splash.
But what's in the OP on the FFT is essentially just the algorithm. That's a little like making cake batter but leaving out the cake, icing, soaking with syrup with Kirschwasser, whipped cream, coffee, etc.! Really, the FFT mostly belongs in an electronic engineering course in signal processing.
Then the book does quite a lot with some discrete optimization. There is a whole stream of such work going back to Ford and Fulkerson, the Hungarian method, algorithms of Dijkstra and Bellman, applications of the network simplex algorithm, etc. So, there is maximum matching, minimum spanning tree, shortest paths, maximum network flows, least cost network flows, etc.
There is some question about teaching this material, especially as computer science: Really, originally the material was mostly optimization in operations research. I know, operations research is nearly a dead field, and optimization is not far behind. So, just why should computer science raise these topics from the dead?
One old reason for studying these topics was, at first glance, some of those problems look like would need an exponential algorithm that enumerated all combinations to get an optimal solution yet there are algorithms that are worst case polynomial or average case polynomial. So, these problems and the associated algorithms are a stake in the ground of combinatorial optimization problems that do have polynomial solutions. So, maybe from this stake in the ground, we can get some guidance in our search to resolve P versus NP. Maybe. And, yes, there are some selected applications, maybe to IP routing! Still, dragging all UI CS students through this material seems a bit questionable.
Then the book also does the simplex algorithm of linear programming. Okay, it's an algorithm, but really it's the core technique in optimization in operations research and is not really discrete. His treatment looks good for being so short, but, again, there is some question about calling simplex part of computer science and dragging all UI CS undergraduates through it. Besides, the UI operations research, applied math, or math departments could charge the UI CS department with academic theft! So, next, UI CS will be teaching calculus? Linear algebra? Art history?
Yes, in each case, the course is teaching an algorithm, but not all of the ones it is teaching are really of the same kind as quicksort, heap sort, merge sort, AVL trees, red-black trees, extendible hashing, perfect hashing, etc. The difference in "kind"? When you've studied, learned, programmed, timed, and used quicksort and thought about how it does well with virtual memory locality of reference, divide and conquer, recursion, and an opportunity to exploit multi-core processors, then you are done with it. But for the FFT, simplex, matroids (which it also touches on), are just getting a peak into what in each case is often a whole book or a whole shelf of books and significant part of a whole field, e.g., electronic engineering, operations research, combinatorial optimization research, etc. Sounds like a way to keep some UI CS undergraduates really busy and sober and doing homework seven nights a week!
E.g., there is
Enders A. Robinson, 'Multichannel Time Series Analysis with Digital Computer Programs', Holden-Day, San Francisco.
So, the main application here is finding oil! So, go "boom" and send a sound wave into the earth. At each different layer, get back a reflection of part of the energy. So, to get back just the layers, just use the FFT.
Also have fun with X-ray diffraction, holography, etc.
For signal processing, the core foundational point is that a 'time-invariant linear system' can be fully described by Fourier theory. Basically the output is a convolution of the input, and the fast way to do a convolution is with the FFT.
The impact of the FFT on signal processing was enormous.
Have fun!
Ok, but [Hint: There is a one-line solution!]
Am I missing something obvious like "it's always a draw"?
have fun!