Improved Space Efficient Algorithms for BFS, DFS and Applications

Space-Efficient Biconnected Components and Recognition of Outerplanar Graphs

“…Banerjee et al [4] independently discovered a different approach to compute the cut vertices of a graph with n vertices and m edges that uses O(n+m) bits and time. They have no algorithm with a space bound that only depends on n.…”

Fast Breadth-First Search in Still Less Space

“…As for (1), every container concerned is regular or on the right side, i.e., the number of such containers is bounded by 2(N − µ). Since the iteration converts all N − µ regular containers to the loose representation, the contribution of (1) is dominated by that of (2). And as for (2), since the number of other conversions is within a constant factor of the number of conversions to the regular representation, it suffices to bound the latter by O(n/λ).…”

Space Efficient Linear Time Algorithms for BFS, DFS and Applications

“…Here we assume that the input graph G is represented using the standard adjacency list along with cross pointers, i.e., for undirected graphs given a vertex u and the position in its list of a neighbor v of u, there is a pointer to the position of u in the list of v. In case of directed graphs, for every vertex u, we have a list of outneighbors of u and a list of in-neighbours of u. And, finally we augment these two lists for every vertex with cross pointers, i.e., for each (u, v) ∈ E, given u and the position of v in out-neighbors of u, there is a pointer to the position of u in in-neighbors of v. This form of input graph representation was introduced recently in [24] and used subsequently in [7,32,34] to design various other space efficient graph algorithms. We note that some of our algorithms will work even with less powerful and the more traditional adjacency list representation.…”