3,550 research outputs found
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 , that either establishes that the pathwidth of a graph is
greater than , or finds a path-decomposition of of width at most
. 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: -{\sc Feedback Vertex Set} and -{\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
Diopside Glass-Ceramics for Dental and Biomedical Applications.
A series of glass compositions with varying equimolar amounts of Na2O:Al2O3 were designed using Appen factors. High purity batch reagents were ball milled for 30 min and transferred to Pt/Rh crucible and melted in an electric furnace (EHF1700, Lenton, UK) at high temperatures then held for 90 min. The molten glass was poured into a graphite mould, annealed at 50oC below the glass transition temperature for 1h and the remaining glass was quenched into water. Glass frits were crushed and ball milled into powders with different particle sizes. Glass powders (PS<125μm) were heat-treated via two-step heat treatment cycles and air quenched. Experimental glasses and glass-ceramics were characterised using X-Ray Diffraction (XRD), Dilatometry, Scanning Electron Microscopy (SEM) and solid state Nuclear Magnetic Resonance (NMR)
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