8044870
The Steiner ratio conjecture for six points
The Steiner problem is to find a shortest network (tree) S in the plane R 2 connecting a given set X of n points. Let T be a shortest tree connecting the points of X and with vertices only at these points. T is called a minimal spanning tree. Let L S and L T denote the lengths of S and T, respectively, and let ρ=L S /L T . ρ is called the Steiner ratio. In this paper one proves the Steiner ratio conjecture for six points. One uses a variational approach
45241819
Minimum Networks in Uniform Orientation Metrics
In this paper we use the variational method to systematically study properties of minimum networks connecting any given set of points (called terminals) in a $\lambda$-plane, in which all lines are in $\lambda$ uniform orientations $i\pi /\lambda\ (0\le i<\lambda )$. We prove a number of angle conditions for Steiner minimum $\lambda$-trees, which are similar to the ones in the Euclidean case. In particular, we show that there exists a Steiner minimum $\lambda$-tree whose minimum angles at Steiner points are $\lfloor 2\lambda /3\rfloor\pi /\lambda$ and whose maximum angles are $\lceil 2\lambda /3\rceil\pi /\lambda$. We also investigate the assignment of nonstraight edges and unequal angles in Steiner minimum $\lambda$-trees, and we prove that there exists a Steiner minimum $\lambda$-tree in which every full component has at most one nonstraight edge. From these properties we are able to devise a number of finite methods for constructing Steiner minimum $\lambda$-trees. One of these methods is based on using algorithms for finding graphical Steiner minimum trees, and the other uses a generalization of the method of Melzak for Euclidean Steiner trees.
22841183
Graham's problem on shortest networks for points on a circle
Suppose a configurationX consists ofn points lying on a circle of radiusr. If at most one of the edges joining neighboring points has length strictly greater thanr, then the Steiner treeS consists of all these edges with a longest edge removed. In order to showS is, in fact, just the minimal spanning treeT, a variational approach is used to show the Steiner ratio for this configuration is at least one and equals one only ifS andT coincide. The variational approach greatly reduces the number of possible Steiner trees that need to be considered.
5902879
Achieving anonymity via clustering
Publishing data for analysis from a table containing personal records, while maintaining individual privacy, is a problem of increasing importance today. The traditional approach of de-identifying records is to remove identifying fields such as social security number, name etc. However, recent research has shown that a large fraction of the US population can be identified using non-key attributes (called quasi-identifiers) such as date of birth, gender, and zip code [15]. Sweeney [16] proposed the k-anonymity model for privacy where non-key attributes that leak information are suppressed or generalized so that, for every record in the modified table, there are at least k−1 other records having exactly the same values for quasi-identifiers. We propose a new method for anonymizing data records, where quasi-identifiers of data records are first clustered and then cluster centers are published. To ensure privacy of the data records, we impose the constraint that each cluster must contain no fewer than a pre-specified number of data records. This technique is more general since we have a much larger choice for cluster centers than k-Anonymity. In many cases, it lets us release a lot more information without compromising privacy. We also provide constant-factor approximation algorithms to come up with such a clustering. This is the first set of algorithms for the anonymization problem where the performance is independent of the anonymity parameter k. We further observe that a few outlier points can significantly increase the cost of anonymization. Hence, we extend our algorithms to allow an ε fraction of points to remain unclustered, i.e., deleted from the anonymized publication. Thus, by not releasing a small fraction of the database records, we can ensure that the data published for analysis has less distortion and hence is more useful. Our approximation algorithms for new clustering objectives are of independent interest and could be applicable in other clustering scenarios as well.
208947786
STREAM: The Stanford Stream Data Manager
16614452
Refactoring as Meta Programming
The importance of refractoring in the development of object oriented programming and management of the evolution of large software systems is discussed. Refractoring is a process that takes an existing program and improves it by transforming the program into a new program that is an improved version of initial program. A major refractoring is always best done as a pair programming activity to reduce risk and manage the complexity. It is stated that while refractoring tools address programs, they seldom address persistent information associated with the current and transformed program.
3170175
Using Objects To Design and Build Radar ESM Systems
This paper describes the application of object-oriented programming to the design of a multiprocessor ESM testbed. The ESM testbed uses an object-oriented development environment which integrates Smalltalk and C language tools with the Harmony real-time operating system in a shared memory multiprocessor. All development for an application is done using personal computers which are themselves processors in the real-time testbed. We first discuss two aspects of the ESM testbed: a framework for investigating ESM signal processing algorithms based on an object-oriented emitter database and blackboard objects which implement probabilistic reasoning; and an object-oriented ESM simulation environment which illustrates the use of object-oriented techniques for the development of complex real-time systems. In the second part of the paper we describe our software engineering approach and tools. Throughout the paper, the role played by object-oriented programming in the design of hybrid multiprocessors is highlighted.
32027945
The Deplorable State of Class Libraries
Various efforts made to redesign and implement important class libraries are discussed. ClassLibs.com is a company dedicated to producing well-engineered quality class libraries and associated compliance test suites with related services. It also provides support, training and customization as additional for fee services. The major vendors have licensed the libraries ensuring that ClassLilbs.com will be able to continue to produce high quality libraries.