19271257
Extremal Cayley Digraphs of Finite Cyclic Groups
Let $\cay(m,A)$ denote the Cayley digraph on ${\bf Z}_m$ generated by $A$, where ${\bf Z}_m$ is the cyclic group of residues modulo $m$. Let $r(m,A)$ denote the average distance of $\cay(m,A)$. For any $r\ge1$ and $k\ge1$ define $m^*(r,k)$ as the largest positive integer $m$ such that the average distance of the Cayley digraph $\hbox{Cay}(m,A)$ is at most $r$ for some set $A$ with $k$ elements. In this paper, an asymptotic formula for $m^*(r,2)$ is proved and a lower bound for $m^*(r,k)$ is also obtained for $k\ge3$. Applications to the construction of optimal distributed loop networks is discussed in this paper. A lower bound of the average order of subsets for asymptotic bases in number theory is proved using the main theorem of this paper.
1493304
On random points in the unit disk
Let n be a positive integer and λ > 0 a real number. Let Vn be a set of n points in the unit disk selected uniformly and independently at random. Define G(λ, n) to be the graph with vertex set Vn, in which two vertices are adjacent if and only if their Euclidean distance is at most λ. We call this graph a unit disk random graph. Let λ = c √ lnn/n and let X be the number of isolated points in G(λ, n). We prove that almost always X ∼ n1−c2 when 0 ≤ c < 1. It is known that if λ = √ (ln n + φ(n))/n where φ(n) → ∞, then G(λ, n) is connected. By extending a method of Penrose, we show that under the same condition on λ, there exists a constant K such that the diameter of G(λ, n) is bounded above by K · 2/λ. Furthermore, with a new geometric construction, we show that when λ = c √ lnn/n and c > 2.26164 · · · , the diameter of G(λ, n) is bounded by (4 + o(1))/λ; and we modify this construction to yield a function c(δ) > 0 such that the diameter is at most 2(1 + δ + o(1))/λ when c > c(δ). ∗This is a preprint of an article accepted for publication in Random Structures and Algorithms c ©2005. †Partially supported by NSF grant DMS-9977354. ‡Partially supported by NSF grant DMS-0245526, DMS-0308827 and a Sloan Fellowship. The author is also affiliated with Dalian University of Technology.
18149163
SMOQE: a system for providing secure access to XML
XML views have been widely used to enforce access control, support data integration, and speed up query answering. In many applications, e.g., XML security enforcement, it is prohibitively expensive to materialize and maintain a large number of views. Therefore, views are necessarily virtual. An immediate question then is how to answer queries on XML virtual views. A common approach is to rewrite a query on the view to an equivalent one on the underlying document, and evaluate the rewritten query. This is the approach used in the Secure MOdular Query Engine (SMOQE). The demo presents SMOQE, the first system to provide efficient support for answering queries over virtual and possibly recursively defined XML views. We demonstrate a set of novel techniques for the specification of views, the rewriting, evaluation and optimization of XML queries. Moreover, we provide insights into the internals of the engine by a set of visual tools.
16011778
A Uniform System for Publishing and Maintaining XML Data
XML has become the prime standard for data exchange on the Web. To exchange data residing in Databases, one needs to publish it in XML. Data publishing is often done with a predefined “schema.” The chapter proposes a new approach for schema-directed publishing of relational data in XML, based on the novel notion of attribute transformation grammars (ATGs). ATGs provide guidance on how to define views conforming to target schemas (DTDs), and automatically ensure schema conformance. The chapter also develops an incremental algorithm for maintaining XML views produced by ATGs, based on new incremental computation techniques that capitalize on the hierarchical structure of XML data and unique features of the ATGs. Taking real-life data from Gene Ontology (GO), this chapter also demonstrates how this system can efficiently publish the GO data in XML with respect to a predefined recursive DTD, and how it incrementally updates the target XML data in response to changes to the underlying GO database.
13944177
A pragmatic approach to formalizing object-oriented modeling and development
Despite recent developments in formal methods, these methods have yet to enter the mainstream of the software industry. We first examine the pragmatic obstacles to making formal methods practical and usable. Then we present a pragmatic approach to integrate a popular object oriented modeling notation UML and a popular formal notation Z. Our approach is distinctive in its emphasis on overcoming the practical obstacles. We also present a light weight supporting tool for our approach. A prototype of the supporting tool is completed. It allows us to demonstrate the feasibility and capability of our approach.
42148814
Using GALS architecture to reduce the impact of long wire delay on FPGA performance
28697957
The maximum size of graphs satisfying a degree condition
Let G be a simple graph of order n without isolated vertices. If the integer h satisfies 
h ⩾ maxυ ϵ V(G)minu ψ N(V)(degGu) 
then G is called an Fn(h)-graph. In this note the maximum size of Fn(h)-graphs is determined. A result of Krol and Veldman on critically h-connected graphs follows as a corollary.