Dana Richards

Steiner tree problems

We give a survey up to 1989 on the Steiner tree problems which include the four important cases of euclidean, rectilinear, graphic, phylogenetic and some of their generalizations. We also provide a rather comprehensive and up-to-date bibliography which covers more than three hundred items.

Distributed genetic algorithms for the floorplan design problem

Designing a VLSI floorplan calls for arranging a given set of modules in the plane to minimize the weighted sum of area and wire-length measures. A method of solving the floorplan design problem using distributed genetic algorithms is presented. Distributed genetic algorithms, based on the paleontological theory of punctuated equilibria, offer a conceptual modification to the traditional genetic algorithms. Experimental results on several problem instances demonstrate the efficacy of this method and indicate the advantages of this method over other methods, such as simulated annealing. The method has performed better than the simulated annealing approach, both in terms of the average cost of the solutions found and the best-found solution, in almost all the problem instances tried. >

VLSI median filters

Median filters have been proposed for the analysis of speech data and in image processing to enhance the data by smoothing the signal and removing noise. Many designs for median filters have been suggested in the literature. The author reviews these designs (most originally given as software filters) and compare them on the basis of suitability for implementation in VLSI. Each design is analyzed in terms of area, time delay, and concurrency. Some new designs are given. The 1-D and 2-D cases are discussed, and recursive median filters are also analyzed. >

Modified matrix encoding technique for minimal distortion steganography

It is well known that all information hiding methods that modify the least significant bits introduce distortions into the cover objects. Those distortions have been utilized by steganalysis algorithms to detect that the objects had been modified. It has been proposed that only coefficients whose modification does not introduce large distortions should be used for embedding. In this paper we propose an efficient algorithm for information hiding in the LSBs of JPEG coefficients. Our algorithm uses modified matrix encoding to choose the coefficients whose modifications introduce minimal embedding distortion. We derive the expected value of the embedding distortion as a function of the message length and the probability distribution of the JPEG quantization errors of cover images. Our experiments show close agreement between the theoretical prediction and the actual embedding distortion. Our algorithm can be used for both steganography and fragile watermarking as well as in other applications in which it is necessary to keep the distortion as low as possible.

Fast heuristic algorithms for rectilinear steiner trees

A fundamental problem in circuit design is how to connectn points in the plane, to make them electrically common using the least amount of wire. The tree formed, a Steiner tree, is usually constructed with respect to the rectilinear metric. The problem is known to be NP-complete; an extensive review of proposed heuristics is given. An early algorithm by Hanan is shown to have anO(n logn) time implementation using computational geometry techniques. The algorithm can be modified to do sequential searching inO(n2) total time. However, it is shown that the latter approach runs inO(n3/2) expected time, forn points selected from anm×m grid. Empirical results are presented for problems up to 10,000 points.

Generalizations of broadcasting and gossiping

Three generalizations of broadcasting and gossiping are considered: conference broadcasting in which broadcasting is done by conference calls, partial gossiping in which every gossip must learn at least k pieces of information, and set to set gossiping in which one subset of the members must learn all of the messages of another subset of the members.

Statistical Geolocation of Internet Hosts

Automated geolocation of IP addresses has impor- tant applications to targeted delivery of local news, advertising and other content over the Internet. Previous measurement-based approaches to geolocation employ active probing to measure delays among a set of landmark nodes with known locations. The location of a target IP address can be approximated by that of the nearest landmark, as determined by the delay measurements. To improve geolocation accuracy, a variation of this approach uses multilateration with geographic distance constraints to obtain a continuous location space rather than the discrete set of landmark locations. Since the previous approaches are fundamentally deterministic, they can only provide relatively loose bounds on the true location of an IP address. We develop a statistical geolocation scheme based on applying kernel density estimation to delay measurements among a set of landmarks. An estimate of the target location is then obtained by maximizing the likelihood of the distances from the target to the landmarks, given the measured delays. This is achieved by an algorithm which combines gradient ascent and force-directed methods. We present experimental results on PlanetLab to demonstrate the superior accuracy of the proposed geolocation scheme compared to previous methods. Index Terms—Geolocation, delay measurements, kernel den- sity estimation, maximum likelihood estimation, force-directed algorithm.

Genetic Algorithms and Punctuated Equilibria in VLSI

The distributed genetic algorithm presented has a population structure that allows the introduction of “ecological opportunity” [Wrig 82] in the evolutionary process in a manner motivated by the macro-evolutionary theory of Eldredge and Gould [Eldr 72]. The K-partition problem is selected from the domain of VLSI design and empirical results are presented to show the advantage derived from the population structure.

An optimal Steiner tree algorithm for a net whose terminals lie on the perimeter of a rectangle

Given a set of input points, the rectilinear Steiner tree problem is to find a minimal-length tree consisting of vertical and horizontal line segments that connects the input points, where it is possible to add new points to minimize the length of the tree. The restricted Steiner tree problem in which all the input points lie on the boundary of a rectangle frequently occurs in VLSI physical design. Since the fastest published algorithm is cubic in the size of the point set, VLSI designers have been forced to use heuristic approximations to the length of the Steiner tree for this problem. A simple, practical, linear-time exact algorithm for finding the Steiner tree for points lying on the boundary of a rectangle which obviates the need for some heuristic algorithms in VLSI design is presented. The analysis of the algorithm is based on the use of a tie-breaking rule that should prove useful for other Steiner tree problems. >

Floorplan design using distributed genetic algorithms

A distributed algorithm for solving the floorplan design problem, called a genetic algorithm with punctuated equilibria (GAPE), is presented. Implementation details and the results of empirical studies are presented. The experiments have demonstrated that GAPE performs consistently better than a recently published simulated annealing approach, with respect to both the average cost of the solutions found and the best solution found.<<ETX>>