Book Algorithms
We know the legend of Paul (Uncle, to some) Erdos and the Erdoslore of Book Proofs, proofs brilliant and perfect from The Book.
To an algorithmus, the question is, what are examples of Book Algorithms? Algorithms is a broad research area and it is hard for any one to select Book Algorithms or to even define one or elicit any consensus at a dinner table of algorithmii. In string matching algorithms, I think the suffix tree algorithm of Karkkainen and Sanders is an example. What about geometry, scheduling, graphs, approximate, random, online or other algorithms, data structures included?
To an algorithmus, the question is, what are examples of Book Algorithms? Algorithms is a broad research area and it is hard for any one to select Book Algorithms or to even define one or elicit any consensus at a dinner table of algorithmii. In string matching algorithms, I think the suffix tree algorithm of Karkkainen and Sanders is an example. What about geometry, scheduling, graphs, approximate, random, online or other algorithms, data structures included?
posted by metoo at 5:22 AM
24 Comments:
A few off the top of my head:
"Russian peasant" multiplication
Euclid's GCD algorithm
Boruvka's MST algorithm
Brepth-first search (uses a quack)
Cooley + Tukey's FFT
Dantzig's simplex algorithm
Knuth-Morris-Pratt string matching
Computational geometry: Clarkson-Shor randomized incremental construction; fractional cascading
Data structures: splay trees; treaps; van Emde Boas trees; cuckoo hashing
Karkainen and Sanders's algorithm is about suffix arrays.
Count my votes for FFT and cuckoo hashing.
A few in data structures, in no particular order:
* cuckoo hashing with variations (Bloomier filters, uniform hashing)
* Dynamic connectivity in O(lg^2 n) by Holm, de Lichtenberg, Thorup.
* LCA/RMQ in linear time and constant time.
* searching with wildcards (the simple algorithm in Cole, Gottlieb, Lewenstein)
* 1d range reporting in linear space and constant time [Alstrup, Brodal, Rauhe]
* 3d range reporting by Nekritch (only the simple existential version)
* approximate nearest neighbor in constant dimension [Chan]
You mean perhaps:
E. Ukkonen. On-line construction of suffix trees. Algorithmica, 14(3):249–260,
1995.
Also I'll add the Fisher algorithm for computing majority on a string in one/two passes using a single counter.
Burrows-Wheeler is also amazingly effective as a compression algorithm. On the same vein Lempel-Ziv never ceases to amaze me. The coder and decoder fit in less than a page of code!
* Inbok: you are right of course, it is an algorithm for suffix sorting, I don't typically make internalize array/tree.
* Jeff: Not clear KMP or splay trees will make my list.
* MIP: LCA/RMQ is cool. Wildcard matching is phenomenally simple and cool.
* Yet another Anonymous: Burrows-Wheeler is a nifty algorithm, almost non-intuitive at first look. yes, I think it will make it to my list too.
Which GCD algorithm? As much as I like Euclid's I might go for the variant with parity checks, subtraction and division by 2 rather than general division with remainder. The implementation of general division is relatively complicated.
Some algorithms to add:
Batcher's bitonic sort
Fischer-Ladner's parallel prefix algorithm
Median of Five
M. Blum, R. Floyd, V. Pratt, R. Rivest, and R. Tarjan. Time bounds for selection. J. Computer and System Sciences, 7:448-461, 1972.
Steve Fortune's Voronoi diagram algorithm.
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