42814281
Fixed Topology Alignment with Recombination
In this paper, we study a new version of multiple sequence alignment, fixed topology alignment with recombination. We show that it can not be approximated within any constant ratio unless P = NP. For a more 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.
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.
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.
9397376
Inferring a DNA Sequence from Erroneous Copies
Abstract We suggest a novel approach for efficiently reconstructing an original DNA sequence from erroneous copies.
5412677
Middleware for streaming 3D progressive meshes over lossy networks
Streaming 3D graphics have been widely used in multimedia applications such as online gaming and virtual reality. However, a gap exists between the zero-loss-tolerance of the existing compression schemes and the lossy network transmissions. In this article, we propose a generic 3D middleware between the 3D application layer and the transport layer for the transmission of triangle-based progressively compressed 3D models. Significant features of the proposed middleware include. 1) handling 3D compressed data streams from multiple progressive compression techniques. 2) considering end user hardware capabilities for effectively saving the data size for network delivery. 3) a minimum cost dynamic reliable set selector to choose the transport protocol for each sublayer based on the real-time network traffic. Extensive simulations with TCP/UDP and SCTP show that the proposed 3D middleware can achieve the dual objectives of maintaining low transmission delay and small distortion, and thus supporting high quality 3D streaming with high flexibility.
360687
Target-oriented scheduling in directional sensor networks
Unlike convectional omni-directional sensors that always have an omni-angle of sensing range, directional sensors may have a limited angle of sensing range due to technical constraints or cost considerations. A directional sensor network consists of a number of directional sensors, which can switch to several directions to extend their sensing ability to cover all the targets in a given area. Power conservation is still an important issue in such directional sensor networks. In this paper, we address the multiple directional cover sets problem (MDCS) of organizing the directions of sensors into a group of non-disjoint cover sets to extend the network lifetime. One cover set, in which the directions cover all the targets, is activated at one time. We prove the MDCS to be NP-complete and propose three heuristic algorithms for the MDCS. Simulation results are also presented to demonstrate the performance of these algorithms.
16584711
PeerWindow: an efficient, heterogeneous, and autonomic node collection protocol
Nodes in peer-to-peer systems need to know the information about others to optimize neighbor selection, resource exchanging, replica placement, load balancing, query optimization, and other collaborative operations. However, how to collect this information effectively is still an open issue. In this paper, we propose a novel information collection protocol, PeerWindow, with which each node can collect a large amount of pointers to other nodes at a very low cost. Compared to existing protocols, PeerWindow is 1) efficient, the cost of collecting 1,000 pointers being less than 1 kbps in a common system environment, 2) heterogeneous, nodes with different capacities collecting different amounts of information, and 3) autonomic, nodes determining their bandwidth cost for node collection by themselves and adjusting it dynamically. PeerWindow can be used in many existing peer-to-peer systems and has tremendous potential for future expansions.
3605809
Performance evaluation for energy efficient topologic control in ad hoc wireless networks
Minimizing total energy to keep an ad hoc wireless network symmetrically connected is an NP-hard problem. Recently, several greedy approximations have been proposed, based on k-restricted decompositions of the network. Their performance ratios are established through estimations of the least upper bound ρk for the ratio between total powers of best possible k-restricted decomposition and the optimal solution. In this paper, we determine the exact value of ρk for all k.
368077
Approximation of Walrasian equilibrium in single-minded auctions
We consider a social optimization model of pricing scheme in single-minded auctions, in cases where Walrasian equilibrium does not exist. We are interested in the maximization of the ratio, R, of happy bidders over all agents, in a feasible allocation-pricing scheme. We show NP-hardness of the optimization problem, establish lower and upper bounds of R, as well as develop greedy algorithms to approximate the optimal value of R.