Amortized Efficiency of a Path Retrieval Data Structure

A data structure is presented for the problem of maintaining a digraph under an arbitrary sequence of two kinds of operations: an Add operation that inserts an arc in the digraph, and a Searchpath operation that checks the presence of a path between a pair of nodes. Our data structure supports both operations in O(n) amortized time and requires O(n2) space, where n is the number of nodes in the digraph.