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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...

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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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Maximization of k-Submodular Function with a Matroid Constraint 17th

Maximization of k-Submodular Function with a Matroid Constra...

引用

17th Annual Conference on Theory and Applications of Models of Computation (TAMC)

作者： Sun, Yunjing Liu, Yuezhu Li, Min Shandong Normal Univ Sch Math & Stat Jinan 250014 Peoples R China

ISBN: (纸本)9783031203497;9783031203503

A k-submodular function is a promotion of a submodular function, whose domain is composed of k disjoint subsets rather than a single subset. In this paper, we give a deterministic algorithm for the non-monotone k-submodular function maximization problem subject to a matroid constraint with approximation factor 1/3. Based on this result, we give a randomized 1/3-approximation algorithm for the problem with faster running time, but the probability of success is (1- e). And we obtain that the complexity of deterministic algorithm and random algorithm is O(N vertical bar D vertical bar(p+ kq)) and O(vertical bar D vertical bar(p log N/epsilon(1) + kq log N/epsilon(2)) logN) respectively, where D is the ground set of the matroid constraint with rank N, p is times of oracle to calculate whether a set is an independent set in this matroid, q is the times of oracle to calculate a value of the k-submodular function, and epsilon, epsilon(1), epsilon(2) are positive parameters with e = max{epsilon(1), epsilon(2)}.

关键词： k-submodular function Matroid constraint Deterministic algorithm randomized algorithm

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NearlyWork-Efficient Parallel algorithm for Digraph Reachability 2018

NearlyWork-Efficient Parallel Algorithm for Digraph Reachabi...

引用

50th Annual ACM SIGACT Symposium on the Theory of Computing (STOC)

作者： Fineman, Jeremy T. Georgetown Univ Washington DC 20057 USA

ISBN: (纸本)9781450355599

One of the simplest problems on directed graphs is that of identifying the set of vertices reachable from a designated source vertex. This problem can be solved easily sequentially by performing a graph search, but efficient parallel algorithms have eluded researchers for decades. For sparse high-diameter graphs in particular, there is no known work-efficient parallel algorithm with nontrivial parallelism. This amounts to one of the most fundamental open questions in parallel graph algorithms: Is there a parallel algorithm for digraph reachability with nearly linear work? This paper shows that the answer is yes. This paper presents a randomized parallel algorithm for digraph reachability and related problems with expected work (O) over tilde (m) and span (Omega) over tilde (n(2/3)), and hence parallelism (Omega) over tilde (m/n(2/3)) = (Omega) over tilde (n(1/3)), on any graph with n vertices and m arcs. This is the first parallel algorithm having both nearly linear work and strongly sublinear span, i.e., span (Omega) over tilde (n(1-epsilon)) for any constant epsilon > 0. The algorithm can be extended to produce a directed spanning tree, determine whether the graph is acyclic, topologically sort the strongly connected components of the graph, or produce a directed ear decomposition, all with work (O) over tilde (m) and span (O) over tilde (n(2/3)). The main technical contribution is an efficient Monte Carlo algorithm that, through the addition of (O) over tilde (n) shortcuts, reduces the diameter of the graph to (Omega) over tilde (n(2/3)) with high probability. While both sequential and parallel algorithms are known with those combinatorial properties, even the sequential algorithms are not efficient, having sequential runtime (Omega) over tilde (m (1)). This paper presents a surprisingly simple sequential algorithm that achieves the stated diameter reduction and runs in O(m) time. Parallelizing that algorithm yields the main result, but doing so involves overcomi

关键词： Parallel algorithm randomized algorithm graph search reachability shortcuts

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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...

引用

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...

引用

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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Computation of probabilistic output admissible set for time-varying uncertain constrained system

Computation of probabilistic output admissible set for time-...

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SICE-ICASE International Joint Conference

作者： Hatanaka, Takeshi Takaba, Kiyotsugu Kyoto Univ Dept Appl Math & Phys Kyoto 6068501 Japan JSPS Tokyo Japan

ISBN: (纸本)9788995003848

This paper considers time-varying uncertain constrained systems, and develops a method for computing a probabilistic output admissible (POA) set which consists of initial states probabilistically assured to satisfy the infinitetime constraint. The algorithm for the time-invariant case has already been presented in Hatanaka and Takaba (2006). This paper shows how this algorithm is extended to the time-varying case when an upper bound of a number called future output admissibility (FOA) index is available. We moreover present two methods for computing an upper bound of the FOA index;probabilistic and deterministic methods.

关键词： constrained system uncertainty maximal output admissible set 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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