Collision detection with a large number of objects

At the moment, I have about a few hundred moving objects on the screen, plus a thousand + stationary objects. For simplicity, you can think of it as a billiard game with a heck of a lot of balls :) Some of them still remain, some others are moving with all kinds of speeds in every possible direction. I need to detect a collage every time every ball hits a different ball. What is the best method, given performance and, well, ease of programming? I am only talking about the algorithm, I assume that I can implement it myself, and suggestions for implementation are welcome;)

The language is C #, XNA 3.1, 2D graphics, the target platform is Windows only (if that matters). Thanks in advance for your help!

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You might want to take a look at the answers to this question .

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