1356
New applications of the incompressibility method: Part II
Abstract The incompressibility method is an elementary yet powerful proof technique. It has been used successfully in many areas (Li and Vitanyi, An Introduction to Kolmogorov Complexity and its Applications, Springer, New york, 1997). To further demonstrate its power and elegance we exhibit new simple proofs using the incompressibility method.
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.
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.
10964754
SETRED: Self-training with Editing
Self-training is a semi-supervised learning algorithm in which a learner keeps on labeling unlabeled examples and retraining itself on an enlarged labeled training set. Since the self-training process may erroneously label some unlabeled examples, sometimes the learned hypothesis does not perform well. In this paper, a new algorithm named Setred is proposed, which utilizes a specific data editing method to identify and remove the mislabeled examples from the self-labeled data. In detail, in each iteration of the self-training process, the local cut edge weight statistic is used to help estimate whether a newly labeled example is reliable or not, and only the reliable self-labeled examples are used to enlarge the labeled training set. Experiments show that the introduction of data editing is beneficial, and the learned hypotheses of Setred outperform those learned by the standard self-training algorithm.
44742126
A New Association Rules Mining Algorithms Based on Directed Itemsets Graph
In this paper, we introduced a new data structure called DISG (Directed itemsets graph) in which the information of frequent itemsets was stored. Based on it, a new algorithm called DBDG (DFS Based -DISG) was developed by using depth first searching strategy. At last we performed a experiment on a real dataset to test the run time of DBDG. The experiment showd that it was efficient for mining dense datasets.
14969576
Semi-Supervised Regression with Co-Training
In many practical machine learning and data mining applications, unlabeled training examples are readily available but labeled ones are fairly expensive to obtain. Therefore, semi-supervised learning algorithms such as co-training have attracted much attention. Previous research mainly focuses on semi-supervised classification. In this paper, a co-training style semi-supervised regression algorithm, i.e. COREG, is proposed. This algorithm uses two k-nearest neighbor regressors with different distance metrics, each of which labels the unlabeled data for the other regressor where the labeling confidence is estimated through consulting the influence of the labeling of unlabeled examples on the labeled ones. Experiments show that COREG can effectively exploit unlabeled data to improve regression estimates.
6156793
Optimum Robot Control for 3D Virtual Fixture in Constrained ENT Surgery
In ENT surgery, the operating volume is very limited. This is especially true in sinus surgery, when the instrument passes through the sinus cavity to reach the pathological area. The sinus bones impose geometric constraints on the work volume. During the surgery, the surgeon needs to take care of the motion of the instrument tip to accomplish some delicate procedure; meanwhile he/she needs to avoid hitting anatomic constraints. In this paper, we present a method to assist the path following task in a constrained area. We project instrument tip motion, boundary information on the joint displacement via robot kinematics, and then use a constrained quadratic optimization algorithm to compute the optimal set of corresponding joint displacements. In the preliminary study, we show that the optimization constrained control can avoid collision with geometric constraints on the work volume, while keeping the precision of the tool motion.
1974621
Engineering high-performance legacy codes as CORBA components for problem-solving environments
This paper describes techniques used to leverage high-performance legacy codes as CORBA components to a distributed problem-solving environment. It first briefly introduces the software architecture adopted by the environment. Then it presents a CORBA oriented wrapper generator (COWG) which can be used to automatically wrap high-performance legacy codes as CORBA components. Two legacy codes have been wrapped with COWG. One is an MPI-based molecular dynamic simulation (MDS) code, the other is a finite element-based computational fluid dynamics (CFD) code for simulating incompressible Navier-Stokes flows. Performance comparisons between runs of the MDS CORBA component and the original MDS legacy code on a cluster of workstations and on a parallel computer are also presented. Wrapped as CORBA components, these legacy codes can be reused in a distributed computing environment. The first case shows that high-performance can be maintained with the wrapped MDS component. The second case shows that a Web 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 high-performance computing environment using a cluster of workstations or a parallel computer.