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Randomized Algorithms for Determining the Majority on Graphs [chapter]

Gianluca De Marco, Andrzej Pelc
2003 Lecture Notes in Computer Science  
We consider randomized algorithms for this task and establish upper and lower bounds on their expected running time.  ...  Our main contribution are lower bounds showing that some simple and natural algorithms for this problem cannot be improved in general. keywords: graph, majority problem, randomized algorithm.  ...  The simple-majority problem on graphs In this section we show that the simple-majority problem on graphs does not allow efficient randomized algorithms.  ... 
doi:10.1007/978-3-540-45138-9_31 fatcat:5lgvv2o2jbacxmcmfzorg372au

Randomized Algorithms for Determining the Majority on Graphs

GIANLUCA DE MARCO, ANDRZEJ PELC
2006 Combinatorics, probability & computing  
We consider randomized algorithms for this task and establish upper and lower bounds on their expected running time.  ...  Our main contribution are lower bounds showing that some simple and natural algorithms for this problem cannot be improved in general. keywords: graph, majority problem, randomized algorithm.  ...  The simple-majority problem on graphs In this section we show that the simple-majority problem on graphs does not allow efficient randomized algorithms.  ... 
doi:10.1017/s0963548306007644 fatcat:tfxtmhy33vbn3pfiq3ikbzvaae

Bisimplicial edges in bipartite graphs

Matthijs Bomhoff, Bodo Manthey
2013 Discrete Applied Mathematics  
The expected time complexity of our new algorithm is O n 2 log n on random bipartite graphs in which each edge is present with a fixed probability p, a polynomial improvement over the fastest algorithm  ...  We present a new deterministic algorithm to find such edges in bipartite graphs.  ...  However, for random bipartite graphs, our new algorithm performs significantly better.  ... 
doi:10.1016/j.dam.2011.03.004 fatcat:57emx6inmbafxb3y3av6fp5oke

Deconstructing the Structure of Sparse Neural Networks [article]

Maxwell Van Gelder, Mitchell Wortsman, Kiana Ehsani
2020 arXiv   pre-print
We find that even after one epoch the structure is mostly determined, allowing us to propose a more efficient algorithm which does not require dense gradients throughout training.  ...  Finally, for a recent dynamic sparsity algorithm we investigate how early in training the structure emerges.  ...  To determine the robustness of each graph type, we introduce an algorithm for sensitivity analysis on neural graph structures.  ... 
arXiv:2012.00172v1 fatcat:egi6pmin2jef3pfu3r2am4av5a

A Novel Algorithm for Adjacent Vertex-Distinguishing Edge Coloring of Large-scale Random Graphs

Zhao Huanping, Zhu Peijin, Li Jingwen, Shi Huojie
2021 Journal of Engineering Science and Technology Review  
The proposed algorithm provides evidence for solving the shortest path of large-scale random graphs.  ...  Sub-graphs were produced in this work by using a nondestructive segmentation algorithm to reduce the scale of random graphs, and random pre-coloring was performed on the edges of each sub-graph.  ...  Acknowledgements The work was supported by the National Natural Science  ... 
doi:10.25103/jestr.143.08 fatcat:pwvqfevzlna4xmp3yiuoaqm6oy

Efficient identifications of structural similarities for graphs

Zheng Fang, Jie Wang
2012 Journal of combinatorial optimization  
To verify the effectiveness of the RWT algorithm, we use three major graph models, namely, the Erdős-Rényi random graphs, the Watts-Strogatz small-world graphs, and the Barabási-Albert preferential-attachment  ...  We show that the RWT algorithm performs well for graphs generated by these models. Our experiment results agree with the actual similarities of generated graphs.  ...  Weibo Gong at University of Massachusetts Ahmerst for providing motivation of the RWT algorithm.  ... 
doi:10.1007/s10878-012-9505-8 fatcat:iqqllrljxfbbrao73o36bgweem

Page 5481 of Mathematical Reviews Vol. , Issue 98I [page]

1998 Mathematical Reviews  
Consequently, the thickness of this class of graphs can be determined with a planarity testing algorithm in linear time.”  ...  For any given 0<a< 1, e>0, and 4, we give a randomized algorithm which runs in polyno- mial time and which, when applied to any given graph G on n vertices with minimum degree > an, outputs a cut d(S)  ... 

Exploring Complex Graphs by Random Walks

Bosiljka Tadić
2003 AIP Conference Proceedings  
We then explore the graph by intentional random walks using local next-near-neighbor search algorithm to navigate through the graph.  ...  The topological properties such as betweenness are determined by an ensemble of independent walkers and efficiency of the search is compared on three different graph topologies.  ...  , an algorithm that governs a random walk on that graph.  ... 
doi:10.1063/1.1571287 fatcat:kpjl7fmyr5fopk3qw3mmrmdj4e

Fast Sequential Creation of Random Realizations of Degree Sequences

Brian Cloteaux
2016 Internet Mathematics  
Instead, we focus on sequential importance sampling (SIS) schemes for random graph creation. A difficulty with SIS schemes is assuring that they terminate in a reasonable amount of time.  ...  Although fast in practice, the Markov chain Monte Carlo (MCMC) method for selecting a realization has limited usefulness for creating large graphs because of memory constraints.  ...  Also, the author would like to thank Peter Mell, Isabel Beichl and especially the anonymous reviewer for their helpful comments in substantially improving the presentation of the paper.  ... 
doi:10.1080/15427951.2016.1164768 pmid:27499709 pmcid:PMC4971584 fatcat:fjxqpdki4fdjzigryerqtcrgjm

Metric Dimension

Richard Tillquist, Rafael Frongillo, Manuel Lladser
2019 Scholarpedia  
In this manuscript, we provide a concise review of the concept of metric dimension for both deterministic as well as random graphs.  ...  Algorithms to approximate this quantity, as well as potential applications, are also reviewed. This work has been partially funded by the NSF IIS grant 1836914.  ...  The exact formula and polynomial time algorithm for finding minimal resolving sets on trees allow the limiting distribution of β(T n ), the metric dimension of a tree or forest chosen uniformly at random  ... 
doi:10.4249/scholarpedia.53881 fatcat:6nzviv2bt5db3bzntw4sgqe4jq

Local Partition in Rich Graphs [article]

Scott Freitas, Hanghang Tong, Nan Cao, Yinglong Xia
2018 arXiv   pre-print
Because local graph partitioning is primarily focused on the network structure of the graph (vertices and edges), it often fails to consider the additional information contained in the attributes.  ...  the proposed local graph partitioning algorithm (AttriPart) to predict the evolution of local communities (LocalForecasting).  ...  This algorithm can be viewed in three major steps: (1) Compute the walk distribution around seed node q in graph B using random walk with restart (line 2).  ... 
arXiv:1803.05084v1 fatcat:zmlbbfcbafgm3fpvftibr4n5e4

Why Does Collaborative Filtering Work? Recommendation Model Validation and Selection By Analyzing Bipartite Random Graphs

Zan Huang, Daniel D. Zeng
2005 Social Science Research Network  
In this paper, we aim to develop initial understanding of the validation and model/algorithm selection issues based on the graph topological modeling methodology.  ...  Using a simulation approach, we observe the deviations of these topological measures for given recommendation datasets from the expected values for simulated random datasets.  ...  Random Graph and Topological Modeling Methodology The main methodology for investigating the randomness of graphs is random graph theory and related graph topological modeling methods [2] .  ... 
doi:10.2139/ssrn.894029 fatcat:ezcda77crff6blfl3ixqk4faze

Minimum information dominating set for critical sampling over graphs

Jianhang Gao, Qing Zhao, Ananthram Swami
2015 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
For general graphs, we develop algorithms for solving both problems based on the concept of essential differential set.  ...  We focus on two fundamental algorithmic problems: (i) how to determine whether a given subset of vertices is an IDS; (ii) how to construct a minimum IDS.  ...  For general graphs, we develop algorithms for solving both problems based on the concept of essential differential set.  ... 
doi:10.1109/icassp.2015.7178512 dblp:conf/icassp/GaoZS15 fatcat:gfakwniin5gp3drop5qsmtikxi

Evaluating Algorithms for Composable Service Placement in Computer Networks

X. Huang, S. Ganapathy, T. Wolf
2009 2009 IEEE International Conference on Communications  
A major operational challenge in such systems is to determine where to perform the required services along the data path.  ...  In this paper, we present an evaluation of several existing and newly developed heuristic algorithms for solving the problem.  ...  of service step search and two other existing service placement algorithms (randomized mapping and layered graph) on a single platform. • A detailed comparison between all three algorithms to determine  ... 
doi:10.1109/icc.2009.5199007 dblp:conf/icc/HuangGW09 fatcat:25wflilskzdftbwf2wp4bmar5q

Instance Complexity and Unlabeled Certificates in the Decision Tree Model

Tomer Grossman, Ilan Komargodski, Moni Naor, Michael Wagner
2020 Innovations in Theoretical Computer Science  
graph is known to the competing algorithm.  ...  We show that instance optimality depends on the group of permutations in consideration. Our proofs rely on techniques from hypothesis testing and analysis of random graphs.  ...  One of their results determines the query complexity of this problem where one of the graphs is "known" to the algorithm and while allowing two-sided errors (this is in the dense graph model).  ... 
doi:10.4230/lipics.itcs.2020.56 dblp:conf/innovations/GrossmanKN20 fatcat:rxtwwje2h5clrg75ls6z4gq4me
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