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RANDOM EDGE can be exponential on abstract cubes

ADVANCES IN MATHEMATICS 2006年第1期204卷 262-277页

作者： Matousek, Jiri Szabo, Tibor ETH Zentrum Inst Theoret Informat Zurich Switzerland Charles Univ Prague Dept Appl Math Prague 11800 1 Czech Republic Charles Univ Prague Inst Theoret Comp Sci ITI Prague 11800 1 Czech Republic

We prove that RANDOM EDGE, the simplex algorithm that always chooses a random improving edge to proceed on, can take a mildly exponential number of steps in the model of abstract objective functions (introduced by Williamson Hoke [Completely unimodal numberings of a simple polytope, Discrete Appl. Math. 20 (1988) 69-81.] and by Kalai [A simple way to tell a simple polytope from its graph, J. Combin. Theory Ser. A 49(2) (1988) 381-383.] under different names). We define an abstract objective function on the n-dimensional cube for which the algorithm, started at a random vertex, needs at least exp(const.n(1/3)) steps with high probability. The best previous lower bound was quadratic. So in order for RANDOM EDGE to succeed in polynomial time, geometry must help. (C) 2005 Elsevier Inc. All rights reserved.

关键词： linear programming simplex algorithm abstract objective function randomized algorithm unique sink orientation

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Online algorithms for searching and exploration in the plane

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COMPUTER SCIENCE REVIEW 2010年第4期4卷 189-201页

作者： Ghosh, Subir Kumar Klein, Rolf Tata Inst Fundamental Res Sch Comp Sci Bombay 400005 Maharashtra India Univ Bonn Inst Comp Sci 1 D-53117 Bonn Germany

In this paper, we survey online algorithms in computational geometry that have been designed for mobile robots for searching a target and for exploring a region in the plane. (C) 2010 Elsevier Inc. All rights reserved.

关键词： Online algorithms Motion planning Competitive ratio Target searching Exploration Approximation algorithms randomized algorithm Computational geometry Shortest path Minimum link path Visibility polygons Watchman route

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Random permutations on distributed, external and hierarchical memory

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INFORMATION PROCESSING LETTERS 1998年第6期67卷 305-309页

作者： Sanders, P Max Planck Inst Informat D-66123 Saarbrucken Germany

A simple randomized algorithm for generating a uniformly distributed random permutation of size n is investigated. It works in time O(n/P + T-comm(n/P, P) + T-prefix (P)) on P processors with high probability, where T-comm(k, P) is the time for randomly sending or receiving k elements on each processor and T-prefix(P) is the time for computing a prefix sum. The algorithm can be directly translated into an optimal external memory algorithm if fast memory for root nB(1 + o(1)) + O(B) elements is available where B is the page size. Due to its simplicity, the same algorithm even outperforms the straightforward method on mainstream workstations if the cache is taken to be the fast memory and the main memory is treated like external memory. The algorithm is almost four times faster on a MIPS R10000 machine. (C) 1998 Elsevier Science B.V. All rights reserved.

关键词： parallel random permutation generation randomized algorithm external memory hierarchical memory cache instruction level parallelism computational complexity

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An HSS Matrix-Inspired Butterfly-Based Direct Solver for Analyzing Scattering From Two-Dimensional Objects

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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS 2017年 16卷 1179-1183页

作者： Liu, Yang Guo, Han Michielssen, Eric Univ Michigan Dept Elect Engn & Comp Sci Ann Arbor MI 48109 USA

A butterfly-based fast direct integral equation solver for analyzing high-frequency scattering from two-dimensional objects is presented. The solver leverages a randomized butterfly scheme to compress blocks corresponding to near-and far-field interactions in the discretized forward and inverse electric field integral operators. The observed memory requirements and computational cost of the proposed solver scale as O(Nlog(2)N) and O(N-1.5 logN), respectively. The solver is applied to the analysis of scattering from electrically large objects spanning over 10 000 wavelengths and modeled in terms of five million unknowns.

关键词： Butterfly scheme electromagnetic scattering fast direct solver multilevel matrix decomposition algorithm (MLMDA) randomized algorithm

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Cache Enabled Cellular Network: algorithm for Cache Placement and Guarantees

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IEEE WIRELESS COMMUNICATIONS LETTERS 2019年第6期8卷 1550-1554页

作者： Krishnendu, S. Bharath, B. N. Bhatia, Vimal Indian Inst Technol Indore Discipline Elect Engn Indore 453552 India Indian Inst Technol Dharwad Dept Elect Engn Dharwad 580011 Karnataka India

This letter presents a novel algorithm for content placement in the small base stations (SBSs) caches in a heterogeneous wireless network. The problem of maximizing the average rate of cache hit in a heterogeneous wireless network for a given probability distribution of content popularity and a given network topology, under the constraint of cache size at each SBS is proposed. The optimal cache placement algorithm turns out to be NP-Hard, and hence, a novel approximate solution is presented. Further, the theoretical guarantees on the performance of the proposed algorithm is also provided. Finally, simulation results demonstrate that the proposed edge caching strategy performs better than the conventional greedy caching policy, least recently used, and least frequently used algorithms.

关键词： Cache placement heterogeneous wireless network greedy algorithm randomized algorithm cache hit

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Adaptive work-stealing with parallelism feedback

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ACM TRANSACTIONS ON COMPUTER SYSTEMS 2008年第3期26卷 1–32页

作者： Agrawal, Kunal Leiserson, Charles E. He, Yuxiong Hsu, Wen Jing MIT Cambridge MA 02139 USA Nanyang Technol Univ Singapore 639798 Singapore

Multiprocessor scheduling in a shared multiprogramming environment can be structured as two-level scheduling, where a kernel-level job scheduler allots processors to jobs and a user-level thread scheduler schedules the work of a job on its allotted processors. We present a randomized work-stealing thread scheduler for fork-join multithreaded jobs that provides continual parallelism feedback to the job scheduler in the form of requests for processors. Our A-STEAL algorithm is appropriate for large parallel servers where many jobs share a common multiprocessor resource and in which the number of processors available to a particular job may vary during the job's execution. Assuming that the job scheduler never allots a job more processors than requested by the job's thread scheduler, A-STEAL guarantees that the job completes in near-optimal time while utilizing at least a constant fraction of the allotted processors. We model the job scheduler as the thread scheduler's adversary, challenging the thread scheduler to be robust to the operating environment as well as to the job scheduler's administrative policies. For example, the job scheduler might make a large number of processors available exactly when the job has little use for them. To analyze the performance of our adaptive thread scheduler under this stringent adversarial assumption, we introduce a new technique called trim analysis, which allows us to prove that our thread scheduler performs poorly on no more than a small number of time steps, exhibiting near-optimal behavior on the vast majority. More precisely, suppose that a job has work T-1 and span T-infinity. On a machine with P processors, A-STEAL completes the job in an expected duration of O(T-1/(P) over tilde + T-infinity + L lg P) time steps, where L is the length of a scheduling quantum, and (P) over tilde denotes the O(T-infinity + L lg P)-trimmed availability. This quantity is the average of the processor availability over all time steps except the

关键词： algorithms performance theory experimentation adaptive scheduling adversary span instantaneous parallelism job scheduling multiprocessing multiprogramming parallelism feedback parallel computation processor allocation randomized algorithm thread scheduling two-level scheduling space sharing trim analysis work work-stealing

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Exact Simulation of the First-Passage Time of Diffusions

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JOURNAL OF SCIENTIFIC COMPUTING 2019年第3期79卷 1477-1504页

作者： Herrmann, S. Zucca, C. Univ Bourgogne Franche Comte CNRS UMR 5584 IMB F-21000 Dijon France Univ Torino Dept Math G Peano Via Carlo Alberto 10 I-10123 Turin Italy

Since diffusion processes arise in so many different fields, efficient technics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations of the first-passage times as a by-product. For efficiency reasons, it is particularly challenging to simulate directly this hitting time by avoiding to construct the whole paths. In the Brownian case, the distribution of the first-passage time is explicitly known and can be easily used for simulation purposes. The authors introduce a new rejection sampling algorithm which permits to perform an exact simulation of the first-passage time for general one-dimensional diffusion processes. The efficiency of the method, which is essentially based on Girsanov's transformation, is described through theoretical results and numerical examples.

关键词： First-passage time Brownian motion Diffusion processes Girsanov's transformation Exact simulation randomized algorithm

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A fast and robust circle detection method using isosceles triangles sampling

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PATTERN RECOGNITION 2016年 54卷 218-228页

作者： Zhang, Hanqing Wiklund, Krister Andersson, Magnus Umea Univ Dept Phys Linneaus Vaeg 9 SE-90187 Umea Sweden

Circle detection using randomized sampling has been developed in recent years to reduce computational intensity. However, randomized sampling is sensitive to noise that can lead to reduced accuracy and false-positive candidates. To improve on the robustness of randomized circle detection under noisy conditions this paper presents a new methodology for circle detection based upon randomized isosceles triangles sampling. It is shown that the geometrical property of isosceles triangles provides a robust criterion to find relevant edge pixels which, in turn, offers an efficient means to estimate the centers and radii of circles. For best efficiency, the estimated results given by the sampling from individual connected components of the edge map were analyzed using a simple clustering approach. To further improve on the accuracy we applied a two-step refinement process using chords and linear error compensation with gradient information of the edge pixels. Extensive experiments using both synthetic and real images have been performed. The results are compared to leading state-of-the-art algorithms and it is shown that the proposed methodology has a number of advantages: it is efficient in finding circles with a low number of iterations, it has high rejection rate of false-positive circle candidates, and it has high robustness against noise. All this makes it adaptive and useful in many vision applications. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Circle detection randomized algorithm Sampling strategy Isosceles triangles

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Parameterized algorithms for min-max 2-cluster editing

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2017年第1期34卷 47-63页

作者： Chen, Li-Hsuan Wu, Bang Ye Natl Chung Cheng Univ Chiayi 621 Taiwan

For a given graph and an integer t, the Min-Max 2-Clustering problem asks if there exists a modification of a given graph into two maximal disjoint cliques by inserting or deleting edges such that the number of the editing edges incident to each vertex is at most t. It has been shown that the problem can be solved in polynomial time for , where n is the number of vertices. In this paper, we design parameterized algorithms for different ranges of t. Let . We show that the problem is polynomial-time solvable when roughly . When , we design a randomized and a deterministic algorithm with sub-exponential time parameterized complexity, i.e., the problem is in SUBEPT. We also show that the problem can be solved in time for and in time for , where .

关键词： Parameterized algorithm Parameterized complexity Graph modification Clustering randomized algorithm Subexponential algorithm

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Scalable wake-up of multi-channel single-hop radio networks

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THEORETICAL COMPUTER SCIENCE 2016年 615卷 23-44页

作者： Chlebus, Bogdan S. De Marco, Gianluca Kowalski, Dariusz R. Univ Colorado Dept Comp Sci & Engn Denver CO 80217 USA Univ Salerno Dipartimento Informat I-84084 Salerno Italy Univ Liverpool Dept Comp Sci Liverpool L69 3BX Merseyside England

We consider single-hop radio networks with multiple channels as a model of wireless networks. There are n stations connected to b radio channels that do not provide collision detection. A station uses all the channels concurrently and independently. Some k stations may become active spontaneously at arbitrary times. The goal is to wake up the network, which occurs when all the stations hear a successful transmission on some channel. Duration of a waking-up execution is measured starting from the first spontaneous activation. We present a deterministic algorithm that wakes up a network in O(k log(1/b) k log n) time, where k is unknown. We give a deterministic scalable algorithm for the special case when b > d log log n, for some constant d > 1, which wakes up a network in O(k/b log n log(b log n)) time, with k unknown. This algorithm misses time optimality by at most a factor of O(log n(log b + log log n)), because any deterministic algorithm requires Omega(k/b log n/k) time. We give a randomized algorithm that wakes up a network within O(k(1/b) In 1/epsilon) rounds with a probability that is at least 1 - epsilon, for any 0 < epsilon < 1, where k is known. We also consider a model of jamming, in which each channel in any round may be jammed to prevent a successful transmission, which happens with some known parameter probability p, independently across all channels and rounds. For this model, we give two deterministic algorithms for unknown k: one wakes up a network in time O(log(-1) (1/p) log n log(1/b) k), and the other in time O(log(-1) (1/p) k/b log n log(b log n)) when the inequality b > log(128b log n) holds, both with probabilities that are at least 1 - 1/poly(n). (c) 2015 Elsevier B.V. All rights reserved.

关键词： Multiple access channel Radio network Multi-channel Wake-up Synchronization Deterministic algorithm randomized algorithm Distributed algorithm

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