The complexity of solving infinite games, including parity, mean payoff, and simple stochastic, is an important open problem in verification, automata, and complexity theory. In this paper, we develop an abstract sett...
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The complexity of solving infinite games, including parity, mean payoff, and simple stochastic, is an important open problem in verification, automata, and complexity theory. In this paper, we develop an abstract setting for studying and solving such games, based on function optimization over certain discrete structures. We introduce new classes of recursively local-global (RLG) and partial recursively local-global (PRLG) functions, and show that strategy evaluation functions for simple stochastic, mean payoff, and parity games belong to these classes. In this setting, we suggest randomized subexponential algorithms appropriate for RLG- and PRLG-function optimization. We show that the subexponential algorithms for combinatorial linear programming, due to Kalai and Matousek, Sharir, Welzl, can be adapted for optimizing the RLG- and PRLG-functions. (c) 2005 Elsevier B.V. All rights reserved.
The paging problem is defined as follows: we are given a two-level memory system, in which one level is a fast memory, called cache, capable of holding k items, and the second level is an unbounded but slow memory. At...
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The paging problem is defined as follows: we are given a two-level memory system, in which one level is a fast memory, called cache, capable of holding k items, and the second level is an unbounded but slow memory. At each given time step, a request to an item is issued. Given a request to an item p, a miss occurs if p is not present in the fast memory. In response to a miss, we need to choose an item q in the cache and replace it by p. The choice of q needs to be made on-line, without the knowledge of future requests. The objective is to design a replacement strategy with a small number of misses. In this paper we use competitive analysis to study the performance of randomized on-line paging algorithms. Our goal is to show how the concept of work functions, used previously mostly for the analysis of deterministic algorithms, can also be applied, in a systematic fashion, to the randomized case. We present two results: we first show that the: competitive ratio of the marking algorithm is exactly 2H(k) - 1. Previously, it was known to be between H-k and 2(Hk). Then we provide a new, H-k-competitive algorithm for paging. Our algorithm, as well as its analysis, is simpler than the known algorithm by McGeoch and Sleator. Another advantage of our algorithm is that it can be implemented with complexity bounds independent of the number of past requests: O(k(2) log k) memory and O(k(2)) time per request. (C) 2000 Elsevier Science B.V. All rights reserved.
We establish essentially optimal bounds on the complexity of initial-value problems in the randomized and quantum settings. For this purpose we define a sequence of new algorithms whose error/cost properties improve f...
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We establish essentially optimal bounds on the complexity of initial-value problems in the randomized and quantum settings. For this purpose we define a sequence of new algorithms whose error/cost properties improve from step to step. These algorithms yield new upper complexity bounds, which differ from known lower bounds by only an arbitrarily small positive parameter in the exponent, and a logarithmic factor. In both the randomized and quantum settings, initial-value problems turn out to be essentially as difficult as scalar integration. (C) 2006 Elsevier Inc. All rights reserved.
An efficient randomized online algorithm for the paging problem for cache size 2 is given, which is 3/2-competitive against an oblivious adversary. The algorithm keeps track of at most one page in slow memory at any t...
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An efficient randomized online algorithm for the paging problem for cache size 2 is given, which is 3/2-competitive against an oblivious adversary. The algorithm keeps track of at most one page in slow memory at any time. A lower bound of 37/24 approximate to 1.5416 is given for the competitiveness of any trackless online algorithm for the same problem, i.e., an algorithm that keeps track of no page outside the cache. (C) 2000 Elsevier Science B.V. All rights reserved.
The strong link between matroids and matching is used to extend the ideas that resulted in the design of random NC (RNC) algorithms for matching to obtain RNC algorithms for the matroid union, intersection, and matchi...
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The strong link between matroids and matching is used to extend the ideas that resulted in the design of random NC (RNC) algorithms for matching to obtain RNC algorithms for the matroid union, intersection, and matching problems, and for linearly representable matroids. As a consequence, RNC algorithms for the well-known problems of finding an arborescence and a maximum cardinality set of edge-disjoint spanning trees in a graph are obtained. The key tools used are linear algebra and randomization.
A probabilistic approach is considered for robust optimization, where a convex objective function is minimized subject to a parameter dependent convex constraint. A novel sequential randomized algorithm is proposed fo...
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ISBN:
(纸本)9781424414970;1424414970
A probabilistic approach is considered for robust optimization, where a convex objective function is minimized subject to a parameter dependent convex constraint. A novel sequential randomized algorithm is proposed for solving this optimization employing the stochastic ellipsoid method. It is shown that the upper bounds of the numbers of random samples and updates of the algorithm are much less than those of the stochastic bisection method utilizing the stochastic ellipsoid method at each iteration. This feature actually leads to a computational advantage, which is demonstrated through a numerical example.
Despite that neural networks have demonstrated their good potential to be used in constructing learners which exhibit strong predictive performance, there are still some uncertainty issues that can greatly affect the ...
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Despite that neural networks have demonstrated their good potential to be used in constructing learners which exhibit strong predictive performance, there are still some uncertainty issues that can greatly affect the effectiveness of the employed supervised learning algorithms, such as class imbalance and labeling errors (or class noise). Technically, imbalanced data resource can cause more difficulties or limitations for learning algorithms to distinguish different classes, while data with labeling errors can lead to an unreasonable problem formulation due to incorrect hypotheses. Indeed, noise and class imbalance are pervasive problems in the domain of educational data analytics. This study aims at developing improved randomized learning algorithms by investigating a novel type of cost function that focuses on the combined effects of class imbalance and class noise. Instead of concerning these uncertainty issues isolation, we present a convex combination of robust and imbalanced modelling objectives, contributing to a generalized formulation of weighted least squares problems by which the improved randomized learner models can be built. Our experimental study on several educational data classification tasks have verified the advantages of our proposed algorithms, in comparison with some existing methods that either takes no account of class imbalance and labeling errors, or merely consider one specific aspect in problem-solving.
Network coding is a method for information transmission in a network, based on the idea of enabling internal nodes to forward a function of the incoming messages, typically a linear combination. In this paper we discu...
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Network coding is a method for information transmission in a network, based on the idea of enabling internal nodes to forward a function of the incoming messages, typically a linear combination. In this paper we discuss generalizations of the network coding problem with additional constraints on the coding functions called network code completion problem, NCCP. We give both randomized and deterministic algorithms for maximum throughput-achieving network code construction for the NCCP in the multicast case. We also introduce the related problem of fixable pairs, investigating when a certain subset of coding coefficients in the linear combination functions can be fixed to arbitrary nonzero values such that the network code can always be completed to achieve maximum throughput. We give a sufficient condition for a set of coding coefficients to be fixable. For both problems we present applications in different wireless and heterogeneous network models. (C) 2014 Elsevier B.V. All rights reserved.
In this paper, we consider the infinite-dimensional integration problem on weighted reproducing kernel Hilbert spaces with norms induced by an underlying function space decomposition of analysis of variance type. The ...
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In this paper, we consider the infinite-dimensional integration problem on weighted reproducing kernel Hilbert spaces with norms induced by an underlying function space decomposition of analysis of variance type. The weights model the relative importance of different groups of variables. We present new randomized multilevel algorithms to tackle this integration problem and prove upper bounds for their randomized error. Furthermore, we provide in this setting the first nontrivial lower error bounds for general randomized algorithms, which, in particular, may be adaptive or nonlinear. These lower bounds show that our multilevel algorithms are optimal. Our analysis refines and extends the analysis provided in [F. J. Hickernell, T. Muller-Gronbach, B. Niu, and K. Ritter, J. Complexity, 26 (2010), pp. 229-254], and our error bounds improve substantially on the error bounds presented there. As an illustrative example, we discuss the unanchored Sobolev space and employ randomized quasi-Monte Carlo multilevel algorithms based on scrambled polynomial lattice rules.
A three-dimensional (3D) grid G sub(ntimesntimesn), n ges 2, is the set of points (vertices) with integer coordinates in [0,n-1]times[0,n-1] together with their connecting edges, which is viewed as a connected 3D set....
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A three-dimensional (3D) grid G sub(ntimesntimesn), n ges 2, is the set of points (vertices) with integer coordinates in [0,n-1]times[0,n-1] together with their connecting edges, which is viewed as a connected 3D set. Alternatively, G sub(ntimesntimesn) can be viewed as the union of 2n super(2) horizontal line segments, called corridors, and n super(2) vertical line segments, called shafts. We view G sub(ntimesntimesn) as representing a building and consider a vision-based pursuit-evasion problem in which a group of mobile robots (pursuers) are required to search for and capture an evader (intruder) hiding in it. The robots and the evader-all called players-are represented by points that move continuously along the edges of G sub(ntimesntimesn). (Two players can be at the same point at one time.) Any continuous move in G sub(ntimesntimesn) is allowed within the speed limit constraint, which is for the evader without loss of generality, and a constant s for the robots The evader is considered captured if there exists a time during the pursuit when his position coincides with the position of one of the robots.
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