13139613
Reversible simulation of irreversible computation
Reversible simulation of irreversible algorithms is analysed in the stylized form of a "reversible" pebble game. While such simulations incur little overhead in additional computation time, they use a large amount of additional memory space during the computation. We show that among all simulations which can be modelled by the pebble game, Bennett's simulation is optimal in that it uses the least auxiliary space for the greatest number of simulated steps. We give a trade-off of storage space versus irreversible erasure. Examples of reversible algorithms are algorithms for quantum computers.
9397376
Inferring a DNA Sequence from Erroneous Copies
Abstract We suggest a novel approach for efficiently reconstructing an original DNA sequence from erroneous copies.
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.
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.
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.
1974621
Engineering high-performance legacy codes as CORBA components for problem-solving environments
This paper describes techniques used to leverage high-performance legacy codes as CORBA components to a distributed problem-solving environment. It first briefly introduces the software architecture adopted by the environment. Then it presents a CORBA oriented wrapper generator (COWG) which can be used to automatically wrap high-performance legacy codes as CORBA components. Two legacy codes have been wrapped with COWG. One is an MPI-based molecular dynamic simulation (MDS) code, the other is a finite element-based computational fluid dynamics (CFD) code for simulating incompressible Navier-Stokes flows. Performance comparisons between runs of the MDS CORBA component and the original MDS legacy code on a cluster of workstations and on a parallel computer are also presented. Wrapped as CORBA components, these legacy codes can be reused in a distributed computing environment. The first case shows that high-performance can be maintained with the wrapped MDS component. The second case shows that a Web user can submit a task to the wrapped CFD component through a Web page without knowing the exact implementation of the component. In this way, a user's desktop computing environment can be extended to a high-performance computing environment using a cluster of workstations or a parallel computer.
41006390
Min-energy voltage allocation for tree-structured tasks
We study job scheduling on processors capable of running at variable voltage/speed to minimize energy consumption. Each job in a problem instance is specified by its arrival time and deadline, together with required number of CPU cycles. It is known that the minimum energy schedule for n jobs can be computed in O(n3) time, assuming a convex energy function. We investigate more efficient algorithms for computing the optimal schedule when the job sets have certain special structures. When the time intervals are structured as trees, the minimum energy schedule is shown to have a succinct characterization and is computable in time O(P) where P is the tree’s total path length. We also study an on-line average-rate heuristics AVR and prove that its energy consumption achieves a small constant competitive ratio for nested job sets and for job sets with limited overlap. Some simulation results are also given.
206858561
Hamiltonian Cycles in Almost Claw-Free Graphs
Abstract. Some known results on claw-free graphs are generalized to the larger class of almost claw-free graphs. In this paper, we prove the following two results and conjecture that every 5-connected almost claw-free graph is hamiltonian. (1). Every 2-connected almost claw-free graph G∉J on n≤ 4 δ vertices is hamiltonian, where J is the set of all graphs defined as follows: any graph G in J can be decomposed into three disjoint connected subgraphs G1, G2 and G3 such that EG(Gi, Gj) = {ui, uj, vivj} for i≠j and i,j = 1, 2, 3 (where ui≠vi∈V(Gi) for i = 1, 2, 3). Moreover the bound 4δ is best possible, thereby fully generalizing several previous results. (2). Every 3-connected almost claw-free graph on at most 5δ−5 vertices is hamiltonian, hereby fully generalizing the corresponding result on claw-free graphs.
13826196
Hourglasses and Hamilton cycles in 4-connected claw-free graphs
We show that if G is a 4-connected claw-free graph in which every induced hourglass subgraph S contains two non-adjacent vertices with a common neighbor outside S, then G is hamiltonian. This extends the fact that 4-connected claw-free, hourglass-free graphs are hamiltonian, thus proving a broader special case of a conjecture by Matthews and Sumner. 2005 Wiley Periodicals, Inc. J Graph Theory 48: 267–276, 2005
54297489
Iso-Map: Energy-Efficient Contour Mapping in Wireless Sensor Networks
Contour mapping is a crucial part of many wireless sensor network applications. Many efforts have been made to avoid collecting data from all the sensors in the network and producing maps at the sink, which is proven to be inefficient. The existing approaches (often aggregation based), however, suffer from heavy transmission traffic and incur large computational overheads on each sensor node. We propose Iso-Map, an energy-efficient protocol for contour mapping, which builds contour maps based solely on the reports collected from intelligently selected ?isoline nodes? in wireless sensor networks. Iso-Map achieves high-quality contour mapping while significantly reducing the generated traffic from O(n) to O(?n), where n is the total number of sensor nodes in the field. The pernode computation overhead is also restrained as a constant. We conduct comprehensive trace-driven simulations to verify this protocol, and demonstrate that Iso-Map outperforms the previous approaches in the sense that it produces contour maps of high fidelity with significantly reduced energy cost.