Consider the problem of parallelizing Johnson's single-source shortest paths algorithm for sparse graphs (Section 10.7.2). One way of parallelizing it is to use p1 processes to maintain the priority queue and p2 processes to perform the computations of the new l values. How many processes can be efficiently used to maintain the priority queue (in other words, what is the maximum value for p1)? How many processes can be used to update the l values? Is the parallel formulation that is obtained by using the p1 + p2 processes cost-optimal? Describe an algorithm that uses p1 processes to maintain the priority queue.