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Almost Chor-Goldreich Sources and Adversarial Random Walks 2023

Almost Chor-Goldreich Sources and Adversarial Random Walks

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55th Annual ACM Symposium on Theory of Computing (STOC) part of the ACM Federated Computing Research Conference (FCRC)

作者： Doron, Dean Moshkovitz, Dana Oh, Justin Zuckerman, David Ben Gurion Univ Negev Beer Sheva Israel Univ Texas Austin Austin TX USA

ISBN: (纸本)9781450399135

A Chor-Goldreich (CG) source is a sequence of random variables Chi = Chi(1) ..... -Chi(t), where each Chi(i) similar to {0, 1}(d) and Chi(i) has delta d min-entropy conditioned on any fixing of Chi = Chi(1) ..... -Chi(i-1). The parameter 0 < delta <= 1 is the entropy rate of the source. We typically think of 3 as constant and C as growing. We extend this notion in several ways, defining almost CG sources. Most notably, we allow each Chi(i) to only have conditional Shannon entropy delta d. We achieve pseudorandomness results for almost CG sources which were not known to hold even for standard CG sources, and even for the weaker model of Santha-Vazirani sources: We construct a deterministic condenser that on input -, outputs a distribution which is close to having constant entropy gap, namely a distribution Z similar to {0, 1}(m) for m approximate to delta dt with min-entropy m-O(1). Therefore, we can simulate any randomized algorithm with small failure probability using almost CG sources with no multiplicative slowdown. This result extends to randomized protocols as well, and any setting in which we cannot simply cycle over all seeds, and a "one-shot" simulation is needed. Moreover, our construction works in an online manner, since it is based on random walks on expanders. Our main technical contribution is a novel analysis of random walks, which should be of independent interest. We analyze walks with adversarially correlated steps, each step being entropy-deficient, on good enough lossless expanders. We prove that such walks (or certain interleaved walks on two expanders), starting from a fixed vertex and walking according to Chi = Chi(1) ..... -Chi(t),, accumulate most of the entropy in Chi

关键词： condensers expander Graphs extractors random Walks randomized algorithm Santha-Vazirani sources

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Quick Detection of High-degree Entities in Large Directed Networks 14

Quick Detection of High-degree Entities in Large Directed Ne...

引用

14th IEEE International Conference on Data Mining (IEEE ICDM)

作者： Avrachenkov, K. Litvak, N. Prokhorenkova, L. Ostroumova Suyargulova, E. Inria Rocquencourt France Univ Twente NL-7500 AE Enschede Netherlands Yandex Moscow Russia

ISBN: (纸本)9781479943036

In this paper we address the problem of quick detection of high-degree entities in large online social networks. Practical importance of this problem is attested by a large number of companies that continuously collect and update statistics about popular entities, usually using the degree of an entity as an approximation of its popularity. We suggest a simple, efficient, and easy to implement two-stage randomized algorithm that provides highly accurate solutions to this problem. For instance, our algorithm needs only one thousand API requests in order to find the top-00 most followed users, with more than 90% precision, in the online social network Twitter with approximately a billion of registered users. Our algorithm significantly outperforms existing methods and serves many different purposes such as finding the most popular users or the most popular interest groups in social networks. An important contribution of this work is the analysis of the proposed algorithm using Extreme Value Theory - a branch of probability that studies extreme events and properties of largest order statistics in random samples. Using this theory we derive an accurate prediction for the algorithm's performance and show that the number of API requests for finding the top-k most popular entities is sublinear in the number of entities. Moreover, we formally show that the high variability of the entities, expressed through heavy-tailed distributions, is the reason for the algorithm's efficiency. We quantify this phenomenon in a rigorous mathematical way.

关键词： application program interfaces randomised algorithms social networking (online) API requests approximation extreme value theory high-degree entities large directed networks online social network Twitter online social networks quick detection randomized algorithm statistics top-k most popular entities algorithm design and analysis Approximation algorithms Indexes Peer-to-peer computing Prediction algorithms Twitter social networks sublinear complexity

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Faster Min-Plus Product for Monotone Instances 2022

Faster Min-Plus Product for Monotone Instances

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54th Annual ACM SIGACT Symposium on Theory of Computing (STOC)

作者： Chi, Shucheng Duan, Ran Xie, Tianle Zhang, Tianyi Tsinghua Univ Beijing Peoples R China Tel Aviv Univ Tel Aviv Israel

In this paper, we show that the time complexity of monotone minplus product of two n x n matrices is (O) over tilde (n((3)(+omega)()/2)) = (O) over tilde (n(2.687)), where omega (n((3)(+omega)()/2)) time, which greatl... 详细信息

ISBN: (纸本)9781450392648

In this paper, we show that the time complexity of monotone minplus product of two n x n matrices is (O) over tilde (n((3)(+omega)()/2)) = (O) over tilde (n(2.687)), where omega < 2.373 is the fast matrix multiplication exponent [Alman and Vassilevska Williams 2021]. That is, when A is an arbitrary integer matrix and B is either row-monotone or columnmonotone with integer elements bounded by O(n), computing the min-plus product C where C-i,C-j = min(k){A(i,k) + B-k,B-j} takes <(O)over tilde>(n((3)(+omega)()/2)) time, which greatly improves the previous time bound of (O) over tilde (n((12+omega)/5)) = (O) over tilde (n(2.875)) [Gu, Polak, Vassilevska Williams and Xu 2021]. Then by simple reductions, this means the case that A is arbitrary and the columns or rows of B are bounded-difference can also be solved in (O) over tilde (n((3)(+omega)()/2)) time, whose previous result gives time complexity of (O) over tilde (n(2.922)) [Bringmann, Grandoni, Saha and Vassilevska Williams 2016]. So the case that both of A and B are bounded-difference also has (O) over tilde (n((3)(+omega)()/2)) time algorithm, whose previous results give time complexities of (O) over tilde (n(2.824)) [Bringmann, Grandoni, Saha and Vassilevska Williams 2016] and (O) over tilde (n(2.779)) [Chi, Duan and Xie 2022]. Many problems are reducible to these problems, such as language edit distance, RNA-folding, scored parsing problem on BD grammars [Bringmann, Grandoni, Saha and Vassilevska Williams 2016]. Thus, their complexities are all improved. Finally, we also consider the problem of min-plus convolution between two integral sequences which are monotone and bounded by O(n), and achieve a running time upper bound of (O) over tilde (n(1.5)). Previously, this task requires running time (O) over tilde (n((9+root 177)/12)) = O(n(1.859)) [Chan and Lewenstein 2015].

关键词： Discrete algorithm randomized algorithm matrix multiplication application

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Solving traveling salesman problem with Nested Queue-Jumping algorithm

Solving traveling salesman problem with Nested Queue-Jumping...

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25th International Conference on Information Technology Interfaces

作者： Zhai, DH Jin, F SW Jiaotong Univ Sch Comp & Comp Engn Chengdu 610031 Peoples R China

ISBN: (纸本)9539676967

This paper presents a new approximate algorithm Nested Queue-Jumping algorithm (NQJA) to solve traveling salesman problem. The proposed algorithm incorporates the thoughts of heuristic algorithm, randomized algorithm and local optimization. Numerical results show that to the small-scale instances, using Queue-Jumping algorithm (QJA) directly can obtain the known optimal solution with a large probability. In the case of large-scale instances, NQJA generates high-quality solution compared to well know heuristic methods. Moreover, the shortest tour to China 144 TSP found by NQJA is shorter than the known optimal tour. It can be a very promising alternative for finding a solution to the TSP. NQJA is specially devised for TSP, But its thought can give elicitation for other NP-hard combinatorial optimization problems.

关键词： traveling salesman problem Nested Queue-Jumping Agorithm (NQJA) Queue-Jumping algorithm (QJA) randomized algorithm

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Almost Linear-Time algorithms for Adaptive Betweenness Centrality using Hypergraph Sketches 14

Almost Linear-Time Algorithms for Adaptive Betweenness Centr...

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20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD)

作者： Yoshida, Yuichi Natl Inst Informat Tokyo Japan Preferred Infrastruct Inc Tokyo Japan

ISBN: (纸本)9781450329569

Betweenness centrality measures the importance of a vertex by quantifying the number of times it acts as a midpoint of the shortest paths between other vertices. This measure is widely used in network analysis. In many applications, we wish to choose the k vertices with the maximum adaptive betweenness centrality, which is the betweenness centrality without considering the shortest paths that have been taken into account by already-chosen vertices. All previous methods are designed to compute the betweenness centrality in a fixed graph. Thus, to solve the above task, we have to run these methods k times. In this paper, we present a method that directly solves the task, with an almost linear runtime no matter how large the value of k. Our method first constructs a hypergraph that encodes the betweenness centrality, and then computes the adaptive betweenness centrality by examining this graph. Our technique can be utilized to handle other centrality measures. We theoretically prove that our method is very accurate, and experimentally confirm that it is three orders of magnitude faster than previous methods. Relying on the scalability of our method, we experimentally demonstrate that strategies based on adaptive betweenness centrality are effective in important applications studied in the network science and database communities.

关键词： Adaptive betweenness centrality Adaptive coverage centrality randomized algorithm

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Self-stabilization and Byzantine Tolerance for Maximal Matching 1

引用

20th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS)

作者： Kunne, Stephan Cohen, Johanne Pilard, Laurence Univ Paris Saclay Univ Paris Sud LRI CNRS Orsay France Univ Paris Saclay LI PaRAD Univ Versailles St Quentin Versailles France

ISBN: (数字)9783030032326

ISBN: (纸本)9783030032326;9783030032319

We analyse the impact of transient and Byzantine faults on the construction of a maximal matching in a general network. We consider the self-stabilizing algorithm called AnonyMatch presented by Cohen et al. [3] for computing such a matching. Since self-stabilization is transient fault tolerant, we prove that this algorithm still works under the more difficult context of arbitrary Byzantine faults. Byzantine nodes can prevent nodes close to them from taking part in the matching for an arbitrarily long time. We give bounds on their impact depending on the distance between a non-Byzantine node and the closest Byzantine, called the containment radius. We present the first algorithm tolerating both transient and Byzantine faults under the fair distributed daemon while keeping the best known containment radius. We prove this algorithm converges in O(max(Delta n, Delta(2)log n)) rounds w.h.p., where n and Delta are the size and the maximum degree of the network, resp.. Additionally, we improve the best known complexity as well as the best containment radius for this problem under the fair central daemon.

关键词： Matching Self-stabilization Byzantine faults randomized algorithm

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Distributed average consensus in sensor networks with quantized inter-sensor communication

Distributed average consensus in sensor networks with quanti...

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33rd IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Kar, Soummya Moura, Jose M. F. Carnegie Mellon Univ Dept Elect & Comp Engn Pittsburgh PA 15213 USA

ISBN: (纸本)9781424414833

The paper studies distributed average consensus in sensor networks, when the sensors exchange quantized data at each time step. We show that randomizing the exchanged sensor data by adding a controlled amount of dither results in almost sure (a.s.) convergence of the protocol, if the network is connected. We explicitly characterize the mean-squared error (with respect to the desired consensus average) and show that, by tuning certain parameters associated with the protocol, the mean-squared error can be made arbitrarily small. We study the trade-offs between the rate of convergence and the resulting mean-squared error. The sensor network topology plays an important role in determining the convergence rate of the algorithm. Our approach, based on the convergence of controlled Markov processes, is very generic and can be applied to many other situations of imperfect communication. Finally, we present numerical studies, which verify our theoretical results.

关键词： distributed consensus quantized information exchange topology Laplacian randomized algorithm

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Fast Neighborhood Rendezvous 40

Fast Neighborhood Rendezvous

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40th IEEE International Conference on Distributed Computing Systems (ICDCS)

作者： Eguchi, Ryota Kitamura, Naoki Izumi, Taisuke Nagoya Inst Technol Dept Comp Sci Nagoya Aichi Japan

ISBN: (纸本)9781728170022

In the rendezvous problem, two computing entities (called agents) located at different vertices in a graph have to meet at the same vertex. In this paper, we consider the synchronous neighborhood rendezvous problem, where the agents are initially located at two adjacent vertices. While this problem can be trivially solved in O(Delta) rounds (Delta is the maximum degree of the graph), it is highly challenging to reveal whether that problem can be solved in o(Delta) rounds, even assuming the rich computational capability of agents. The only known result is that the time complexity of O(root n) rounds is achievable if the graph is complete and agents are probabilistic, asymmetric, and can use whiteboards placed at vertices. Our main contribution is to clarify the situation (with respect to computational models and graph classes) admitting such a sublinear-time rendezvous algorithm. More precisely, we present two algorithms achieving fast rendezvous additionally assuming bounded minimum degree, unique vertex identifier, and accessibility to neighborhood IDs. The first algorithm runs within (O) over tilde(root n Delta/delta + n/delta) rounds for graphs of the minimum degree larger than root n, where n is the number of vertices in the graph, and delta is the minimum degree of the graph. The second algorithm assumes that the largest vertex ID is O(n), and achieves (O) over tilde (n/root delta)-round time complexity without using whiteboards. These algorithms attain o(Delta)-round complexity in the case of delta = omega(root nlogn) and delta = omega(n(2/3) log(4/3) n) respectively. We also prove that three unconventional assumptions of our algorithm, bounded minimum degree, accessibility to neighborhood IDs, and initial distance one, are all inherently necessary for attaining fast rendezvous. That is, one can obtain the Omega(n)-round lower bound if either one of them is removed.

关键词： rendezvous randomized algorithm sublinear-time algorithm whiteboards

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Partitioned Search with Column Resampling for Locating Array Construction 12

Partitioned Search with Column Resampling for Locating Array...

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12th IEEE International Conference on Software Testing, Verification and Validation (ICST)

作者： Lanus, Erin Colbourn, Charles J. Montgomery, Douglas C. Arizona State Univ Sch Comp Informat & Decis Syst Engn Tempe AZ 85281 USA

ISBN: (纸本)9781728108889

Locating arrays are designs used in combinatorial testing with the property that every set of d t-way interactions appears in a unique set of tests. Using a locating array to conduct fault testing ensures that faulty interactions can be located when there are d or fewer faults. Locating arrays are fairly new and few techniques have been explored for their construction. Most of the available work is limited to finding only one fault. Known general methods require a covering array of strength t+ d and produce many more tests than are needed. We present Partitioned Search with Column Resampling (PSCR), a randomized computational search algorithmic framework to verify if an array is ((d) over bar, t)-locating by partitioning the search space to decrease the number of comparisons. If a candidate array is not locating, random resampling is performed until a locating array is constructed or an iteration limit is reached. Results are compared against known locating array constructions from covering arrays of higher strength and against published results of mixed level locating arrays for parameters of real-world systems. The use of PSCR to build larger locating arrays from a variety of ingredient arrays is explored.

关键词： locating array fault location combinatorial testing randomized algorithm

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Efficient algorithms for Graph Coloring on GPU 24

Efficient Algorithms for Graph Coloring on GPU

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24th IEEE International Conference on Parallel and Distributed Systems (ICPADS)

作者： Nguyen Quang Anh Pham Fan, Rui Nanyang Technol Univ Sch Comp Sci & Engn Singapore Singapore ShanghaiTech Univ Sch Informat Sci & Technol Shanghai Peoples R China

ISBN: (纸本)9781538673089

Graph coloring is an important problem in computer science and engineering with numerous applications. As the size of data increases today, graphs with millions of nodes are becoming commonplace. Parallel graph coloring algorithms on high throughput graphics processing units (GPUs) have recently been proposed to color such large graphs efficiently. We present two new graph coloring algorithms for GPUs which improve upon existing algorithms both in coloring speed and quality. The first algorithm, counting-based Jones-Plassmann (CJP), uses counters to implement the classic Jones-Plassmann parallel coloring heuristic in a work-efficient manner. The second algorithm, conflict coloring (CC) achieves higher parallelism than CJP, and is based on optimistically coloring the graph using estimates of the chromatic number. We compared CC and CJP with two state-of-the-art GPU coloring algorithms, csrcolor [1] and Deveci et al's [2] vertex/edge-based algorithms (which we call VEB), as well as the sequential CPU algorithm ColPack [3]. In terms of coloring quality, CJP and CC are both far better than csrcolor, while CJP uses 10% fewer colors than VEB on average and CC uses 10% more. Compared to ColPack, CJP and CC use 1.3 x and 1.5x more colors on nonbipartite graphs, resp. In terms of speed, CJP is on average 1.5 - 2x faster than the other algorithms, while CC is 2.7 - 4.3x faster.

关键词： graph coloring parallel GPU high performance randomized algorithm

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