45579896
Full Minimal Steiner Trees on Lattice Sets
Given a finite set of points P in the Euclidean plane, the Steiner problem asks us to constuct a shortest possible network interconnecting P. Such a network is known as a minimal Steiner tree. The Steiner problem is an intrinsically difficult one, having been shown to be NP-hard [7]; however, it often proves far more tractable if we restrict our attention to points in special geometric configurations. One such restriction which has generated considerable interest is that of finding minimal Steiner trees for nice sets of integer lattice points. The first significant result in this direction was that of Chung and Graham [4], which, in effect, precisely characterized the minimal Steiner trees for any horizontal 2_n array of integer lattice points. In 1989, Chung et al. [3] examined a related problem, which they described as the Checkerboard Problem. They asked how to find a minimal Steiner tree for an n_n square lattice, that is, a collection of n_n points arranged in a regular lattice of unit squares like the corners of the cells of article no. TA962752
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.
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
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.
10580031
A polynomial time algorithm for rectilinear Steiner trees with terminals constrained to curves
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.
53234593
Actra-a multitasking/multiprocessing smalltalk
41519577
Anonymizing Tables
We consider the problem of releasing tables from a relational database containing personal records, while ensuring individual privacy and maintaining data integrity to the extent possible. One of the techniques proposed in the literature is k-anonymization. A release is considered k-anonymous if the information for each person contained in the release cannot be distinguished from at least k–1 other persons whose information also appears in the release. In the k-Anonymityproblem the objective is to minimally suppress cells in the table so as to ensure that the released version is k-anonymous. We show that the k-Anonymity problem is NP-hard even when the attribute values are ternary. On the positive side, we provide an O(k)-approximation algorithm for the problem. This improves upon the previous best-known O(klog k)-approximation. We also give improved positive results for the interesting cases with specific values of k — in particular, we give a 1.5-approximation algorithm for the special case of 2-Anonymity, and a 2-approximation algorithm for 3-Anonymity.
1329133
Model driven development: the case for domain oriented programming
In this paper, we offer an alternative vision for domain driven development (3D). Our approach is model driven and emphasizes the use of generic and specific domain oriented programming (DOP) languages. DOP uses strong specific languages, which directly incorporate domain abstractions, to allow knowledgeable end users to succinctly express their needs in the form of an application computation. Most domain driven development (3D) approaches and techniques are targeted at professional software engineers and computer scientists. We argue that DOP offers a promising alternative. Specifically we are focused on empowering application developers who have extensive domain knowledge as well as sound foundations in their professions, but may not be formally trained in computer science.We provide a brief survey of DOP experiences, which show that many of the best practices such as patterns, refactoring, and pair programming are naturally and ideally practiced in a Model Driven Development (MDD) setting. We compare and contrast our DOP with other popular approaches, most of which are deeply rooted in the OO community.Finally we highlight challenges and opportunities in the design and implementation of such languages.
15059814
Caching queues in memory buffers
Motivated by the need for maintaining multiple, large queues of data in modern high-performance systems, we study the problem of caching queues in memory under the following simple, but widely applicable, model. At each clock-tick, any number of data items may enter the various queues, while data-items are consumed from the heads of the queues. Since the number of unconsumed items may exceed memory buffer size, some items in the queues need to be spilled to secondary storage and later moved back into memory for consumption. We provide online queue-caching algorithms under a number of interesting cost models.