15731393
Fixed topology alignment with recombination
Abstract In this paper, we study a new version of multiple sequence alignment, fixed topology alignment with recombination. We show that it cannot be approximated within any constant ratio unless P=NP. For a restricted version, we show that the problem is MAX-SNP-hard. This implies that there is no PTAS for this version unless P=NP. We also propose approximation algorithms for a special case, where each internal node has at most one recombination child and any two merge paths for different recombination nodes do not share any common node.
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.
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.
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.
13977817
Analysis of multi-hop traffic grooming in WDM mesh networks
Traffic grooming is an essential functionality of WDM optical networks to provision multi-granularity subwave-length connections. Depending on the number of lightpaths allowed in a connection route, traffic grooming can be classified as single-hop traffic grooming (SH-TG) and multi-hop traffic grooming (MH-TG). MH-TG is more general and resource-efficient than SH-TG, because it allows connections from different source-destination pairs to share the bandwidth of a lightpath. In this paper, we propose a MH-TG algorithm, namely the fixed-order multi-hop (FOMH) grooming algorithm, based on the fixed-alternate routing approach. We introduce the grooming node selection (GNS) problem in MH-TG and propose three grooming policies, namely exhaustive sequential (ES), limited-hop sequential (LHS) and load sharing (LS) policies, to address the GNS problem. Given that the analysis of MH-TG is a relatively unexplored area, we propose an analytical model to evaluate the blocking performance of MH-TG using FOMH and the LS grooming policy. To address the multi-layered routing and multi-rate connection characteristics of traffic grooming, we introduce a novel multi-level decomposition approach in our analytical model which decomposes traffic at four different levels, namely alternate path, connection route, lightpath and link levels. The Erlang fixed-point approximation method is used to solve the analytical model. Numerical results show that analytical results matches well with simulation results. We also evaluate the effect of the grooming policies, the number of virtual hops (lightpaths) within a connection route and the number of alternate paths on the performance of the grooming algorithm.
32860736
Nonrigid motion recovery for 3D surfaces
We present a spline-based nonrigid motion and point correspondence recovery method for 3D surfaces. This method is based on differential geometry. Shape information is used to recover the point correspondences. In contrast to the majority of shape-based methods, which assume that shape (unit normal, curvature) changes are minimum after motion, our method focuses on the nonrigid relationship between before-motion and after-motion shapes. This nonrigid shape relationship is described by modeling the underlying nonrigid motion; we model it as a spline transformation, which has global control over the entire motion field along with the local deformation integrated within. This provides our method certain advantages over some pure differential geometric methods, which also utilize the nonrigid shape relationship but only work on local areas without a global control. For example, motion regularity is hard to implement in these pure differential geometric methods but is not a problem when the motion field is controlled by a spline transformation. The orthogonal parameterization requirement of the nonrigid shape relationship has to be approximated in these previous methods but is easy to meet in our method. Furthermore, the small deformation constraint introduced by the previous works is relaxed in our method. Experiments on both synthetic and real motions have been conducted. The quantitative and qualitative evaluations of our method are presented. The application of our method to the human tongue motion analysis is also presented in this paper.
13258925
Truthful Topology Control inWireless Ad Hoc Networks with Selfish Nodes
In wireless mobile ad hoc networks (MANETs), energy is a crucial resource. Topology control technology allows network nodes to reduce their transmission power while preserving the network connectivity. A MANET is a non-cooperative system so that only when a node earns its payment, which can cover its cost, the cooperation can be stimulated. We design a truthful topology control mechanism (TRUECON) for MANETs to induce the selfish, but rational, network nodes to collaborate. Truth-telling is a dominant strategy in TRUECON. A node needs to reveal its true value in order to obtain the maximum expected utility. We prove the overpayment of TRUECON has a bound depending on different radio propagation models
46138782
Leveraging legacy codes to distributed problem-solving environments: a Web services approach
This paper presents WSOWG, a Web-services-oriented wrapper generator for automatically wrapping non-networked legacy codes as Web services for reuse in distributed problem-solving environments. Using WSOWG, a finite element based computational fluid dynamics (CFD) legacy code has been wrapped as a Web service. A problem-solving environment for simulating incompressible Navier-Stokes flows has also been implemented. A user makes use of the CFD service through a Web page without knowing the exact implementation of the service. In this way, a user's computing environment can be extended to a heterogeneous distributed computing environment. Performance evaluation shows that the overhead to invoke the CFD Web service generated by WSOWG using Simple Object Access Protocol (SOAP) and CORBA Internet Inter-ORB Protocol (IIOP) is reasonable compared with that of invoking another CFD Web service manually wrapped from the CFD legacy code using SOAP only.