8308439
From Gene Trees to Species Trees
This paper studies various algorithmic issues in reconstructing a species tree from gene trees under the duplication and the mutation cost model. This is a fundamental problem in computational molecular biology. Our main results are as follows. 
A linear time algorithm is presented for computing all the losses in duplications associated with the least common ancestor mapping from a gene tree to a species tree. This answers a problem raised recently by Eulenstein, Mirkin, and Vingron [J. Comput. Bio., 5 (1998), pp. 135--148]. The complexity of finding an optimal species tree from gene trees is studied. The problem is proved to be NP-hard for the duplication cost and for the mutation cost. Further, the concept of reconciled trees was introduced by Goodman et al. and formalized by Page for visualizing the relationship between gene and species trees. We show that constructing an optimal reconciled tree for gene trees is also NP-hard. Finally, we consider a general reconstruction problem and show it to be NP-hard even for the well-known nearest neighbor interchange distance. A new and efficiently computable metric is defined based on the duplication cost. We show that the problem of finding an optimal species tree from gene trees is NP-hard under this new metric but it can be approximated within factor 2 in polynomial time. Using this approximation result, we propose a heuristic method for finding a species tree from gene trees with uniquely labeled leaves under the duplication cost. Our experimental tests demonstrate that when the number of species is larger than 15 and gene trees are close to each other, our heuristic method is significantly better than the existing program in Page's GeneTree 1.0 that starts the search from a random tree.
9397376
Inferring a DNA Sequence from Erroneous Copies
Abstract We suggest a novel approach for efficiently reconstructing an original DNA sequence from erroneous copies.
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.
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.
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.
33110840
A Level Set Approach for Shape Recovery of Open Contours
In this paper, a geometric deformable model for shape recovery of open contours in noisy images is presented. We use two level set functions to model the open contour and find the end points of the open contour as the intersection of the two level set functions. The evolutions of both level set functions do not depend on the gradient of the images, as in the classical geometric deformable models, but are decided by a region-based band velocity. The band velocity is different from region information introduced by other deformable models which can only be used to find the closed contours in images, it is designed for evolutions of both closed and open contours and particularly unique for contours which are open and do not enclose any region. Prior shape information is also integrated into the contour evolution process, which prevents two level set functions from intersecting at other places than at the contour end points. With the described method open contours can be recovered from noisy images. Successful experiments on several data sets are presented in this paper.
12850359
Recognition of operator motions for real-time assistance using virtual fixtures
Hidden Markov Models (HMMs) are used for automatic segmentation and recognition of user motions. A new algorithm for real-time HMM recognition was developed. The segmentation results are used to provide appropriate assistance in a combined curve following and object avoidance task. This assistance takes the form of a virtual fixture, whose compliance can be altered online. Recognition and assistance experiments were performed using force and position data recorded from a cooperative manipulation system, where a robot and a human operator hold an instrument simultaneously. Recognition accuracy exceeds 90%, even when the users training the HMMs differ from those executing the task. For a task consisting of both path following and avoidance motions, an HMM-based virtual fixture switches the compliance from low to high when the user is trying to move away from the path. The HMM method improves operator performance in comparison with a constant virtual fixture and no virtual fixture.
751784
An Efficient Algorithm for Computing Optimal Discrete Voltage Schedules
We consider the problem of job scheduling on a variable voltage processor with d discrete voltage/speed levels. We give an algorithm which constructs a minimum energy schedule for n jobs in O(dnlogn) time. Previous approaches solve this problem by first computing the optimal continuous solution in O(n 3 ) time and then adjusting the speed to discrete levels. In our approach, the optimal discrete solution is characterized and computed directly from the inputs. We also show that O(n log n) time is required, hence the algorithm is optimal for fixed d.
1687904
PGGA: A predictable and grouped genetic algorithm for job scheduling
This paper presents a predictable and grouped genetic algorithm (PGGA) for job scheduling. The novelty of the PGGA is two-fold: (1) a job workload estimation algorithm is designed to estimate a job workload based on its historical execution records and (2) the divisible load theory (DLT) is employed to predict an optimal fitness value by which the PGGA speeds up the convergence process in searching a large scheduling space. Comparison with traditional scheduling methods, such as first-come-first-serve (FCFS) and random scheduling, heuristics, such as a typical genetic algorithm, Min-Min and Max-Min indicates that the PGGA is more effective and efficient in finding optimal scheduling solutions.
20792301
An Efficient Algorithm for Computing Optimal Discrete Voltage Schedules
We consider the problem of job scheduling on a variable voltage processor with d discrete voltage/speed levels. We give an algorithm which constructs a minimum energy schedule for n jobs in O(dnlog n) time. Previous approaches solve this problem by first computing the optimal continuous solution in O(n3) time and then adjusting the speed to discrete levels. In our approach, the optimal discrete solution is characterized and computed directly from the inputs. We also show that O(nlog n) time is required, hence the algorithm is optimal for fixed d.