A tree-based distributed algorithm for the K-entry critical section problem

We present a token-based algorithm for solving the K-entry critical section problem. Based on Raymond´s (1989) tree-based approach, we regard the nodes as being arranged in a directed tree structure, and all messages used in the algorithm are sent along the directed edges of the tree. There are K tokens in the system; we use a bag structure at each node to record the collection of the neighboring nodes, possibly with multiple occurrences of the same node, through which the K tokens can be located. As a result, there are K paths from each node leading to the K tokens in the system. Our algorithm requires at most 2 KD messages for a node to enter the CS, where D is the diameter of the tree. Therefore, when the diameter D is much smaller than N, the number of nodes, e.g. D=O(1) as in a star or D=O(logN) as in a binary tree, our algorithm´s upper bound on the number of messages per CS is smaller than those previously reported