Directory protocols are more scalable than snooping protocols because they send explicit request and invalidate messages to those nodes that have copies of a block, while snooping protocols broadcast all requests and invalidates to all nodes. Consider the 16-processor system illustrated in Figure 4.42 and assume that all caches not shown have invalid blocks. For each of the sequences below, identify which nodes receive each request and invalidate.
a. [10] <4.4> P0: write 100 <-- 80
b. [10] <4.4> P0: write 108 <-- 88
c. [10] <4.4> P0: write 118 <-- 90
d. [10] <4.4> P1: write 128 <-- 98