Reddit reviews Combinatorial Optimization: Algorithms and Complexity (Dover Books on Computer Science)
We found 5 Reddit comments about Combinatorial Optimization: Algorithms and Complexity (Dover Books on Computer Science). Here are the top ones, ranked by their Reddit score.
Dover Publications
Linear programming:
Combinatorial optimization:
Game theory:
Combinatorial game theory:
I'll just leave these two quality references here for those of you that care about these branches of mathematics:
https://www.amazon.com/Convex-Optimization-Stephen-Boyd/dp/0521833787/ref=pd_lpo_sbs_14_img_1?_encoding=UTF8&psc=1&refRID=TVGGPQ59DZ58S2XSXMGD
https://www.amazon.com/Combinatorial-Optimization-Algorithms-Complexity-Computer/dp/0486402584
And for those of you who like to throw in a little probability theory to the mix for more real-world situations...
https://www.amazon.com/Introduction-Stochastic-Programming-Operations-Engineering/dp/1461402360
Linear programming isn't actually programming, the quick dirty description is linear algebra, but with inequalities. This book is a good introduction, plus it's cheap. It does include pseudo code if you want to get into coding.
Combinatorial Optimization: Algorithms and Complexity (Dover Books on Computer Science) https://www.amazon.com/dp/0486402584/ref=cm_sw_r_cp_apa_i_5m-4AbFH5EZT8
Sure, there are a few directions you could go:
Algorithms: A basic understanding of how to think about and analyze algorithms is pretty necessary if you were to go into combinatorial optimization and is a generally useful topic to know in general. CLRS is the most famous introductory book on algorithms, and it gets the job done. It's long, but I thought it was decent enough. There are also plenty of video lectures on algorithms online; I liked the MIT OpenCourseWare of this class.
Graph Theory: Many combinatorial optimization problems involve graphs, so you would definitely want to know some graph theory. It's also super interesting, and definitely worth learning regardless! West is a good book with lots of exercises. Bondy and Murty and Diestel also have good books, which are freely available in PDF if you do a google search. Since you're doing a project on traffic optimization, you might find network flows interesting. Networks are directed graphs, where you think about moving "flow" across the edges of the graph, so they are useful for modelling a lot of real-life problems, including traffic. Ahuja is the best book I know on network flows.
Linear and Integer Programming: Many optimization problems can be described as maximizing (or minimizing) some linear function subject to a set of linear constraints. These are linear programs (LPs). If the variables need to take on integer values, then you have an integer program (IP). Most combinatorial optimization problems can be formulated as integer programs. Integer programming is NP-hard, but in practice there are methods that can solve most IPs , even very large ones, relatively quickly. So, if you actually want to optimize things in real-life this is a very useful thing to know. There's also a mathematically rich field of developing methods to solve IPs. It's a bit of a different flavor than the rest of this stuff, but it's definitely a fertile area of research. Bertsimas is good for learning linear programming. Unfortunately, I don't have a good recommendation for learning integer programming from scratch. Perhaps the chapters in Papadimitriou - Combinatorial Optimization would be a good introduction.
Approximation Algorithms: This is about algorithms which quickly (in polynomial time) find provably good but not necessarily optimal solutions to NP-hard problems. Williamson and Shmoys have a great book that is freely available here.
The last book I'd recommend is Schrijver. This is the bible for the field. I put it here at the end because it's more of a reference book rather than something you could read cover to cover, but it's REALLY good.
Lastly, if you like traffic optimization, maybe look up what people are doing in operations research departments. A lot of OR is about modelling real problems with math and analyzing the models, so this would include things like traffic optimization, vehicle routing problems, designing smart electric grids, financial engineering, etc.
Edit: Not sure why my links aren't all formatting correctly... sorry!
Combinatorial Optimization, algorithms and complexity. It treats a large amount of graph and combinatorial algorithms, and gives a solid introduction to NP/P/NP-Complete/NP-Hard/Big O etc.