Showing papers by "Robert E. Tarjan published in 1982"

The Recognition of Series Parallel Digraphs

Abstract: We present a linear-time algorithm to recognize the class of vertex series-parallel (VSP) digraphs. Our method is based on the relationship between VSP digraphs and the class of edge series-paralle...

Asymptotically tight bounds on time-space trade-offs in a pebble game

Abstract: Asymptotically Ught tune-space trade-offs for pebblmg three d~fferent classes of directed aeychc graphs are derived Let N be the size of the graph, S the number of avadable pebbles, and T the time necessary for pebbling the graph A time-space trade-off of the form ST = O(N 2) ls proved for pebbhng (usmg only black pebbles) a specml class of permutaaon graphs that tmplement the bR-reversal permutation. If we are allowed to use black and whtte pebbles~ the time-space trade-off is shown to be of the form (:) r = o T¢ +0(~ . A tune-space trade-off of the form /N\\OIN/S~ T= S O I ~ ) ~s proved for pebbling a class of graphs constructed by stacking superconcentrators m series. This tunespace trade-off holds whether we use only black or black and white pebbles A tune-space trade-off of the form T -$2 2°~N/s) Is proved for the class of all directed acychc graphs This trade-off also holds whether we use only black or black and white pebbles

Symbolic Program Analysis in Almost-Linear Time

Abstract: This paper describes an algorithm to construct, for each expression in a given program text, a symbolic expression whose value is equal to the value of the text expression for all executions of the program. We call such a mapping from text expressions to symbolic expressions a cover. Covers are useful in such program optimization techniques as constant propagation and code motion. The particular cover constructed by our methods is in general weaker than the covers obtainable by the methods of [Ki], [FKU], [RL], [R2] but our method has the advantage of being very efficient. It requires $O(m\alpha (m,n) + l)$ operations if extended bit vector operations have unit cost, where n is the number of vertices in the control flow graph of the program, m is the number of edges, l is the length of the program text, and $\alpha $ is related to a functional inverse of Ackermann’s function [T2]. Our method does not require that the program be well-structured nor that the flow graph be reducible.

Efficient Algorithms for a Family of Matroid Intersection Problems ; CU-CS-214-82

Abstract: Consider a matroid where each element has a real-valued cost and a color, red or green; a base is sought that contains q red elements and has smallest possible cost. An algorithm for the problem on general matroids is presented, along with a number of variations. Its efficiency is demonstrated by implementations on specific matroids. In all cases but one, the running time matches the best-known algorithm for the problem without the red element constraint: On graphic matroids, a smallest spanning tree with q red edges can be found in time O(n log n) more than what is needed to find a minimum spanning tree. A special case is finding a smallest spanning tree with a degree constraint; here the time is only O(m + n) more than that needed to find one minimum spanning tree. On transversal and matching matroids, the time is the same as the best-known algorithms for a minimum cost base. This also holds for transversal matroids for convex graphs, which model a scheduling problem on unit-length jobs with release times and deadlines. On partition matroids, a linear-time algorithm is presented. Finally an algorithm related to our general approach finds a smallest spanning tree on a directed graph, where the given root has a degree constraint. Again the time matches the best-known algorithm for the problem without the red element (i.e., degree) constraint.