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I'm trying to solve a set cover problem.

To put it shortly, my problem is about covering a $N \times M$ grid, by using various rectangles which have associated cost depending on their shape and position. A bit like Tetris, but not quite the same (since I have different costs depending on shape and position).

A common approach seems to be using lagrangian relaxation and subgradients to get lower/upper bounds, then do branch and bound. Though I am not sure if it is the most modern approach, I would like to learn about classical results on those subjects from a theoretical standpoint. If you know more efficient techniques, I'll also be interested.

What books or resources would you recommend ? So far I found Korte's Combinatorial Optimization, but I don't know if it is the most indicated book for those subjects. Thanks,

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