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2008 International Conference on Machine Learning and Cybernetics(2008机器学习与控制论国际会议)

作者： SHOU-QIANG WANG DA-MING ZHU School of Computer Science and Technology Shandong University Jinan 250100China Department of Inf School of Computer Science and Technology Shandong University Jinan 250100China

Clustering analysis is one of the important problems in the fields of data mining and machine learning. There are many different clustering methods. Among them, k-means clustering is one of the most popular schemes owing to its simple and practicality. This paper investigates the approximate algorithm for the A-means clustering by means of selecting the k initial points from the input point set. An expected 2-approximation algorithm is presented in this paper. Meanwhile, an efficient algorithm for selecting the initial points is also proposed. At last some experimental results are given to test the valid of these algorithms.

关键词： Clustering A-means clustering randomized algorithm

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Polynomial factorization: a success story 03

Polynomial factorization: a success story

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Proceedings of the 2003 international symposium on Symbolic and algebraic computation

作者： Erich Kaltofen North Carolina State University Raleigh NC

ISBN: (纸本)9781581136418

The problem of factoring a polynomial in a single or severalvariables over a finite field, the rational numbers or the complexnumbers is one of the success stories in the discipline of symboliccomputation. In the early 1960s implementors investigated theconstructive methods known from classical algebra books, but--withthe exception of Gauss's distinct degree factorizationalgorithm--found the algorithms quite inefficient in practice [16].The contributions in algorithmic techniques that have been madeover the next 40 years are truly a hallmark of symbolic *** early pioneers, Berlekamp, Musser, Wang, Weinberger,Zassenhaus and others applied new ideas like randomization, thateven before the now famous algorithms for primality testing byRabin and Strassen, and like generic programming with coefficientdomains as abstract data classes, and they introduced the powerfulHensel lifting lemma to computer algebra. We note that whilede-randomization for integer primality testing has beenaccomplished recently [1], the same remains open for the problem ofcomputing a root of a polynomial modulo a large prime [12, ResearchProblem 14.48].Polynomial-time complexity for rational coefficients wasestablished in the early 1980s by the now-famous lattice basisreduction algorithm of A. Lenstra, H. W. Lenstra, Jr., and ***ász. The case of many variables first became anapplication of the DeMillo and Lipton/Schwartz/Zippel lemma [30]and then triggered a fundamental generalization from the standardsparse (distributed) representation of polynomials to the one bystraight line and black box programs [11, 17, 19]. Effectiveversions of the Hilbert irreducibility theorem are needed for theprobabilistic analysis, which serendipitously later have alsoplayed a role in the PCP characterization of NP[2]. Unlike many other problems in commutative algebra andalgebraic geometry, such as algebraic system solving, thepolynomial factoring problem is of probabilistic polynomial-timeco

关键词： polynomial factorization symbolic/numeric hybrid method straight line program lattice basis reduction randomized algorithm black box polynomial

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Approximating center points with iterative radon points

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INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY & APPLICATIONS 1996年第3期6卷 357-377页

作者： Clarkson, KL Eppstein, D Miller, GL Sturtivant, C Teng, SH AT&T BELL LABS MURRAY HILLNJ 07974 UNIV CALIF IRVINE DEPT INFORMAT & COMP SCIIRVINECA 92717 CARNEGIE MELLON UNIV SCH COMP SCIPITTSBURGHPA 15213 UNIV MINNESOTA DEPT COMP SCIMINNEAPOLISMN 55455 MIT DEPT MATHCAMBRIDGEMA 02139

We give a practical and provably good Monte Carlo algorithm for approximating center points. Let P be a set of n points in R(d). A point c is an element of R(d) is a beta-center point of P if every closed halfspace containing c contains at least pn points of P. Every point set has a 1/(d + 1)-center point;our algorithm finds an Omega(1/d(2))-center point with high probability. Our algorithm has a small constant factor and is the first approximate center point algorithm whose complexity is subexponential in d. Moreover, it can be optimally parallelized to require O(log(2) dloglogn) time. Our algorithm has been used in mesh partitioning methods and can be used in the construction of high breakdown estimators for multivariate datasets in statistics. It has the potential to improve results in practice for constructing weak epsilon-nets. We derive a variant of our algorithm whose time bound is fully polynomial in d and linear in n, and show how to combine our approach with previous techniques to compute high quality center points more quickly.

关键词： geometric approximation center point computational geometry iterative method randomized algorithm

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Two probabilistic algorithms for planar motion detection

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IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 1997年第3期E80D卷 371-381页

作者： Fermin, I Imiya, A Ichikawa, A Chiba Univ Chiba-shi Japan

We introduce two probabilistic algorithms to determine the motion parameters of a planar shape without knowing a priori the point-to-point correspondences. If the target is limited to rigid objects, an Euclidean transformation can be expressed as a linear equation with six parameters, i.e. two translational parameters and four rotational parameters (the axis of rotation and the rotational speed about the axis). These parameters can be determined by applying the randomized Hough transform. One remarkable feature of our algorithms is that the calculations of the translation and rotation parameters are performed by using points randomly selected from two image frames that are acquired at different times. The estimation of rotation parameters is done using one of two approaches, which we call the triangle search and the polygon search algorithms respectively. Both methods focus on the intersection points of a boundary of the 2D shape and the circles whose centers are located at the shape's centroid and whose radii are generated randomly. The triangle search algorithm randomly selects three different intersection points in each image, such that they form congruent triangles, and then estimates the rotation parameter using these two triangles. However, the polygon search algorithm employs all the intersection points in each image, i.e. all the intersection points in the two image frames form two polygons, and then estimates the rotation parameter with aid of the vertices of these two polygons.

关键词： rigid motion randomized algorithm point correspondences planar shape motion parameters randomized Hough transform

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Zip Trees

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ACM TRANSACTIONS ON algorithmS 2021年第4期17卷 34-34页

作者： Tarjan, Robert E. Levy, Caleb C. Timmel, Stephen Princeton Univ Dept Comp Sci 35 Olden St Princeton NJ 08544 USA Intertrust Technol Sunnyvale CA 94085 USA Sunshine 165 Univ AveSuite 5 Palo Alto CA USA Virginia Tech Dept Math 225 Stanger St Blacksburg VA 24061 USA

We introduce the zip tree,(1) a form of randomized binary search tree that integrates previous ideas into one practical, performant, and pleasant-to-implement package. A zip tree is a binary search tree in which each node has a numeric rank and the tree is (max)-heap-ordered with respect to ranks, with rank ties broken in favor of smaller keys. Zip trees are essentially treaps [8], except that ranks are drawn from a geometric distribution instead of a uniform distribution, and we allow rank ties. These changes enable us to use fewer random bits per node. We perform insertions and deletions by unmerging and merging paths (unzipping and zipping) rather than by doing rotations, which avoids some pointer changes and improves efficiency. The methods of zipping and unzipping take inspiration from previous top-down approaches to insertion and deletion by Stephenson [10], Martinez and Roura [5], and Sprugnoli [9]. From a theoretical standpoint, this work provides two main results. First, zip trees require onlyO(log logn) bits (with high probability) to represent the largest rank in an n-node binary search tree;previous data structures require O(logn) bits for the largest rank. Second, zip trees are naturally isomorphic to skip lists [7], and simplify Dean and Jones' mapping between skip lists

关键词： Zip tree randomized algorithm binary search tree treap skip list

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Analyzing Information Retrieval Systems Using Peer-to-Peer Information

Analyzing Information Retrieval Systems Using Peer-to-Peer I...

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2009 Asia-Pacific Conference on Information Processing

作者： Jiang Zhengzheng Library Changsha University of Science and Technology Changsha 410004, China Yong Huang School of Civil Engineering Hunan University Changsha 410082, China

The hardware and architecture approach to randomized algorithms is defined not only by the evaluation of systems that paved the way for the emulation of digital-to-analog converters, but also by the essential need for expert systems. After years of important research into IPv7, we show the understanding of the Turing machine. Our focus here is not on whether the infamous psychoacoustic algorithm for the important unification of SCSI disks and systems by M. Bharadwaj et al. runs in O(n) time, but rather on proposing an analysis of linked lists.

关键词： information Retrieval peer-to-peer information randomized algorithm

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Nonlinear Discrete Optimization

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丛书名： Zurich lectures in advanced mathematics

2010年

作者： Shmuel Onn

ISBN: (数字)9783037195932

ISBN: (纸本)9783037190937

This monograph develops an algorithmic theory of nonlinear discrete optimization. It introduces a simple and useful setup which enables the polynomial time solution of broad fundamental classes of nonlinear combinatorial optimization and integer programming problems in variable dimension. An important part of this theory is enhanced by recent developments in the algebra of Graver bases. The power of the theory is demonstrated by deriving the first polynomial time algorithms in a variety of application areas within operations research and statistics, including vector partitioning, matroid optimization, experimental design, multicommodity flows, multi-index transportation and privacy in statistical databases. The monograph is intended for graduate students and researchers. It is accessible to anyone with standard undergraduate knowledge and mathematical maturity.

关键词： Integer programming combinatorial optimization optimization linear programming stochastic programming randomized algorithm approximation algorithm polynomial time transportation problem multi index transportation problem transshipment problem multicommodity flow congestion game spanning tree matroid submodular function matching partitioning clustering polytope zonotope edge direction totally unimodular matrix test set Graver base contingency table statistical table multiway table disclosure control data security privacy algebraic statistics experimental design Frobenius number Grobner base Hilbert scheme zero-dimensional ideal

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Content Placement and Service Scheduling in Femtocell Caching Networks

Content Placement and Service Scheduling in Femtocell Cachin...

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IEEE Global Communications Conference

作者： Teng Liu Alhussein A. Abouzeid Department of Electrical Computer and Systems Engineering Rensselaer Polytechnic Institute

ISBN: (纸本)9781509013296

This work considers the joint problem of content placement and service scheduling in femtocell caching networks, to maximize the traffic volume served from the cache. The problem is modeled as a Markov decision process. We combine the Edmonds-Karp algorithm and the marginal allocation algorithm to develop an efficient centralized policy called Infinite CAche-filling (ICA), which can get arbitrarily close to optimal asymptotically as the estimation time window increases. We also design a randomized algorithm called Infinite CAche-filling with Probabilistic scheduling (ICAP) that takes into consideration the femtocells service capability due to interference or multiplexing techniques. We derive a lower bound on the expected discounted hit count of ICAP. We also derive an upper bound on the probability that the performance of ICAP degrades from this expected value. Numerical results show that ICAP scales well and converges relatively fast in response to request pattern changes.

关键词： Content-centric networking Femtocell network Markov decision process randomized algorithm randomized algorithms Markov chain Femtocell networks Femtocells Allocation algorithm Cache memory Traffic volume Content distribution

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Breaking the $ilde$Omega($sqrt{n})$ Barrier: Fast Consensus under a Late Adversary 18

Breaking the $ilde$Omega($sqrt{n})$ Barrier: Fast Consensus ...

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Proceedings of the 30th on Symposium on Parallelism in algorithms and Architectures

作者： Peter Robinson Christian Scheideler Alexander Setzer McMaster University Hamilton ON Canada Paderborn University Paderborn Germany

ISBN: (纸本)9781450357999

We study the consensus problem in a synchronous distributed system of n nodes under an adaptive adversary that has a slightly outdated view of the system and can block all incoming and outgoing communication of a constant fraction of the nodes in each round. Motivated by a result of Ben-Or and Bar-Joseph (1998), showing that any consensus algorithm that is resilient against a linear number of crash faults requires $\tilde Ømega(\sqrtn )$ rounds in an n -node network against an adaptive adversary, we consider a late adaptive adversary, who has full knowledge of the network state at the beginning of the previous round and unlimited computational power, but is oblivious to the current state of the nodes. % Our main contributions are randomized distributed algorithms that achieve consensus with high probability among all except a small constant fraction of the nodes (i.e.,\ "almost-everywhere'') against a late adaptive adversary who can block up to ε n$ nodes in each round, for a small constant ε >0$. Our first protocol achieves binary almost-everywhere consensus and also guarantees a decision on the majority input value, thus ensuring plurality consensus. We also present an algorithm that achieves the same time complexity for multi-value consensus. Both of our algorithms succeed in $O(łog n)$ rounds with high probability, thus showing an exponential gap to the $\tildeØmega(\sqrtn )$ lower bound of Ben-Or and Bar-Joseph for strongly adaptive crash-failure adversaries, which can be strengthened to $Ømega(n)$ when allowing the adversary to block nodes instead of permanently crashing them. Our algorithms are scalable to large systems as each node contacts only an (amortized) constant number of peers in each communication round. We show that our algorithms are optimal up to constant (resp.\ sub-logarithmic) factors by proving that every almost-everywhere consensus protocol takes $Ømega(łog_d n)$ rounds in the worst case, where d is an upper bound on the number of communicat

关键词： almost-everywhere consensus probabilistic analysis adaptive adversary randomized algorithm

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Load Balancing in Cloud-based Flow Security System

Load Balancing in Cloud-based Flow Security System

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2017 2nd International Conference on Advanced Materials Science and Environment Engineering(AMSEE2017)

作者： Gang HE Yue-jian XIAO Beijing Key Laboratory of Network System Architecture and Convergence Beijing University of Posts and Telecommunications

In the context of load balancing [1], Lu et al. proposed a novel class of algorithms called Join-Idle-Queue(JIQ) for distributed load balancing in large systems, where a group of dispatchers distribute jobs to a cluster of parallel servers. Each dispatcher maintains a queue called Idle-Queue for idle servers. When a job arrives to a dispatcher at random, the dispatcher sends it to a server which in the head of the Idle-Queue, or to a random server if the Idle-Queue is empty. Meanwhile conversely,when a server has no jobs, it actively requests to be placed on an Idle-Queue. Although this algorithm was shown to be quite effective [2,3], it is defective in some respects. This paper presents several new improvements, which makes the algorithm more effective, especially in Cloud-based Flow Security System(CFS). These improvements focus primarily on these aspects, such as the definition of idle server, data concurrency while choosing an Idle-Queue, etc. The experimental results show that the improved load balancing algorithm can improve the utilization of resources in a certain extent.

关键词： Cloud computing Load balancing Join-Idle-Queue algorithm randomized algorithm

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