Jon Bentley - Academia.edu (original) (raw)

Papers by Jon Bentley

Lecture Notes in Computer Science, 1981

Kung [!979b] has recently enunciated a set of princip!es for designing algorithms for ;mpiementat... more Kung [!979b] has recently enunciated a set of princip!es for designing algorithms for ;mpiementation in Very Large Scare Integrated circuitry (VLSI), and supported these principles by displaying a number of particular algorithms based on various "communication geometries". In this ...

The objective of this note is to show that the problem of recognizing whether or not two graphs a... more The objective of this note is to show that the problem of recognizing whether or not two graphs are isomorphic and the problem of counting all isomorphisms between the graphs are polynomial-time equivalent. Since no NP-complete problem is known for which checking and counting are polynomial-time reducible to each other this result lends evidence to the conjecture that graph isomorphism is not ‘NPcomplete [ 11, [3]. Given two undirected graphs G1(V1, El), G,(Vz, &) with vertex sets Vr, V2 and edge sets El, Ez we say that Gr is isomorphic to Gz, Gi z Gz if there exists a bijection u: V1 + r/2 such thal: (x, y)E El if and only if (ox, uy) E Ez for all X, y E Vr . A permutation p of the vertices V of G(V, E) is called an automorphism if for every (x, y) E E also @x, py) E E. The set of all automorphisms of G forms the automorphism group aut G. The orbits of the vertices V under the action of aut G mtie up the automorphism partition 3) of G. Two nodes X, y E V belong to the same cell of 9 iff there exists an element p E aut G such that p;w =y. We are concerned with the time required to solve certain graph-theoretical problems. A problem Pi is polynomially reducible to a problem pZ, P1 ap pZ, if the existence of a polynornial algorithm for Ps implies the existence of a polynomial algorithm for Pi. Two problems are po’:nomially equivalent if each is polynomially reducible to the other. The following graph problems will be examined:

Hawaii International Conference on System Sciences, Jan 3, 2005

Lecture Notes in Computer Science, 2004

Experimental Algorithms, 2006

Algorithmic experiments come in all sizes. A jumbo testbed for the Traveling Salesman Problem, fo... more Algorithmic experiments come in all sizes. A jumbo testbed for the Traveling Salesman Problem, for instance, can take years to build, and additional years can be spent designing and running insightful experiments. This talk concentrates on tiny algorithmic experiments that can be conducted in a few minutes. Such experiments include parameter estimation, hypothesis testing, determining functional forms, and conducting horse races. This talk also describes how tiny Math, Science and Engineering (MSE) can be done in one’s head or on the back of the proverbial envelope, and shows how to apply it to professional problems and problems in everyday life.

Computers & Chemistry, 1987

... A PROGRAM FOR PHOTOTYPESETTING CHEMICAL STRUCTURE DIAGRAMS JON L. BENTLEY, LmN W. JELINSKI an... more ... A PROGRAM FOR PHOTOTYPESETTING CHEMICAL STRUCTURE DIAGRAMS JON L. BENTLEY, LmN W. JELINSKI and BRIAN W. KERNIGHAN ... sofware is available for three-dimensional molecular graphics, especially for biomolecules (Diamond, 1984; Rowlett, ...

IEEE Computer - COMPUTER, 1979

Abstract : The field of algorithm design is concerned with the development of efficient methods f... more Abstract : The field of algorithm design is concerned with the development of efficient methods for solving computational problems. Although the field traces its roots to theoretical computer science, recent algorithmic advances have drastically reduced the costs of real computations. For this reason it is important that anyone involved with computing have at least a cursory knowledge of the area. This paper surveys the field of algorithm design in two ways: first by the study of a few problems in detail, and then by a systematic view of the field. The orientation of this paper is towards the practitioner of computing (in either software or hardware); the goals of the paper are to provide both an understanding of the field and a feeling for what it can do for me. (Author)

Acta Informatica, 1980

... 3.4 for the case N--9. In that figure the bold vertical lines represent block boundaries and ... more ... 3.4 for the case N--9. In that figure the bold vertical lines represent block boundaries and the regular vertical lines represent unit boundaries; each horizontal line represents a 1-range structure. Level 1 Level 2 ... Efficient Worst-Case Data Structures for Range Searching 163 ...

… -Mellon Univ., Pittsburgh, PA. …, 1980

This paper presents a statistical study of the components on VLSI chips. We examine the size and ... more This paper presents a statistical study of the components on VLSI chips. We examine the size and shape of components, and their placement over the chip area. The data is useful for building efficient VLSI design tools: the form of the distribution shows that some simple strategies ...

We investigate problems and applications associated with computing the empirical cumulative distr... more We investigate problems and applications associated with computing the empirical cumulative distribution function of N points in kdimensional space and employ a multidimensional divide-and-conquer technique that gives rise to a compact data structure for geometric and statistical search. problems. We are able to show how to compute a large number of important statistical quantities much faster than was previously possible.

20th Annual Symposium on Foundations of Computer Science (sfcs 1979), 1979

ACM SIGACT News, 1980

The approximate complexity of divide-and-conquer algorithms is often described by recurrence rela... more The approximate complexity of divide-and-conquer algorithms is often described by recurrence relations of the formT(n) = kT(n/c) + f(n).The only well-defined method currently used for solving such recurrences consists of solution tables for fixed functions f and varying k and c. In this note we describe a unifying method for solving these recurrences that is both general in applicability and easy to apply. This method is appropriate both as a classroom technique and as a tool for practicing algorithm designers.

Proceedings of the eighth annual ACM symposium on Theory of computing - STOC '76, 1976