39390325
Average-Case Complexity of Shellsort
We prove a general lower bound on the average-case complexity of Shellsort: the average number of data-movements (and comparisons) made by a p-pass Shellsort for any incremental sequence is Ω(pn 1+1/p ) for every p. The proof method is an incompressibility argument based on Kolmogorov complexity. Using similar techniques, the average-case complexity of several other sorting algorithms is analyzed.
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.
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.
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.
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.
8001978
MAPBOT: a Web based map information retrieval system
Abstract Many types of information are geographically referenced and interactive maps provide a natural user interface to such data. However, map presentation in geographical information systems and on the Web is closed related to traditional cartography and provides a very limited interactive experience. In this paper, we present MAPBOT, an interactive Web based map information retrieval system in which Web users can easily and efficiently search geographical information with the assistance of a user interface agent (UIA). Each kind of map feature such as a building or a motorway works as an agent called a Maplet. Each Maplet has a user interface level to assist the user to find information of interest and a graphic display level that controls the presence and the appearance of the feature on the map. The semantic relationships of Maplets are defined in an Ontology Repository provided by the system which is used by the UIA to assist a user to semantically and efficiently search map information interested. An Ontology Editor with a graphic user interface has been implemented to update the Ontology Repository. Visualization on the client is based on Scalable Vector Graphics which provides a high quality Web map.
10855228
Generating Symbolic Interpolants for Scattered Data with Normal Vectors
Algorithms to generate a triangular or a quadrilateral interpolant with G1-continuity are given in this paper for arbitrary scattered data with associated normal vectors over a prescribed triangular or quadrilateral decomposition. The interpolants are constructed with a general method to generate surfaces from moving Bézier curves under geometric constraints. With the algorithm, we may obtain interpolants in complete symbolic parametric forms, leading to a fast computation of the interpolant. A dynamic interpolation solid modelling software package DISM is implemented based on the algorithm which can be used to generate and manipulate solid objects in an interactive way.
10085490
Circumferences of regular claw-free graphs
A known result obtained independently by Fan and Jung is that every 3-connected k-regular graph on n vertices contains a cycle of length at least min{3k,n}. This raises the question of how much can be said about the circumferences of 3-connected k-regular claw-free graphs. In this paper, we show that every 3-connected k-regular claw-free graph on n vertices contains a cycle of length at least min{6k-17,n}.
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.