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This paper deals with the multicriteria 0-1 knapsack problem (KP) with k-min objectives (MkMIN-KP) in which the first objective is of classical sum type and the remaining objectives are k-min objective functions. The k-min objectives are ordinal objectives, aiming at the maximization of the k th smallest objective coefficient in any feasible knapsack solution with at least k items in the knapsack. We develop efficient algorithms for the determination of the complete nondominated set of MkMIN-KP. 相似文献
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Tag systems were invented by Emil Leon Post and proven recursively unsolvable by Marvin Minsky. These production systems have proved to be very useful in constructing small universal (Turing complete) systems for several different classes of computational systems, including Turing machines, and are thus important instruments for studying limits or boundaries of solvability and unsolvability. Although there are some results on tag systems and their limits of solvability and unsolvability, there are hardly any that consider both the shift number v and the number of symbols μ. This paper aims to contribute to research on limits of solvability and unsolvability for tag systems, taking into account these two parameters. The main result is the reduction of the 3n+1-problem to a surprisingly small tag system. It indicates that the present unsolvability line–defined in terms of μ and v–for tag systems might be significantly decreased. 相似文献
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Solomonoff’s central result on induction is that the prediction of a universal semimeasure M converges rapidly and with probability 1 to the true sequence generating predictor μ, if the latter is computable. Hence, M is eligible as a universal sequence predictor in the case of unknown μ. Despite some nearby results and proofs in the literature, the stronger result of convergence for all (Martin-Löf) random sequences remained open. Such a convergence result would be particularly interesting and natural, since randomness can be defined in terms of M itself. We show that there are universal semimeasures M which do not converge to μ on all μ-random sequences, i.e. we give a partial negative answer to the open problem. We also provide a positive answer for some non-universal semimeasures. We define the incomputable measure D as a mixture over all computable measures and the enumerable semimeasure W as a mixture over all enumerable nearly measures. We show that W converges to D and D to μ on all random sequences. The Hellinger distance measuring closeness of two distributions plays a central role. 相似文献
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Isil Oz Haluk Rahmi Topcuoglu Mahmut Kandemir Oguz Tosun 《Journal of Parallel and Distributed Computing》2012
Continuously reducing transistor sizes and aggressive low power operating modes employed by modern architectures tend to increase transient error rates. Concurrently, multicore machines are dominating the architectural spectrum today in various application domains. These two trends require a fresh look at resiliency of multithreaded applications against transient errors from a software perspective. In this paper, we propose and evaluate a new metric called the Thread Vulnerability Factor (TVF). A distinguishing characteristic of TVF is that its calculation for a given thread (which is typically one of the threads of a multithreaded application) does not depend on its code alone, but also on the codes of the threads that share resources and data with that thread. As a result, we decompose TVF of a thread into two complementary parts: local and remote. While the former captures the TVF induced by the code of the target thread, the latter represents the vulnerability impact of the threads that interact with the target thread. We quantify the local and remote TVF values for three architectural components (register file, ALUs, and caches) using a set of ten multithreaded applications from the Parsec and Splash-2 benchmark suites. Our experimental evaluation shows that TVF values tend to increase as the number of cores increases, which means the system becomes more vulnerable as the core count rises. We further discuss how TVF metric can be employed to explore performance–reliability tradeoffs in multicores. Reliability-based analysis of compiler optimizations and redundancy-based fault tolerance are also mentioned as potential usages of our TVF metric. 相似文献
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A new variance-based global sensitivity analysis technique 总被引:2,自引:0,他引:2
A new set of variance-based sensitivity indices, called W-indices, is proposed. Similar to the Sobol’s indices, both main and total effect indices are defined. The W-main effect indices measure the average reduction of model output variance when the ranges of a set of inputs are reduced, and the total effect indices quantify the average residual variance when the ranges of the remaining inputs are reduced. Geometrical interpretations show that the W-indices gather the full information of the variance ratio function, whereas, Sobol’s indices only reflect the marginal information. Then the double-loop-repeated-set Monte Carlo (MC) (denoted as DLRS MC) procedure, the double-loop-single-set MC (denoted as DLSS MC) procedure and the model emulation procedure are introduced for estimating the W-indices. It is shown that the DLRS MC procedure is suitable for computing all the W-indices despite its highly computational cost. The DLSS MC procedure is computationally efficient, however, it is only applicable for computing low order indices. The model emulation is able to estimate all the W-indices with low computational cost as long as the model behavior is correctly captured by the emulator. The Ishigami function, a modified Sobol’s function and two engineering models are utilized for comparing the W- and Sobol’s indices and verifying the efficiency and convergence of the three numerical methods. Results show that, for even an additive model, the W-total effect index of one input may be significantly larger than its W-main effect index. This indicates that there may exist interaction effects among the inputs of an additive model when their distribution ranges are reduced. 相似文献
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Motivated by the famous 3n+1 conjecture, we call a mapping from Z to Zresidue-class-wise affine if there is a positive integer m such that it is affine on residue classes (mod m). This article describes a collection of algorithms and methods for computation in permutation groups and monoids formed by residue-class-wise affine mappings. 相似文献
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Given a graph G, an integer k, and a demand set D={(s1,t1),…,(sl,tl)}, the k-Steiner Forest problem finds a forest in graph G to connect at least k demands in D such that the cost of the forest is minimized. This problem was proposed by Hajiaghayi and Jain in SODA’06. Thereafter, using a Lagrangian relaxation technique, Segev et al. gave the first approximation algorithm to this problem in ESA’06, with performance ratio O(n2/3logl). We give a simpler and faster approximation algorithm to this problem with performance ratio O(n2/3logk) via greedy approach, improving the previously best known ratio in the literature. 相似文献
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A canal surface is an envelope of a one-parameter family of spheres. In this paper we present an efficient algorithm for computing the implicit equation of a canal surface generated by a rational family of spheres. By using Laguerre and Lie geometries, we relate the equation of the canal surface to the equation of a dual variety of a certain curve in 5-dimensional projective space. We define the μ-basis for arbitrary dimension and give a simple algorithm for its computation. This is then applied to the dual variety, which allows us to deduce the implicit equations of the dual variety, the canal surface and any offset to the canal surface. 相似文献
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We give simple, self-contained proofs of the basic hardness results for the classes W[t] of the weft hierarchy. We extend these proofs to higher levels of the hierarchy and illuminate the distinctions among its classes. The anti-monotone collapse at W[1,s] and the normalization of weft-t formulas arise as by-products of the proofs. 相似文献
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Recently, Universum data that does not belong to any class of the training data, has been applied for training better classifiers. In this paper, we address a novel boosting algorithm called UAdaBoost that can improve the classification performance of AdaBoost with Universum data. UAdaBoost chooses a function by minimizing the loss for labeled data and Universum data. The cost function is minimized by a greedy, stagewise, functional gradient procedure. Each training stage of UAdaBoost is fast and efficient. The standard AdaBoost weights labeled samples during training iterations while UAdaBoost gives an explicit weighting scheme for Universum samples as well. In addition, this paper describes the practical conditions for the effectiveness of Universum learning. These conditions are based on the analysis of the distribution of ensemble predictions over training samples. Experiments on handwritten digits classification and gender classification problems are presented. As exhibited by our experimental results, the proposed method can obtain superior performances over the standard AdaBoost by selecting proper Universum data. 相似文献
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In this paper, we investigate the fault-tolerant capabilities of the k-ary n-cubes for even integer k with respect to the hamiltonian and hamiltonian-connected properties. The k-ary n-cube is a bipartite graph if and only if k is an even integer. Let F be a faulty set with nodes and/or links, and let k?3 be an odd integer. When |F|?2n-2, we show that there exists a hamiltonian cycle in a wounded k-ary n -cube. In addition, when |F|?2n-3, we prove that, for two arbitrary nodes, there exists a hamiltonian path connecting these two nodes in a wounded k-ary n-cube. Since the k-ary n -cube is regular of degree 2n, the degrees of fault-tolerance 2n-3 and 2n-2 respectively, are optimal in the worst case. 相似文献
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K-way hypergraph partitioning has an ever-growing use in parallelization of scientific computing applications. We claim that hypergraph partitioning with multiple constraints and fixed vertices should be implemented using direct K-way refinement, instead of the widely adopted recursive bisection paradigm. Our arguments are based on the fact that recursive-bisection-based partitioning algorithms perform considerably worse when used in the multiple constraint and fixed vertex formulations. We discuss possible reasons for this performance degradation. We describe a careful implementation of a multi-level direct K-way hypergraph partitioning algorithm, which performs better than a well-known recursive-bisection-based partitioning algorithm in hypergraph partitioning with multiple constraints and fixed vertices. We also experimentally show that the proposed algorithm is effective in standard hypergraph partitioning. 相似文献
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One of the early results concerning the asynchronous π-calculus which significantly contributed to its popularity is the capability of encoding the output prefix of the (choiceless) π-calculus in a natural and elegant way. Encodings of this kind were proposed by Honda and Tokoro, by Nestmann and (independently) by Boudol. We investigate whether the above encodings preserve De Nicola and Hennessy’s testing semantics. In this sense, it turns out that, under some general conditions, no encoding of the output prefix is able to preserve the must testing. This negative result is due to (a) the non-atomicity of the sequences of steps which are necessary in the asynchronous π-calculus to mimic synchronous communication, and (b) testing semantics’ sensitivity to divergence. 相似文献
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For a set T of n points (terminals) in the plane, a Manhattan network on T is a network N(T)=(V,E) with the property that its edges are horizontal or vertical segments connecting points in V⊇T and for every pair of terminals, the network N(T) contains a shortest l1-path between them. A minimum Manhattan network on T is a Manhattan network of minimum possible length. The problem of finding minimum Manhattan networks has been introduced by Gudmundsson, Levcopoulos, and Narasimhan [J. Gudmundsson, C. Levcopoulos, G. Narasimhan, Approximating a minimum Manhattan network, Nordic Journal of Computing 8 (2001) 219–232. Proc. APPROX’99, 1999, pp. 28–37] and its complexity status is unknown. Several approximation algorithms (with factors 8, 4, and 3) have been proposed; recently Kato, Imai, and Asano [R. Kato, K. Imai, T. Asano, An improved algorithm for the minimum Manhattan network problem, ISAAC’02, in: LNCS, vol. 2518, 2002, pp. 344–356] have given a factor 2-approximation algorithm, however their correctness proof is incomplete. In this paper, we propose a rounding 2-approximation algorithm based on an LP-formulation of the minimum Manhattan network problem. 相似文献
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The local b-function bf,p(s) of an n-variate polynomial f∈C[x] (x=(x1,…,xn)) at a point p∈Cn is constant on each stratum of a stratification of Cn. We propose a new method for computing such a stratification and bf,p(s) on each stratum. In the existing method proposed in Oaku (1997b), a primary ideal decomposition of an ideal in C[x,s] is needed and our experiment shows that the primary decomposition can be a bottleneck for computing the stratification. In our new method, the computation can be done by just computing ideal quotients and examining inclusions of algebraic sets. The precise form of a stratum can be obtained by computing the decomposition of the radicals of the ideals in C[x] defining the stratum. We also introduce various techniques for improving the practical efficiency of the implementation and we show results of computations for some examples. 相似文献
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We consider orthogonal drawings of a plane graph G with specified face areas. For a natural number k, a k-gonal drawing of G is an orthogonal drawing such that the boundary of G is drawn as a rectangle and each inner face is drawn as a polygon with at most k corners whose area is equal to the specified value. In this paper, we show that every slicing graph G with a slicing tree T and a set of specified face areas admits a 10-gonal drawing D such that the boundary of each slicing subgraph that appears in T is also drawn as a polygon with at most 10 corners. Such a drawing D can be found in linear time. 相似文献
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This paper aims at investigating properties of homomorphisms which preserve the bordered words. The bordered words are classified into d1-words and d2-words, where the length of the proper border of d2-word is greater than half of it. Some characterizations of d1-word-preserving homomorphism are studied. Some relationships among d-primitivity-preserving homomorphisms, d1-word-preserving homomorphisms, and d2-word-preserving homomorphisms are investigated. We show that every d-primitivity-preserving homomorphism is d1-word-preserving and every d1-word-preserving homomorphism is d2-word-preserving. 相似文献