Finding Articulation Points of Large Graphs in Linear Time

Abstract

Given an n-node m-edge graph G, the articulation points of graph G can be found in $\mathcal {O}(m+n)$ time in the RAM model, through a DFS-based algorithm. In the semi-streaming model for large graphs, where memory is limited to $\mathcal {O}(n \mathop {\mathrm {polylog}}n)$ and edges may only be accessed in one or more sequential passes, no efficient DFS algorithm is known, so another approach is needed.

We show that the articulation points can be found in $\mathcal {O}(m+n)$ time using $\mathcal {O}(n)$ space and one sequential pass of the graph. The previous best algorithm in the semi-streaming model also uses $\mathcal {O}(n)$ space and one pass, but has running time $\mathcal {O}(m\alpha (n)+n\log n)$, where $\alpha$ denotes the inverse of Ackermann function.

This research was supported in part by NSF grants CNS-1408782, IIS-1247750 and by Ministry of Science and Technology, Taiwan, Grant MOST 103-2221-E-001-033.