W. E. Donath

Bio: W. E. Donath is an academic researcher from IBM. The author has contributed to research in topics: Upper and lower bounds & Interface (computing). The author has an hindex of 4, co-authored 5 publications receiving 912 citations.

Lower bounds for the partitioning of graphs

Abstract: Let a k-partition of a graph be a division of the vertices into k disjoint subsets containing m1 ≥ m2,..., ≥mk vertices. Let Ec be the number of edges whose two vertices belong to different subsets. Let λ1 ≥ λ2, ..., ≥ λk, be the k largest eigenvalues of a matrix, which is the sum of the adjacency matrix of the graph plus any diagonal matrix U such that the suomf all the elements of the sum matrix is zero. Then Ec ≥ 1/2Σr=1k-mrλr. A theorem is given that shows the effect of the maximum degree of any node being limited, and it is also shown that the right-hand side is a concave function of U.C omputational studies are madoef the ratio of upper bound to lower bound for the two-partition of a number of random graphs having up to 100 nodes.

Wire length distribution for placements of computer logic

Abstract: It is shown from simple theoretical considerations that the distribution fk of wire lengths for a good two-dimensional placement on a square Manhattan grid should be of the form fk = g/kγ (1 ≤ k ≤ L) and fk ≅ 0 (k > L), where γ is related to the Rent partitioning exponent p by the equation 2p + γ ≅ 3. Three placements were investigated and the distribution functions for wire length were found to follow the above relationships.

Equivalence of memory to Random Logic

Abstract: A model of the design process for computer logic is used to estimate the number of bits of memory required to replace a so-called "random logic" circuit. The model can also be used to compare the respective time delays of array logic and random logic.

Algorithm and average-value bounds for assignment problems

Abstract: A new suboptimal intermediate-speed algorithm which use n2 In n steps is developed for the assignment problem Upper and lower bounds are derived, using this algorithm and other methods, for the average values of three classes of n × n assignment problems: 1 When the elements of the matrix are random numbers uniformly distributed over the range 0 to 1, the average optimal value is smaller than 237 and larger than 1 for problems with large n Experimentally the value is about 16 2 When the elements of the matrix are random numbers such that the probability of being less than x is xk+1 (k ≠ 0), asymptotic expressions for the upper and lower bounds of the average optimal value are Cknk/(k+1) and Ck[(k+1)/k]nk/(k+1) respectively 3 When each column of the matrix is a random permutation of the integers 1 to n, asymptotic upper and lower bounds are 237n and 154n, respectively Experimentally the value is about 18n

Stand-alone wiring program for Josephson logic

Abstract: This paper describes a channel routing wiring program and its interface to the user. Of particular interest are its interface facilities, which permit manual update of the routing, pre-routing, and incremental routing. A hierarchical organization of the logic is feasible, which permits moving of complex entities, such as latches, adders and others, as complete entities. The internal wiring of these entities could either be done manually and be fixed before layout, which would be desirable when the wiring was used as a delay line, or could be left to the wiring program, which would route them more flexibly. The features above are made possible by the special-interface organization used here. In this interface the pins on the devices can be directly addressed, relatively addressed, and indirectly addressed; a simple macrocompiler permits the hierarchical organization of the data.

Data Mining: Concepts and Techniques

Abstract: The increasing volume of data in modern business and science calls for more complex and sophisticated tools. Although advances in data mining technology have made extensive data collection much easier, it's still always evolving and there is a constant need for new techniques and tools that can help us transform this data into useful information and knowledge. Since the previous edition's publication, great advances have been made in the field of data mining. Not only does the third of edition of Data Mining: Concepts and Techniques continue the tradition of equipping you with an understanding and application of the theory and practice of discovering patterns hidden in large data sets, it also focuses on new, important topics in the field: data warehouses and data cube technology, mining stream, mining social networks, and mining spatial, multimedia and other complex data. Each chapter is a stand-alone guide to a critical topic, presenting proven algorithms and sound implementations ready to be used directly or with strategic modification against live data. This is the resource you need if you want to apply today's most powerful data mining techniques to meet real business challenges. * Presents dozens of algorithms and implementation examples, all in pseudo-code and suitable for use in real-world, large-scale data mining projects. * Addresses advanced topics such as mining object-relational databases, spatial databases, multimedia databases, time-series databases, text databases, the World Wide Web, and applications in several fields. *Provides a comprehensive, practical look at the concepts and techniques you need to get the most out of real business data

Normalized cuts and image segmentation

Abstract: We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We applied this approach to segmenting static images, as well as motion sequences, and found the results to be very encouraging.

Normalized cuts and image segmentation

Abstract: We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We have applied this approach to segmenting static images and found results very encouraging.

A tutorial on spectral clustering

Abstract: In recent years, spectral clustering has become one of the most popular modern clustering algorithms. It is simple to implement, can be solved efficiently by standard linear algebra software, and very often outperforms traditional clustering algorithms such as the k-means algorithm. On the first glance spectral clustering appears slightly mysterious, and it is not obvious to see why it works at all and what it really does. The goal of this tutorial is to give some intuition on those questions. We describe different graph Laplacians and their basic properties, present the most common spectral clustering algorithms, and derive those algorithms from scratch by several different approaches. Advantages and disadvantages of the different spectral clustering algorithms are discussed.