Shortest Weighted Paths I Parallel and Sequential Data

When graphs are implemented using tables and sets, the cost of finding and updating a vertex in the table is (logn) work and span. We can improve the asymptotic performance of certain algorithms if these operations are constant work. An array is an obvious data structure that has constant lookup, but in a functional setting the cost of changing a value in the array requires copying the whole area in order to maintain data persistency.