Disjoint compatibility graph of non-crossing matchings of points in convex position

Let $X_{2k}$ be a set of $2k$ labeled points in convex position in the plane. We consider geometric non-intersecting straight-line perfect matchings of $X_{2k}$. Two such matchings, $M$ and $M'$, are disjoint compatible if they do not have common edges, and no edge of $M$ crosses an edge of $M'$. Denote by $\mathrm{DCM}_k$ the graph whose vertices correspond to such matchings, and two vertices are adjacent if and only if the corresponding matchings are disjoint compatible. We show that for each $k \geq 9$, the connected components of $\mathrm{DCM}_k$ form exactly three isomorphism classes -- namely, there is a certain number of isomorphic small components, a certain number of isomorphic medium components, and one big component. The number and the structure of small and medium components is determined precisely.Comment: 46 pages, 30 figure

On the Number of Pseudo-Triangulations of Certain Point Sets

We pose a monotonicity conjecture on the number of pseudo-triangulations of any planar point set, and check it on two prominent families of point sets, namely the so-called double circle and double chain. The latter has asymptotically $12^n n^{\Theta(1)}$ pointed pseudo-triangulations, which lies significantly above the maximum number of triangulations in a planar point set known so far.Comment: 31 pages, 11 figures, 4 tables. Not much technical changes with respect to v1, except some proofs and statements are slightly more precise and some expositions more clear. This version has been accepted in J. Combin. Th. A. The increase in number of pages from v1 is mostly due to formatting the paper with "elsart.cls" for Elsevie

ESTIMATING THE COST OF FOOD SAFETY REGULATION TO THE NEW ZEALAND SEAFOOD INDUSTRY

In New Zealand, the Animal Products Act 1999 requires all animal product processing businesses to have a HACCP-based risk management program by the end of 2002. This paper attempts to measure the effects of such regulation on the variable cost of production of the New Zealand seafood industry. Using the framework developed by Antle (2000), a model of quality-adjusted translog cost function is estimated using census of production data from 1929 to 1998. Our results show that variable costs could increase from 2% to 22% or from 2 cents to 19 cents per kilogram.HACCP, compliance costs, seafood, Production Economics,

Improved alkaline electrochemical cell

Addition of lead ions to electrolyte suppresses zinc dendrite formation during charging cycle. A soluble lead salt can be added directly or metallic lead can be incorporated in the zinc electrode and allowed to dissolve into the electrolyte

Linear transformation distance for bichromatic matchings

Let $P=B\cup R$ be a set of $2n$ points in general position, where $B$ is a set of $n$ blue points and $R$ a set of $n$ red points. A \emph{$BR$-matching} is a plane geometric perfect matching on $P$ such that each edge has one red endpoint and one blue endpoint. Two $BR$-matchings are compatible if their union is also plane. The \emph{transformation graph of $BR$-matchings} contains one node for each $BR$-matching and an edge joining two such nodes if and only if the corresponding two $BR$-matchings are compatible. In SoCG 2013 it has been shown by Aloupis, Barba, Langerman, and Souvaine that this transformation graph is always connected, but its diameter remained an open question. In this paper we provide an alternative proof for the connectivity of the transformation graph and prove an upper bound of $2n$ for its diameter, which is asymptotically tight

Geodesic-Preserving Polygon Simplification

Polygons are a paramount data structure in computational geometry. While the complexity of many algorithms on simple polygons or polygons with holes depends on the size of the input polygon, the intrinsic complexity of the problems these algorithms solve is often related to the reflex vertices of the polygon. In this paper, we give an easy-to-describe linear-time method to replace an input polygon $\mathcal{P}$ by a polygon $\mathcal{P}'$ such that (1) $\mathcal{P}'$ contains $\mathcal{P}$, (2) $\mathcal{P}'$ has its reflex vertices at the same positions as $\mathcal{P}$, and (3) the number of vertices of $\mathcal{P}'$ is linear in the number of reflex vertices. Since the solutions of numerous problems on polygons (including shortest paths, geodesic hulls, separating point sets, and Voronoi diagrams) are equivalent for both $\mathcal{P}$ and $\mathcal{P}'$, our algorithm can be used as a preprocessing step for several algorithms and makes their running time dependent on the number of reflex vertices rather than on the size of $\mathcal{P}$

Testing the Relationships between Marketing Strategies and Customer Retention: The Growth of Hotels and Guesthouses in Upper East Region, Ghana

Organizations continually seek new ways to acquire, retain and increase business, since the cost of losing customers is rising. This study investigated the marketing strategies employed by hotels and guesthouses in the Upper East Region of Ghana. The main objective of the research was to examine the effects of marketing strategies on customer retention in the region. In a qualitative and quantitative study of 87 owners/managers of hotels and guesthouses in the region were selected with the use of the simple random sampling technique from 2 municipals and 5 districts.  A structured questionnaire was used to collect data from owners/managers of hotel/guesthouses in the region. The results revealed a positive relationship between pricing, product/service, promotion, place and physical evidence strategies with customer retention for growth of small hotels/guesthouses. It is suggested that these hotels and guesthouses should employ coordinated marketing strategies in their transactions to attain higher performance. This performance can be achieved if managers/owners and employees work together to ensure provision of quality goods and services to satisfy customers. Keywords: Marketing, Retention, customers, Strategies, Managers, Business