Kenneth J. Supowit

Bio: Kenneth J. Supowit is an academic researcher from Princeton University. The author has contributed to research in topics: Circle graph & Outerplanar graph. The author has an hindex of 8, co-authored 11 publications receiving 964 citations.

Finding the optimal variable ordering for binary decision diagrams

Abstract: The ordered binary decision diagram is a canonical representation for Boolean functions, presented by R.E. Bryant (1985) as a compact representation for a broad class of interesting functions derived from circuits. However, the size of the diagram is very sensitive to the choice of ordering on the variables; hence, for some applications, such as differential cascode voltage switch (DCVS) trees, it becomes extremely important to find the ordering leading to the most compact representation. An algorithm for this problem with time complexity O(n/sup 2/3/sup n/) is presented. This represents an improvement over the previous best algorithm. >

Delaunay graphs are almost as good as complete graphs

Abstract: LetS be any set ofN points in the plane and let DT(S) be the graph of the Delaunay triangulation ofS. For all pointsa andb ofS, letd(a, b) be the Euclidean distance froma tob and let DT(a, b) be the length of the shortest path in DT(S) froma tob. We show that there is a constantc (≤((1+?5)/2) ??5.08) independent ofS andN such that % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVy0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaie% aacaWFebGaa8hvaiaa-HcacaWGHbGaaiilaiaadkgacaWFPaaabaGa% amizaiaa-HcacaWGHbGaaiilaiaadkgacaWFPaaaaiabgYda8iaado% gacaGGUaaaaa!4248! $$\frac{{DT(a,b)}}{{d(a,b)}}< c.$$

Finding the Optimal Variable Ordering for Binary Decision Diagrams

Abstract: The ordered binary decision diagram is a canonical representation for Boolean functions, presented by Bryant as a compact representation for a broad class of interesting functions derived from circuits. However, the size of the diagram is very sensitive to the choice of ordering on the variables; hence for some applications, such as Differential Cascode Voltage Switch (DCVS) trees, it becomes extremely important to find the ordering leading to the most compact representation. We present an algorithm for this problem with time complexity O(n/sup 2/3/sup n/), an improvement over the previous best, which required O(n!2/sup n/).

Delaunay graphs are almost as good as complete graphs

Abstract: Let S be any set of N points in the plane and let DT(S) be the graph of the Delaunay triangulation of S. For all points a and b of S, let d(a, b) be the Euclidean distance from a to b and let DT(a, b) be the length of the shortest path in DT(S) from a to b. We show that there is a constant c(≤ 1+√5/2 π ≈ 5.08) independent of S and N such that DT(a, b)/d(a, b) ≪ c.

Recognizing circle graphs in polynomial time

Abstract: The main result of this paper is an 0([V] x [E]) time algorithm for deciding whether a given graph is a circle graph, that is, the intersection graph of a set of chords on a circle. The algorithm utilizes two new graph-theoretic results, regarding necessary induced subgraphs of graphs having neither articulation points nor similar pairs of vertices. Furthermore, as a substep of the algorithm, it is shown how to find in 0([V] x [E]) time a decomposition of a graph into prime graphs, thereby improving on a result of Cunningham.

Voronoi diagrams—a survey of a fundamental geometric data structure

Abstract: Computational geometry is concerned with the design and analysis of algorithms for geometrical problems. In addition, other more practically oriented, areas of computer science— such as computer graphics, computer-aided design, robotics, pattern recognition, and operations research—give rise to problems that inherently are geometrical. This is one reason computational geometry has attracted enormous research interest in the past decade and is a well-established area today. (For standard sources, we refer to the survey article by Lee and Preparata [19841 and to the textbooks by Preparata and Shames [1985] and Edelsbrunner [1987bl.) Readers familiar with the literature of computational geometry will have noticed, especially in the last few years, an increasing interest in a geometrical construct called the Voronoi diagram. This trend can also be observed in combinatorial geometry and in a considerable number of articles in natural science journals that address the Voronoi diagram under different names specific to the respective area. Given some number of points in the plane, their Voronoi diagram divides the plane according to the nearest-neighbor

Graph Coloring Problems

Abstract: Planar Graphs. Graphs on Higher Surfaces. Degrees. Critical Graphs. The Conjectures of Hadwiger and Hajos. Sparse Graphs. Perfect Graphs. Geometric and Combinatorial Graphs. Algorithms. Constructions. Edge Colorings. Orientations and Flows. Chromatic Polynomials. Hypergraphs. Infinite Chromatic Graphs. Miscellaneous Problems. Indexes.

Algorithms for VLSI Physical Design Automation

Abstract: From the Publisher: This work covers all aspects of physical design. The book is a core reference for graduate students and CAD professionals. For students, concept and algorithms are presented in an intuitive manner. For CAD professionals, the material presents a balance of theory and practice. An extensive bibliography is provided which is useful for finding advanced material on a topic. At the end of each chapter, exercises are provided, which range in complexity from simple to research level.

On sparse spanners of weighted graphs

Abstract: Given a graphG, a subgraphG' is at-spanner ofG if, for everyu,v ?V, the distance fromu tov inG' is at mostt times longer than the distance inG. In this paper we give a simple algorithm for constructing sparse spanners for arbitrary weighted graphs. We then apply this algorithm to obtain specific results for planar graphs and Euclidean graphs. We discuss the optimality of our results and present several nearly matching lower bounds.