Showing papers by "Robert E. Tarjan published in 1971"

Efficient algorithms for graph manipulation

Abstract: Efficient algorithms are presented for partitioning a graph into connected components, biconnected components and simple paths. The algorithm for partitioning of a graph into simple paths is iterative and each iteration produces a new path between two vertices already on paths. (The start vertex can be specified dynamically.) If V is the number of vertices and E is the number of edges each algorithm requires time and space proportional to max(V,E) when executed on a random access computer.

Depth-first search and linear graph algorithms

Abstract: The value of depth-first search or "backtracking" as a technique for solving graph problems is illustrated by two examples. An algorithm for finding the biconnected components of an undirected graph and an improved version of an algorithm for finding the strongly connected components of a directed graph are presented. The space and time requirements of both algorithms are bounded by k1V + k2E + k3 for some constants k1, k2, and k3, where V is the number of vertices and E is the number of edges of the graph being examined.

Planarity testing in V log V steps: extended abstract

Abstract: An efficient algorithm is presented for determining whether or not a given graph is planar. If V is the number of vertices in the graph, the algorithm requires time proportional to V log V and space proportional to V when run on a random-access computer. The algorithm constructs the facial boundaries of a planar representation without backup, using extensive list-processing features to speed computation. The theoretical time bound improves on that of previously published algorithms. Experimental evidence indicates that graphs with a few thousand edges can be tested within seconds.

An Analytical Positive Manifold Algorithm for Use With Latent Class Analysis

Abstract: A simple computational method for latent class analysis is that of Gibson (1951, 1962). For the method to be adapted to computers, however, it is necessary to use an algorithm that will rotate the intermediate solution to a positive manifold result. Such algorithms have not appeared in the literature. A positive manifold algorithm which has proven successful is developed and presented with comments on its use.