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Random Walks: A Review of Algorithms and Applications

Feng Xia, Jiaying Liu, Hansong Nie, Yonghao Fu, Liangtian Wan, Xiangjie Kong
2019 IEEE Transactions on Emerging Topics in Computational Intelligence  
In this paper, we aim to provide a comprehensive review of classical random walks and quantum walks.  ...  We first review the knowledge of classical random walks and quantum walks, including basic concepts and some typical algorithms.  ...  Spitzer [2] gives a complete review of random walks for mathematical researchers and clearly presents the mathematical principles of random walks.  ... 
doi:10.1109/tetci.2019.2952908 fatcat:kdgnz5odunbw7dknnrplvkchzy

Quantum random walks without walking

K. Manouchehri, J. B. Wang
2009 Physical Review A. Atomic, Molecular, and Optical Physics  
Quantum random walks have received much interest due to their non-intuitive dynamics, which may hold the key to a new generation of quantum algorithms.  ...  We present a scheme for walking on arbitrarily complex graphs, which can be realized using a variety of quantum systems such as a BEC trapped inside an optical lattice.  ...  Whilst the so called classical random walks have been successfully utilized in such a diverse range of applications, quantum random walks are expected to provide us with a new paradigm for solving many  ... 
doi:10.1103/physreva.80.060304 fatcat:7ewsm4p4cbbvbcxixxojlu7hya

Recommending random walks

Zachary M. Saul, Vladimir Filkov, Premkumar Devanbu, Christian Bird
2007 Proceedings of the the 6th joint meeting of the European software engineering conference and the ACM SIGSOFT symposium on The foundations of software engineering - ESEC-FSE '07  
We use a random-walk approach, mimicking the more focused behavior of a developer, who browses the caller-callee links in the callgraph of a large program, seeking routines that are likely to be related  ...  Inspired by Kleinberg's work[10], we approximate the steady-state of an infinite random walk on a subset of a callgraph in order to rank the functions by their steady-state probabilities.  ...  New random-walk algorithm: We introduce a fast, simple, accurate algorithm, called FRAN (Finding with RANdom walks) that is based on the steady state of a random walk on the callgraph neighborhood (inspired  ... 
doi:10.1145/1287624.1287629 dblp:conf/sigsoft/SaulFDB07 fatcat:arcutyhhy5ebbooug2c7syd4le

Simulation optimization: a review of algorithms and applications

Satyajith Amaran, Nikolaos V. Sahinidis, Bikram Sharda, Scott J. Bury
2015 Annals of Operations Research  
approaches used, reviews some of the diverse applications that have been tackled by these methods, and speculates on future directions in the field.  ...  To address specific features of a particular simulation---discrete or continuous decisions, expensive or cheap simulations, single or multiple outputs, homogeneous or heterogeneous noise---various algorithms  ...  A review of random search methods is presented in [8, 149] .  ... 
doi:10.1007/s10479-015-2019-x fatcat:basfhipyijbwdaiajbhyb4v65y

Simulation optimization: a review of algorithms and applications

Satyajith Amaran, Nikolaos V. Sahinidis, Bikram Sharda, Scott J. Bury
2014 4OR  
approaches used, reviews some of the diverse applications that have been tackled by these methods, and speculates on future directions in the field.  ...  To address specific features of a particular simulation-discrete or continuous decisions, expensive or cheap simulations, single or multiple outputs, homogeneous or heterogeneous noise-various algorithms  ...  A review of random search methods is presented in and Ólafsson (2006) .  ... 
doi:10.1007/s10288-014-0275-2 fatcat:vhxf65lcpvhibgka3fm7q2avfu

Accelerating Random Walks [chapter]

Wei Wei, Bart Selman
2002 Lecture Notes in Computer Science  
Some of the most successful procedures combine a form of random walk with a greedy bias.  ...  We introduce a technique that leads to significant speedups of random walk style procedures on structured problem domains.  ...  Acknowledgements We thank Carla Gomes and Henry Kautz for useful discussions. This research was supported with grants from AFOSR, DARPA, NSF, and the Alfred P. Sloan Foundation.  ... 
doi:10.1007/3-540-46135-3_15 fatcat:4m5bapgxrjekjmcvir3jwret6e

Implementing the quantum random walk

B. C. Travaglione, G. J. Milburn
2002 Physical Review A. Atomic, Molecular, and Optical Physics  
Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle.  ...  Here, we propose a scheme to implement the quantum random walk on a line and on a circle in an ion trap quantum computer.  ...  For a review of the theory and applications for random walks, see for example Barber and Ninham ͓5͔.  ... 
doi:10.1103/physreva.65.032310 fatcat:tij6yrs46nhwzkfpi5fdnrs2ue

Random walks based modularity

Robin Devooght, Amin Mantrach, Ilkka Kivimäki, Hugues Bersini, Alejandro Jaimes, Marco Saerens
2014 Proceedings of the 23rd international conference on World wide web - WWW '14  
Indeed, recent studies have shown restrictions of optimizing modularity, for instance its resolution limit. We introduce here a novel, formal and welldefined modularity measure based on random walks.  ...  Quantifying the statistical surprise in the arrangement of the edges of the network has led to simple and powerful algorithms.  ...  Part of this work has been funded by the European Union 7th Framework Programme ARCOMEM and Social Sensor projects, by the Spanish Centre for the Development of Industrial Technology under the CENIT program  ... 
doi:10.1145/2566486.2567986 dblp:conf/www/DevooghtMKBJS14 fatcat:tjdwcrvyirfotaal4cgdxegml4

Quantum stochastic walks: A generalization of classical random walks and quantum walks

James D. Whitfield, César A. Rodríguez-Rosario, Alán Aspuru-Guzik
2010 Physical Review A. Atomic, Molecular, and Optical Physics  
QSWs provide a new framework to the study of quantum algorithms as well as of quantum walks with environmental effects.  ...  We show how the family of possible QSWs encompasses both the classical random walk (CRW) and the quantum walk (QW) as special cases, but also includes more general probability distributions.  ...  Many classical algorithms, such as most Markov-chain Monte Carlo algorithms, are based on classical random walks (CRW), a probabilistic motion through the vertices of a graph.  ... 
doi:10.1103/physreva.81.022323 fatcat:la2ra2qcmbayljqvxxcstjxwii

Random Walk-steered Majority Undersampling [article]

Payel Sadhukhan, Arjun Pakrashi, Brian Mac Namee
2021 arXiv   pre-print
Random walk, a powerful tool for perceiving the proximities of connected points in a graph, is used to identify the majority points which lie close to the minority class of a class-imbalanced dataset.  ...  In this work, we propose Random Walk-steered Majority Undersampling (RWMaU), which undersamples the majority points of a class imbalanced dataset, in order to balance the classes.  ...  .: Learning from class-imbalanced data: Review of methods and applications. Expert Systems with Applications 73, 220-239 (2017) 11.  ... 
arXiv:2109.12423v1 fatcat:7ybtbok4a5befb6innpvpinqvu

Aperiodic Quantum Random Walks

P. Ribeiro, P. Milman, R. Mosseri
2004 Physical Review Letters  
We generalize the quantum random walk protocol for a particle in a one-dimensional chain, by using several types of biased quantum coins, arranged in aperiodic sequences, in a manner that leads to a rich  ...  In contrast, random sequences leads to diffusive spreading, similar to the classical random walk behaviour. We also describe how to experimentally implement these aperiodic sequences.  ...  Aslangul and J. Vidal for several and fruitful discussions and comments  ... 
doi:10.1103/physrevlett.93.190503 pmid:15600819 fatcat:lyevzj5sejgf5hoblgud5q5gr4

Relation between random walks and quantum walks

Stefan Boettcher, Stefan Falkner, Renato Portugal
2015 Physical Review A. Atomic, Molecular, and Optical Physics  
Based on studies on four specific networks, we conjecture a general relation between the walk dimensions d_w of discrete-time random walks and quantum walks with the (self-inverse) Grover coin.  ...  As in the classical case, the solution ρ(x,t) in space and time of this quantum walk equation exhibits a scaling collapse for a variable x^d_w/t in the weak limit, which defines d_w and illuminates fundamental  ...  of many classic textbooks on random walks and diffusion [10, 22] .  ... 
doi:10.1103/physreva.91.052330 fatcat:4q7wi4uyl5etlohrhd6s2wtqwi

Random Walks for Image Segmentation

L. Grady
2006 IEEE Transactions on Pattern Analysis and Machine Intelligence  
Given a small number of pixels with user-defined (or pre-defined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach  ...  This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary  ...  Therefore, we limit our review to supervised and/or graph-based algorithms. Additional work on random walks and combinatorial harmonic functions will also be discussed. A.  ... 
doi:10.1109/tpami.2006.233 pmid:17063682 fatcat:yahgsrydurasbnpuzhzqxorpqa

Random Walks in Hypergraph

Abdelghani Bellaachia, Mohammed Al-Dhelaan
2021 International Journal of Education and Information Technologies  
We study and analyze our generalized form of random walks suitable for the structure of hypergraphs.  ...  Random walks on graphs have been extensively used for a variety of graph-based problems such as ranking vertices, predicting links, recommendations, and clustering.  ...  ACKNOWLEDGMENT The second author would like to acknowledge the full scholarship and financial support by King Saud University, Riyadh, Saudi Arabia.  ... 
doi:10.46300/9109.2021.15.2 fatcat:dczbocmggfeh5dt3lvx4wsnf6m

TTLed Random Walks for Collaborative Monitoring

Yaniv Altshuler, Shlomi Dolev, Yuval Elovici, Nadav Aharony
2010 2010 INFOCOM IEEE Conference on Computer Communications Workshops  
In compliance with the instruction of the TPP algorithm, the movement of the agents is done according to the random walk algorithm.  ...  Short random walks have been used in the past, albeit for different tasks [5] .  ... 
doi:10.1109/infcomw.2010.5466697 fatcat:24cxhsa52rh6rnupgq4plqrsuu
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