The mutual exclusion problem: partII—statement and solutions
Journal of the ACM (JACM)
Algorithms for mutual exclusion
Algorithms for mutual exclusion
Algorithms for scalable synchronization on shared-memory multiprocessors
ACM Transactions on Computer Systems (TOCS)
Bounds on shared memory for mutual exclusion
Information and Computation
The communication requirements of mutual exclusion
Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures
A new solution of Dijkstra's concurrent programming problem
Communications of the ACM
Additional comments on a problem in concurrent programming control
Communications of the ACM
Solution of a problem in concurrent programming control
Communications of the ACM
The Performance of Spin Lock Alternatives for Shared-Memory Multiprocessors
IEEE Transactions on Parallel and Distributed Systems
Linear Lower Bounds on Real-World Implementations of Concurrent Objects
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
An Ω (n log n) lower bound on the cost of mutual exclusion
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Tight RMR lower bounds for mutual exclusion and other problems
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Mutual Exclusion with O(log^2 Log n) Amortized Work
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
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Mutual Exclusion is a fundamental problem in distributed computing, and the problem of proving upper and lower bounds on the RMR complexity of this problem has been extensively studied. Here, we give matching lower and upper bounds on how RMR complexity trades off with space. Two implications of our results are that constant RMR complexity is impossible with subpolynomial space and subpolynomial RMR complexity is impossible with constant space for cache-coherent multiprocessors, regardless of how strong the hardware synchronization operations are. To prove these results we show that the complexity of mutual exclusion, which can be "messy" to analyze because of system details such as asynchrony and cache coherence, is captured precisely by a simple and purely combinatorial game that we design. We then derive lower and upper bounds for this game, thereby obtaining corresponding bounds for mutual exclusion. The lower bounds for the game are proved using potential functions.