Showing papers by "Robert E. Tarjan published in 1973"
TL;DR: The number of comparisons required to select the i-th smallest of n numbers is shown to be at most a linear function of n by analysis of a new selection algorithm-PICK.
1,384 citations
TL;DR: Efficient algorithms are presented for partitioning a graph into connected components, biconnected components and simple paths and each iteration produces a new path between two vertices already on paths.
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 of 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.
1,000 citations
TL;DR: An algorithm for dividing a graph into triconnected components is presented and is both theoretically optimal to within a constant factor and efficient in practice.
Abstract: An algorithm for dividing a graph into triconnected components is presented. When implemented on a random access computer, the algorithm requires $O(V + E)$ time and space to analyze a graph with V vertices and E edges. The algorithm is both theoretically optimal to within a constant factor and efficient in practice.
903 citations
30 Apr 1973
TL;DR: An algorithm for testing whether a flow graph is reducible is described, which uses depth-first search to reveal the structure of the flow graph and a good method for computing disjoint set unions to determine reducibility from the search information.
Abstract: Many problems in program optimization have been solved by applying a technique called interval analysis to the flow graph of the program. A flow graph which is susceptible to this type of analysis is called reducible. This paper describes an algorithm for testing whether a flow graph is reducible. The algorithm uses depth-first search to reveal the structure of the flow graph and a good method for computing disjoint set unions to determine reducibility from the search information. When the algorithm is implemented on a random access computer, it requires O(E log* E) time to analyze a graph with E edges, where log* x = min{i/logix≤1}. The time bound compares favorably with the O(E log E) bound of a previously known algorithm.
180 citations
TL;DR: An algorithm for determining whether two triconnected planar graphs are isomorphic is presented and the asymptotic growth rate of the algorithm is bounded by a constant times log where |V| is the number of vertices in the graphs.
83 citations
01 Apr 1973
TL;DR: In this paper, it was shown that no more than 5.4305 n comparisons are ever required and a lower bound of 9% of the required number of comparisons for extreme values of i was also proved.
Abstract: (1) The number of comparisons required to select the i-th smallest of n numbers is shown to be at most a linear function of n by analysis of a new selection algorithm -- PICK. Specifically, no more than 5.4305 n comparisons are ever required. This bound is improved for extreme values of i, and a new lower bound on the requisite number of comparisons is also proved. (2) A new selection algorithm is presented which is shown to be very efficient on the average, both theoretically and practically. The number of comparisons used to select the i-th smallest of n numbers is n + min(i,n-i) + o(n). A lower bound within 9% of the above formula is also derived.
1 citations