Computing Vertex-Disjoint Paths in Large Graphs Using MAOs

We consider the problem of computing k in N internally vertex-disjoint paths between special vertex pairs of simple connected graphs. For general vertex pairs, the best deterministic time bound is, since 42 years, O(min{k,sqrt{n}}m) for each pair by using traditional flow-based methods. The restriction of our vertex pairs comes from the machinery of maximal adjacency orderings (MAOs). Henzinger showed for every MAO and every 1 <= k <= delta (where delta is the minimum degree of the graph) the existence of k internally vertex-disjoint paths between every pair of the last delta-k+2 vertices of this MAO. Later, Nagamochi generalized this result by using the machinery of mixed connectivity. Both results are however inherently non-constructive. We present the first algorithm that computes these k internally vertex-disjoint paths in linear time O(m), which improves the previously best time O(min{k,sqrt{n}}m). Due to the linear running time, this algorithm is suitable for large graphs. The algorithm is simple, works directly on the MAO structure, and completes a long history of purely existential proofs with a constructive method. We extend our algorithm to compute several other path systems and discuss its impact for certifying algorithms

Counting and Sampling Markov Equivalent Directed Acyclic Graphs

Exploring directed acyclic graphs (DAGs) in a Markov equivalence class is pivotal to infer causal effects or to discover the causal DAG via appropriate interventional data. We consider counting and uniform sampling of DAGs that are Markov equivalent to a given DAG. These problems efficiently reduce to counting the moral acyclic orientations of a given undirected connected chordal graph on n vertices, for which we give two algorithms. Our first algorithm requires O(2(n)n(4)) arithmetic operations, improving a previous super-exponential upper bound. The second requires O (k! 2(k) k(2)n) operations, where k is the size of the largest clique in the graph; for bounded-degree graphs this bound is linear in n. After a single run, both algorithms enable uniform sampling from the equivalence class at a computational cost linear in the graph size. Empirical results indicate that our algorithms are superior to previously presented algorithms over a range of inputs; graphs with hundreds of vertices and thousands of edges are processed in a second on a desktop computer.Peer reviewe

2018 FSDG Combined Abstracts

https://scholarworks.gvsu.edu/fsdg_abstracts/1000/thumbnail.jp

A cumulative index to a continuing bibliography on aeronautical engineering

This bibliography is a cumulative index to the abstracts contained in NASA-SP-7037(184) through NASA-SP-7037(195) of Aeronautical Engineering: A Continuing Bibliography. NASA SP-7037 and its supplements have been compiled through the cooperative efforts of the American Institute of Aeronautics and Astronautics (AIAA) and the National Aeronautics and Space Administration (NASA). This cumulative index includes subject, personal author, corporate source, foreign technology, contract, report number, and accession number indexes