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Combinatorial Optimization: Algorithms and Complexity (Dover Books on Computer Science)

Christos H. Papadimitriou, Kenneth Steiglitz · 2 HN comments
HN Books has aggregated all Hacker News stories and comments that mention "Combinatorial Optimization: Algorithms and Complexity (Dover Books on Computer Science)" by Christos H. Papadimitriou, Kenneth Steiglitz.
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Amazon Summary
This clearly written, mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NP-complete problems, more. All chapters are supplemented by thought-provoking problems. A useful work for graduate-level students with backgrounds in computer science, operations research, and electrical engineering. "Mathematicians wishing a self-contained introduction need look no further." — American Mathematical Monthly.
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Mathematical Optimization still has many subfields that can be of interest. I guess that non-linear mathematical optimization is most more typical for many machine learning applications. Many pratical applications in scheduling, logistics, planning etc used linear (integer) programming and combinatorial optimization. The following are some points towards that body of literature.

Alexander Schrijver [1] has lecture notes on Combinatorial Optimization on his website [2]. He also has an affordable 1800 page three volume set of books "Combinatorial Optimization - Polyhedra and Efficiency" [3], although I would say it is better suited as reference material because it is quite densely written.

There is also the classic book "Combinatorial Optimization - Algorithms and Complexity" [4] by Papadimitriou (Bill Gates' MSc thesis supervisor) and Steiglitz that is a nice introduction to the topic as well.

"In Pursuit of the Traveling Salesman - Mathematics at the Limits of Computation" by William J. Cook [5] is a more popular science book on the history of the Traveling Salesman Problem, that also explains how linear programming is used in the state of the art solvers, but is of course focuses on a very specific problem. There is also a book that contains all the scientific and mathematical details by Applegate, Bixby, Chvátal and Cook [6] if that is preferred.

In recent years, there is a trend that mathematical optimization researchers work more with ML. In particular Dimitris Bertsimas has done some work on the intersection of those area's in recent years [7] and apparently has a book on the topic as well [8] (but I am not familiar with it).

[1] https://homepages.cwi.nl/~lex/ [2] https://homepages.cwi.nl/~lex/files/dict.pdf [3] https://www.springer.com/us/book/9783540443896 [4] https://www.amazon.com/Combinatorial-Optimization-Algorithms... [5] https://press.princeton.edu/books/paperback/9780691163529/in... [6] http://www.math.uwaterloo.ca/tsp/book/index.html [7] https://dbertsim.mit.edu/papers/ [8] https://www.dynamic-ideas.com/books/machine-learning-under-a...

gjm11
Papadimitriou was not Gates's MSc thesis supervisor. Gates never did an MSc (nor indeed completed his BSc -- he dropped out of college to found some computer company or other).

What did happen is that Papadimitriou and Gates were co-authors of a paper about pancake sorting. (https://en.wikipedia.org/wiki/Pancake_sorting)

Good deal, Papadimitriou is the author of this well-regarded book,

  http://www.amazon.com/gp/product/0486402584
that somehow luckily wound up with Dover.
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