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Concurrent Systems/notes/1b - Peterson algorithm.md

@@ -136,4 +136,12 @@ It satisfies MUTEX and starvation freedom. It does not satisfy bounded bypass:
 - when the first process wakes up, it can pass to level 2 and eventually win
 - but the sleep can be arbitrary long and in the meanwhile the other two processes may have entered an unbounded number of CSs
 
-Easy to generalize to k-MUTEX.
+Easy to generalize to k-MUTEX.
+
+Peterson's algorithm cost $O(n^2)$
+A first way to reduce this cost is by using a tournament of MUTEX between pairs of processes:
+![[Pasted image 20250304082459.png|350]]
+
+Of course this is a binary tree, and the height of a binary tree is logaritmic to the number of leaves. A process then wins after $\lceil \log_{2}n \rceil$ competitions $\to O(\log n)$ cost.
+
+But we can do better. Let's see an idea of a constant-time algorithm.