Graph-based real-time fault diagnostics

A real-time fault detection and diagnosis capability is absolutely crucial in the design of large-scale space systems. Some of the existing AI-based fault diagnostic techniques like expert systems and qualitative modelling are frequently ill-suited for this purpose. Expert systems are often inadequately structured, difficult to validate and suffer from knowledge acquisition bottlenecks. Qualitative modelling techniques sometimes generate a large number of failure source alternatives, thus hampering speedy diagnosis. In this paper we present a graph-based technique which is well suited for real-time fault diagnosis, structured knowledge representation and acquisition and testing and validation. A Hierarchical Fault Model of the system to be diagnosed is developed. At each level of hierarchy, there exist fault propagation digraphs denoting causal relations between failure modes of subsystems. The edges of such a digraph are weighted with fault propagation time intervals. Efficient and restartable graph algorithms are used for on-line speedy identification of failure source components

Join-Reachability Problems in Directed Graphs

For a given collection G of directed graphs we define the join-reachability graph of G, denoted by J(G), as the directed graph that, for any pair of vertices a and b, contains a path from a to b if and only if such a path exists in all graphs of G. Our goal is to compute an efficient representation of J(G). In particular, we consider two versions of this problem. In the explicit version we wish to construct the smallest join-reachability graph for G. In the implicit version we wish to build an efficient data structure (in terms of space and query time) such that we can report fast the set of vertices that reach a query vertex in all graphs of G. This problem is related to the well-studied reachability problem and is motivated by emerging applications of graph-structured databases and graph algorithms. We consider the construction of join-reachability structures for two graphs and develop techniques that can be applied to both the explicit and the implicit problem. First we present optimal and near-optimal structures for paths and trees. Then, based on these results, we provide efficient structures for planar graphs and general directed graphs

Dynamic Dominators and Low-High Orders in DAGs

We consider practical algorithms for maintaining the dominator tree and a low-high order in directed acyclic graphs (DAGs) subject to dynamic operations. Let G be a directed graph with a distinguished start vertex s. The dominator tree D of G is a tree rooted at s, such that a vertex v is an ancestor of a vertex w if and only if all paths from s to w in G include v. The dominator tree is a central tool in program optimization and code generation, and has many applications in other diverse areas including constraint programming, circuit testing, biology, and in algorithms for graph connectivity problems. A low-high order of G is a preorder of D that certifies the correctness of D, and has further applications in connectivity and path-determination problems. We first provide a practical and carefully engineered version of a recent algorithm [ICALP 2017] for maintaining the dominator tree of a DAG through a sequence of edge deletions. The algorithm runs in O(mn) total time and O(m) space, where n is the number of vertices and m is the number of edges before any deletion. In addition, we present a new algorithm that maintains a low-high order of a DAG under edge deletions within the same bounds. Both results extend to the case of reducible graphs (a class that includes DAGs). Furthermore, we present a fully dynamic algorithm for maintaining the dominator tree of a DAG under an intermixed sequence of edge insertions and deletions. Although it does not maintain the O(mn) worst-case bound of the decremental algorithm, our experiments highlight that the fully dynamic algorithm performs very well in practice. Finally, we study the practical efficiency of all our algorithms by conducting an extensive experimental study on real-world and synthetic graphs

07281 Abstracts Collection -- Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs

From 8th to 13th July 2007, the Dagstuhl Seminar ``Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Strong Phonics Base to Build Better Readers

The biggest problem educators are encountering with emergent readers is their lack of phonological awareness. For a child to become a successful reader, they must have a solid understanding of basic and higher phonological rules. The education system has become so focused on standardized testing in the upper elementary grades they have lost focus on the primary grades. There must be a balance between the primary grades (Kindergarten through 2nd) and the secondary grades (3rd-5th). In Kindergarten through second grade a student is learning to read, by third grade that student should have all the basic phonics skills they need to know read to learn. Unfortunately, this is not the case many students have not been taught the phonics skills necessary to begin learning to read in third grade. This action research paper will focus on the importance of a strong phonics base to help build better readers

Hamiltonian problems for reducible flowgraphs

In this paper, we discuss hamiltonian problems for reducible flowgraphs. The main result is finding, in linear time, the unique hamiltonian cycle, if it exists. In order to obtain this result, two other related problems are solved: finding the hamiltonian path starting at the source vertex and finding the hamiltonian cycle given the hamiltonian path