Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given a mutual exclusion algorithm MXd for \({d \geq 2}\) threads, a mutual exclusion algorithm for \({N > d}\) threads can be built in a tree of degree d with N leaves, with the critical section at the root of the tree. This tournament solution seems obviously correct and efficient. The present note proves the correctness, and formalizes the efficiency in terms of concurrent complexity by means of Bounded Unity. If the tree is balanced, the throughput is logarithmic in N. If moreover MXd satisfies FCFS (first-come first-served), the worst case individual delay of the tournament algorithm is of order N. This is optimal.
['Wim H. Hesselink']
I am writing a research paper on a idea Tournaments for mutual exclusion: verification and concurrent complexity
[{"from": "human", "value": "I am writing a research paper on a idea Tournaments for mutual exclusion: verification and concurrent complexity"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given a mutual exclusion algorithm MXd for \\({d \\geq 2}\\) threads, a mutual exclusion algorithm for \\({N > d}\\) threads can be built in a tree of degree d with N leaves, with the critical section at the root of the tree. This tournament solution seems obviously correct and efficient. The present note proves the correctness, and formalizes the efficiency in terms of concurrent complexity by means of Bounded Unity. If the tree is balanced, the throughput is logarithmic in N. If moreover MXd satisfies FCFS (first-come first-served), the worst case individual delay of the tournament algorithm is of order N. This is optimal."}]