This paper presents the design, implementation and testing of the critical path analysis technique on the IPS performance measurement tool for parallel and distributed programs. We create a precedence graph of a program’s activities (Program Activity Graph) with the data collected during the execution of a program. The critical path, the longest path in the program activity graph, represents th...

In a general model for square-wave bursting oscillations, we examine the fast transition between the slowly varying quiescent and active phases. In this type of bursting, the transition occurs at a saddle-node (SN) bifurcation point of the fast-variable subsystem when the slow variable is taken to be the bifurcation parameter. A critical case occurs when the SN bifurcation point is also a stead...

Let T be a tree with n nodes, in which each edge is associated with a length and a weight. The density-constrained longest (heaviest) path problem is to find a path of T with maximum path length (weight) whose path density is bounded by an upper bound and a lower bound. The path density is the path weight divided by the path length. We show that both problems can be solved in optimal O(n logn) ...

A digraph obtained by replacing each edge of a complete multipartite graph by an arc or a pair of mutually opposite arcs with the same end vertices is called a semicomplete multipartite digraph. L. Volkmann (1998) raised the following question: Let D be a strong semicomplete multipartite digraph with a longest path of length l. Does there exist a strong spanning oriented subgraph of D with a lo...

Corrádi and Hajnal [1] showed that any graph of order at least 3k with minimum degree at least 2k contains k vertex-disjoint cycles. This minimum degree condition is sharp, because the complete bipartite graph K2k−1,n−2k+1 does not contain k vertex-disjoint cycles. About the existence of vertex-disjoint cycles of the same length, Thomassen [4] conjectured that the same minimum degree condition ...

Methods for sizing project and feeding buffers for critical chain project management are investigated. Experiments indicate that – in the absence of bias, and for certain classes of bias – buffer consumption is independent of the mean duration of a chain. Generally the popular method – a buffer size equal to 50% of the longest path leading to it – gives rise to excessively large buffers. Buffer...

We study distance properties of a general class of random directed acyclic graphs (DAGs). In a DAG, many natural notions of distance are possible, for there exists multiple paths between pairs of nodes. The distance of interest for circuits is the maximum length of a path between two nodes. We give laws of large numbers for the typical depth (distance to the root) and the minimum depth in a ran...

The longest path problem on graph G is a classic problem which is to find a simple path such that the number of vertices of the path is maximum among all possible paths of G. In this paper, we show that the longest path problem can be solved in linear time on permutation graphs.

Culberson and Rudnicki [J.C. Culberson, P. Rudnicki, A fast algorithm for constructing trees from distance matrices, Inform. Process. Lett. 30 (4) (1989) 215–220] gave an algorithm that reconstructs a degree d restricted tree from its distance matrix. According to their analysis, it runs in time O(dn logd n) for topological trees. However, this turns out to be false; we show that the algorithm ...

Weconsider a directed graph on the integerswith a directed edge fromvertex i to j present with probability n−1, whenever i < j , independently of all other edges. Moreover, to each edge (i, j) we assign weight n−1(j − i). We show that the closure of vertex 0 in such a weighted random graph converges in distribution to the Poisson-weighted infinite tree as n → ∞. In addition, we derive limit the...