9 research outputs found
Spanning Properties of Theta-Theta-6
We show that, unlike the Yao-Yao graph , the Theta-Theta graph
defined by six cones is a spanner for sets of points in convex
position. We also show that, for sets of points in non-convex position, the
spanning ratio of is unbounded.Comment: 13 pages, 9 figure
Spanning Properties of Theta-Theta-6
We show that, unlike the YaoâYao graph YY6, the ThetaâTheta graph ÎÎ6 defined by six cones is a spanner for sets of points in convex position. We also show that, for sets of points in non-convex position, the spanning ratio of ÎÎ6 is unbounded
Pi/2-Angle Yao Graphs are Spanners
We show that the Yao graph Y4 in the L2 metric is a spanner with stretch
factor 8(29+23sqrt(2)). Enroute to this, we also show that the Yao graph Y4 in
the Linf metric is a planar spanner with stretch factor 8.Comment: 20 pages, 9 figure
Large bichromatic point sets admit empty monochromatic 4-gons
We consider a variation of a problem stated by ErdËos
and Szekeres in 1935 about the existence of a number
fES(k) such that any set S of at least fES(k) points in
general position in the plane has a subset of k points
that are the vertices of a convex k-gon. In our setting
the points of S are colored, and we say that a (not necessarily
convex) spanned polygon is monochromatic if
all its vertices have the same color. Moreover, a polygon
is called empty if it does not contain any points of
S in its interior. We show that any bichromatic set of
n â„ 5044 points in R2 in general position determines
at least one empty, monochromatic quadrilateral (and
thus linearly many).Postprint (published version
Semantic discovery and reuse of business process patterns
Patterns currently play an important role in modern information systems (IS) development and their use has mainly been restricted to the design and implementation phases of the development lifecycle. Given the increasing significance of business modelling in IS development, patterns have the potential of providing a viable solution for promoting reusability of recurrent generalized models in the very early stages of development. As a statement of research-in-progress this paper focuses on business process patterns and proposes an initial methodological framework for the discovery and reuse of business process patterns within the IS development lifecycle. The framework borrows ideas from the domain engineering literature and proposes the use of semantics to drive both the discovery of patterns as well as their reuse