Consider a binary, perfectly balanced tree of processes of height n where all leaf nodes have the same distance from the root; so there is a total number of m = 2 n − 1 nodes in the tree. Assume that the root is the coordinator of the commit protocol. Determine the number of messages and forced log writes for the presumed-nothing (i.e., basic 2PC), presumed-abort, and presumed-commit protocols for the following situations:
(a) all processes have performed updates and the transaction commits,
(b) all processes have performed updates and the transaction aborts,
(c) all nonroot nodes are read-only and the transaction commits,
(d) all leaf nodes are read-only and the transaction commits
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