1702188
New Applications of the Incompressibility Method
The incompressibility method is an elementary yet powerful proof technique based on Kolmogorov complexity [13]. We show that it is particularly suited to obtain average-case computational complexity lower bounds. Such lower bounds have been difficult to obtain in the past by other methods. In this paper we present four new results and also give four new proofs of known results to demonstrate the power and elegance of the new method.
9397376
Inferring a DNA Sequence from Erroneous Copies
Abstract We suggest a novel approach for efficiently reconstructing an original DNA sequence from erroneous copies.
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.
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.
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.
871253
Kolmogorov Complexity Arguments in Combinatorics
Abstract The utility of a Kolmogorov complexity method in combinatorial theory is demonstrated by several examples.
30829488
Vertex pancyclism in claw-free graphs
Abstract In this paper, we show four sufficient conditions for vertex pancyclicity in claw-free graphs. These results improve, respectively, results of Broersma and Veldman, Gould and Jacobson, and Ryjacek. In particular, we prove that if G is a 3-connected claw-free graph such that the vertices of degree 1 of every induced bull have a common neighbor in G then every vertex of G is contained in a cycle of all possible lengths except for four and five. We conjecture that almost all pancyclic claw-free graphs with minimum degree at least three are vertex pancyclic.
3009418
The hamiltonian index of a graph and its branch-bonds
Let $G$ be an undirected and loopless finite graph that is not a path. The minimum $m$ such that the iterated line graph $L^m(G)$ is hamiltonian is called the hamiltonian index of $G,$ denoted by $h(G).$ A reduction method to determine the hamiltonian index of a graph $G$ with $h(G)\geq 2$ is given here. With it we will establish a sharp lower bound and a sharp upper bound for $h(G)$, respectively, which improves some known results of P.A. Catlin et al. [J. Graph Theory 14 (1990)] and H.-J. Lai [Discrete Mathematics 69 (1988)]. Examples show that $h(G)$ may reach all integers between the lower bound and the upper bound.
4489692
Inferring Queue Sizes in Access Networks by Active Measurement
Router queues can impact both round-trip times and throughput. Yet little is publicly known about queue provisioning employed by Internet services providers for the routers that control the access links to home computers. This paper proposes QFind, a black-box measurement technique, as a simple method to approximate the size of the access queue at last mile router. We evaluate QFind through simulation, emulation, and measurement. Although precise access queue results are limited by receiver window sizes and other system events, we find there are distinct difference between DSL and cable access queue sizes.
905924
Resource Monitoring with Globus Toolkit 4
The past few years have seen the Grid rapidly evolving towards a service-oriented computing infrastructure. With the OGSA facilitating this evolution, it is expected that WSRF will be acting as the main an enabling technology to drive the Grid further. Resource monitoring plays a critical role in managing a large-scale Grid system. This paper presents GREMO, a lightweight resource monitor developed with Globus Toolkit 4 (GT4) for monitoring CPU and memory of computing nodes in a Windows and Linux environments.
4909789
On Pancyclic Claw-Free Graphs