16380533
On the Approximation of Shortest Common Supersequences and Longest Common Subsequences
Finding shortest common supersequences (SCS) and longest common subsequences (LCS) for a given set of sequences are two well-known NP-hard problems. They have important applications in many areas including computational molecular biology (e.g., sequence alignment), data compression, planning, text editing (e.g., diff function in UNIX), etc. [1, 6, 7, 8, 10, 17, 19, 22, 23, 24, 26, 27]. The question of approximating SCS and LCS was raised 15 years ago in [19]. A lot of fruitless effort has been spent in searching for such approximation algorithms.
14168735
Inductive Reasoning and Kolmogorov Complexity
Abstract Reasoning to obtain the “truth” about reality, from external data, is an important, controversial, and complicated issue in man's effort to understand nature. (Yet, today, we try to make machines do this.) There have been old useful principles, new exciting models, and intricate theories scattered in vastly different areas including philosophy of science, statistics, computer science, and psychology. We focus on inductive reasoning in correspondence with ideas of R. J. Solomonoff. While his proposals result in perfect procedures, they involve the noncomputable notion of Kolmogorov complexity. In this paper we develop the thesis that Solomonoff's method is fundamental in the sense that many other induction principles can be viewed as particular ways to obtain computable approximations to it. We demonstrate this explicitly in the cases of Gold's paradigm for inductive inference, Rissanen's minimum description length (MDL) principle, Fisher's maximum likelihood principle, and Jaynes' maximum entropy principle. We present several new theorems and derivations to this effect. We also delimit what can be learned and what cannot be learned in terms of Kolmogorov complexity, and we describe an experiment in machine learning of handwritten characters. We also give an application of Kolmogorov complexity in Valiant style learning, where we want to learn a concept probably approximately correct in feasible time and examples.
43310555
Twist-Rotation Transformations of Binary Trees and Arithmetic Expressions
The paper studies the computational complexity and efficient algorithms for the twist?rotation transformations of binary trees, which is equivalent to the transformation of arithmetic expressions over an associative and commutative binary operation. The main results are (1) a full binary tree with n labeled leaves can be transformed into any other in at most 3nlogn+2n twist and rotation operations, (2) deciding the twist?rotation distance between two binary trees is NP-complete, and (3) the twist?rotation transformation can be approximated with ratio 6logn+4 in polynomial time for full binary trees with n uniquely labeled leaves.
9397376
Inferring a DNA Sequence from Erroneous Copies
Abstract We suggest a novel approach for efficiently reconstructing an original DNA sequence from erroneous copies.
871253
Kolmogorov Complexity Arguments in Combinatorics
Abstract The utility of a Kolmogorov complexity method in combinatorial theory is demonstrated by several examples.
553776
Linear approximation of shortest superstrings
We consider the following problem: given a collection of strings s1, ••• ,sm, find the shortest string s such that each s; appears as a substring (a consecutive block) of s. Although this problem is known to be NP-hard, a simple greedy procedure appears to do quite well and is routinely used in DNA sequencing and data compression practice, namely: repeatedly merge the pair of (distinct) strings with maximum overlap until only one string remains. Let n denote the A. Blum was supported by a National Science Foundation (NSF) Graduate Fellowship. Part of this work was done while A. Blum was visiting AT & T Bell Labs. T. Jiang was supported in part by a grant from SERB, McMaster University and NSERC Operating Grant OGP0046613. M. Li was supported in part by the NSERC Operating Grants OGP0036747 and OGP0046506. J. Tromp was supported in part by NSERC Grant OGP0036747 while the author was visiting at the University of Waterloo. Authors' present addresses: A. Blum, School of Computer Science, Carnegie-Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213. E-mail: avrim@theory.cs.cmu.edu; T. Jiang, Department of Computer Science, McMaster University, Hamilton, Ont., Canada L8S 4Kl. E-mail: jiang<Q•maccs. mcmaster.ca; M. Li, Department of Computer Science, University of Waterloo, Waterloo, Ont., Canada N3L 30 I. E-mail: mli@watmath.waterloo.edu; J. Tromp, CWI, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands. E-mail: tromp@cwi.nl; M. Yannakakis, Room 2C-319, AT&T Bell Labs, 600 Mountain Avenue, Murray Hill, NJ 07974. E-mail: mihalis@research.att.com. Permission to copy without fee all or part of this material is granted provided that the copies arc not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. © 1994 ACM 0004-5411/94/0700-0630$03.50 Journal of the Association for Computing Machinery, Vol. 41, No. 4, July 1994, pages 630-647. Linear Approximation of Shortest Superstrings 631 length of the optimal superstring. A common conjecture states that the above greedy procedure produces a superstring of length O(n) (in fact, 2n), yet the only previous nontrivial bound known for any polynomial-time algorithm is a recent O(n log n) result. We show that the greedy algorithm does in fact achieve a constant factor approximation, proving an upper bound of 4n. Furthermore, we present a simple modified version of the greedy algorithm that we show produces a superstring of length at most 3n. We also show the superstring problem to be MAX SNP-hard, which implies that a polynomial-time approximation scheme for this problem is unlikely.
16510993
Rational quadratic approximation to real algebraic curves
An algorithm is proposed to give a global approximation to an implicit real plane algebraic curve with rational quadratic B-splines. The algorithm consists of three steps: curve segmentation, segment approximation and curve tracing. The curve is first divided into so-called triangle convex segments. Then each segment is approximated with several rational quadratic Bezier curves. At last, the curve segments are connected into several maximal branches and each branch is represented by a B-spline curve resulting in a C/sup 1/ global parameterization for the curve branch. Due to the detailed geometric analysis, high accuracy of approximation may be achieved with a small number of quadratic segments. The final approximation based on quadratic spline curves keeps many important geometric features and gives a refined topological structure of the original curve.
45496659
Migrating legacy codes to distributed computing environments: a CORBA approach
Abstract This paper describes techniques used to migrate legacy codes as CORBA components to a distributed problem solving environment (PSE). It presents a CORBA compliant wrapper generator (WG), which can be used to automatically wrap high performance legacy codes in C or Fortran as CORBA components for reuse in the PSE. Using WG, a finite element based computational fluid dynamics (CFD) legacy code has been wrapped as a CORBA component and a PSE for simulating incompressible Navier-Stokes flows has been implemented. A user can submit a task to the wrapped CFD component through a Web page without knowing the exact implementation of the component. In this way, a user's desktop computing environment can be extended to a computing environment using a cluster of workstations or a parallel computer.
12322208
Gemini: Probabilistic Routing Algorithm in Structured P2P Overlay
In this paper, we propose a new structured overlay protocol, which is more efficient and scalable than previous ones. We call it Gemini, because its routing table consists of two parts, one containing nodes with common prefix and the other containing nodes with common suffix. Gemini routes messages to their destinations in just 2 hops, with a very high probability of 0.99. When running in a p2p network of 5,000,000 peers, each Gemini node consumes only 6 messages per second for maintenance. This cost, as well as routing table size, varies as a \(O {\sqrt{N}}\) function to the overlay scale, so Gemini can also run well in an even larger environment.
8200318
A Web Service for Exchanging Procedural CAD Models Between Heterogeneous CAD Systems
It is a challenging issue to exchange procedural CAD models between heterogeneous CAD systems. In this paper, we extend the synchronized collaborative design environment among heterogeneous CAD systems, which we developed previously, to a Web services based platform for exchange of procedural CAD models between heterogeneous CAD systems. First, the real-time exchange of one single operation is extended to the exchange of a complete procedural CAD model between heterogeneous CAD systems. Second, Web services technology is adopted to encapsulate the procedural CAD model exchange functions to a standard interface, which is then released on the Internet and can be easily used by remote developers in their windows applications, Web applications, and so on. Finally, a Web service for exchange of procedural CAD models between SolidWorks and Autodesk Mechanical Desktop is realized.
979117
The software architecture of a distributed problem-solving environment
This paper describes the functionality and software architecture of a generic problem-solving environment (PSE) for collaborative computational science and engineering. A PSE is designed to provide transparent access to heterogeneous distributed computing resources, and is intended to enhance research productivity by making it easier to construct, run, and analyze the results of computer simulations. Although implementation details are not discussed in depth, the role of software technologies such as CORBA, Java, and XML is outlined. An XML-based component model is presented. The main features of a Visual Component Composition Environment for software development, and an Intelligent Resource Management System for scheduling components, are described. Some prototype implementations of PSE applications are also presented. Copyright 2000 John Wiley & Sons, Ltd.