Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

All of the methods of the graph ADT that can be implemented with the edge list
structure in O(1) time can also be implemented in O(1) time with the adjacency
list structure, using essentially the same algorithms. In addition, being able to
provide access between vertices and edges in both directions allows us to speed
up the performance of a number of the graph methods by using an adjacency list
structure instead of an edge list structure. Table 13.2 summarizes the performance
of the adjacency list structure implementation of a graph, assuming that
collections V and E and the incidence collections of the vertices are all
implemented with doubly linked lists. For a vertex v, the space used by the
incidence collection of v is proportional to the degree of v, that is, it is O(deg(v)).
Thus, by Proposition 13.6, the space requirement of the adjacency list structure is
O(n + m).
Table 13.2: Running times of the methods of a
graph implemented with the adjacency list structure.
The space used is O(n + m), where n is the number of
vertices and m is the number of edges.
Operation
Time
vertices
O(n)
edges
O(m)
endVertices, opposite
O(1)
incidentEdges(v)
O(deg(v))
areAdjacent(v,w)
O(min(deg(v),deg(w))
replace
O(1)
804