Analyze the performance of Luby's shared-address-space algorithm for finding a maximal independent set of vertices on sparse graphs described in Section 10.7.1. What is the parallel run time and speedup of this formulation?
Problem 10.14 Consider Dijkstra's single-source shortest paths algorithm for sparse graphs (Section 10.7). We can parallelize this algorithm on a p-process hypercube by splitting the n adjacency lists among the processes horizontally; that is, each process gets n/p lists. What is the parallel run time of this formulation? Alternatively, we can partition the adjacency list vertically among the processes; that is, each process gets a fraction of each adjacency list. If an adjacency list contains m elements, then each process contains a sublist of m/p elements. The last element in each sublist has a pointer to the element in the next process. What is the parallel run time and speedup of this formulation? What is the maximum number of processes that it can use?