Combinatorial optimization

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1. sargstuffJun 2024
   basics / inexpensive but dated:

   * Graph Theory And Its Applications by Jonathan Gross and Jay Yellen

   * Introduction to Graph Theory by Richard J. Trudeau

   comprehensive/expensive:

   * Graph Theory And Its Applications by Jonathan Gross and Jay Yellen

   * graph theory with computer systems emphasis: Applied Combinatorics by Alan Tucker

   misc other sources:

   * graph theory: https://diestel-graph-theory.com/

   * Harris' Combinatorics and Graph Theory

   * Graph Theory by Douglas B West

   * combinatorial Optimization by Papadimitriou and Steiglitz

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2. pcboumanJul 2021
   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...

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3. julesNov 2010
   I really enjoyed Solar, and really anything from Ian McEwan. Ammaniti is good fun too. But currently I'm reading mostly books for classes; Combinatorial Optimization by Papadimitriou and Spivak's Calculus on Manifolds, Solid State Physics, Introduction to Linear Analysis, Measure and Integration Theory, Lectures on the Coupling Method, Particles and Nuclei etc...
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