Showing papers by "Robert E. Tarjan published in 1974"

Efficient Planarity Testing

Abstract: This paper describes an efficient algorithm to determine whether an arbitrary graph G can be embedded in the plane. The algorithm may be viewed as an iterative version of a method originally proposed by Auslander and Parter and correctly formulated by Goldstein. The algorithm used depth-first search and has O(V) time and space bounds, where V is the number of vertices in G. An ALGOL implementation of the algorithm succesfully tested graphs with as many as 900 vertices in less than 12 seconds.

Finding Dominators in Directed Graphs

Abstract: This paper describes an algorithm for finding dominators in an arbitrary directed graph. The algorithm uses depth-first search and efficient algorithms for computing disjoint set unions and manipulating priority queues to achieve a time bound of $O(V\log V + E)$ if V is the number of vertices and E is the number of edges in the graph. This bound compares favorably with the $O(V(V + E))$ time bound of previously known algorithms for finding dominators in arbitrary directed graphs, and with the $O(V + E\log E)$ time bound of a known algorithm for finding dominators in reducible graphs. If $E \geqq V\log V$, the new algorithm requires $O(E)$ time and is optimal to within a constant factor.

Edge-disjoint spanning trees, dominators, and depth-first search.

Abstract: This paper presents an algorithm for finding two edge-disjoint spanning trees rooted at a fixed vertex of a directed graph. The algorithm uses depth-first search, an efficient method for computing disjoint set unions, and an efficient method for computing dominators. It requires O(V log V + E) time and O(V + E) space to analyze a graph with V vertices and E edges.