1. (10 points) Consider the following problem called Renaming. There are n processes which have indices in range 1..N where N >> n. We would like these processes to get a new name in the range of 1..M where M n * (n+ 1)/2. How will you construct a function int rename(int j) that returns a unique name to each process in the range 1..M. Every invocation of rename ) should terminate and no two processes should obtain the same name. Your function should not use old index to compute a new index, i.e., it should satisfy the index independence property that if a process whose index is i obtains the new name v, then the process could have obtained the same new name v if its index had been j different from i. (Hint: Use enough splitters to split the input stream of threads) 1. (10 points) Consider the following problem called Renaming. There are n processes which have indices in range 1..N where N >> n. We would like these processes to get a new name in the range of 1..M where M n * (n+ 1)/2. How will you construct a function int rename(int j) that returns a unique name to each process in the range 1..M. Every invocation of rename ) should terminate and no two processes should obtain the same name. Your function should not use old index to compute a new index, i.e., it should satisfy the index independence property that if a process whose index is i obtains the new name v, then the process could have obtained the same new name v if its index had been j different from i. (Hint: Use enough splitters to split the input stream of threads)