A simple linear-time algorithm for finding path-decompositions of small width

We described a simple algorithm running in linear time for each fixed constant $k$, that either establishes that the pathwidth of a graph $G$ is greater than $k$, or finds a path-decomposition of $G$ of width at most $O(2^{k})$. This provides a simple proof of the result by Bodlaender that many families of graphs of bounded pathwidth can be recognized in linear time.Comment: 9 page

Obstructions to within a few vertices or edges of acyclic

Finite obstruction sets for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. It has been known for several years that, in principle, obstruction sets can be mechanically computed for most natural lower ideals. In this paper, we describe a general-purpose method for finding obstructions by using a bounded treewidth (or pathwidth) search. We illustrate this approach by characterizing certain families of cycle-cover graphs based on the two well-known problems: $k$-{\sc Feedback Vertex Set} and $k$-{\sc Feedback Edge Set}. Our search is based on a number of algorithmic strategies by which large constants can be mitigated, including a randomized strategy for obtaining proofs of minimality.Comment: 16 page

Determination of the Relationship between Strength and Test Method for Glass Fibre Epoxy Composite Coupons using Weibull analysis

The paper offers a practical approach to applying probability statistics to composites. A method is presented for the prediction of tensile strengths from flexural strength tests and vice versa and that quantifies how processing affects mechanical properties with respect to component size. This quantification was used by GKN Technology to evaluate manufacture before fatigue testing of composites.Glass fibre epoxy composite test coupons exhibit variability in their tensile strength data dependent on the test method used. The three common test standards are for tensile, three-point flexure and four-point flexure and it is accepted that flexure tests yield higher strengths than tensile tests. Tests were carried out on coupons of a woven E-glass epoxy composite for each type of test. The data for each test was found to fit a two-parameter Weibull distribution. The Weibull moduli for each of the test methods were approximately the same. This Weibull modulus is used to relate the strengths for different test methods using an equivalent volume method. It was found that the strength variability is dependent only on the equivalent volumes of test coupons and thus, a method is proposed for the prediction of tensile strengths from flexural strength tests and vice versa

JOURNAL OF ELECTRONIC TESTING: Theory and Applications,6,255-258 (1995)

This letter is a supplement of the table of the minimal cost one-dimensional linear hybrid cellular automata with the maximum length cycle by Zhang, Miller, and Muzio [IEE Electronics Letters, 27(18):1625-1627, August 1991]

Finding Minor-Order Obstruction Sets: Feedback Vertex Set ≤ 2

We describe an application of an obstruction set computation platform that identifies the previously unknown obstruction sets for the k-Feedback Vertex Set problem, for k = 1 and k = 2. Finite obstruction sets for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem (GMT). It has been known for several years that, in principle, obstruction sets can be mechanically computed for most natural lower ideals. Focusing on FVS, we describe an implementation of this finite-state obstruction set computation theory. The implementation is based on a number of algorithmic strategies by which large constants can be mitigated, including a randomized strategy for obtaining proofs of minimality. The computation is based in part on interesting and substantial problem-specific results

Forbidden minors to graphs with small feedback sets

AbstractFinite obstruction set characterizations for lower ideals in the minor order are guaranteed to exist by the graph minor theorem. In this paper we characterize several families of graphs with small feedback sets, namely k1-FEEDBACK VERTEX SET, k2-Feedback EDGE SET and (k1,k2)-FEEDBACK VERTEX/EDGE SET, for small integer parameters k1 and k2. Our constructive methods can compute obstruction sets for any minor-closed family of graphs, provided the pathwidth (or treewidth) of the largest obstruction is known