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Sparse Quasi-Random Graphs

Fan Chung, Ronald Graham
2002 Combinatorica  
In this paper, we extend our study of quasi-randomness to sparse graphs, i.e., graphs on n vertices with o(n 2 ) edges.  ...  Examples of t-quasi-random graph families There are a variety of constructions for sparse quasi-random graph families which have appeared in the literature. We mention several of these here.  ... 
doi:10.1007/s004930200010 fatcat:24kuyy4j6rdmvovivgqhaexeym

Short paths in quasi-random triple systems with sparse underlying graphs

Joanna Polcyn, Vojtech Rödl, Andrzej Ruciński, Endre Szemerédi
2006 Journal of combinatorial theory. Series B (Print)  
The regularity lemma for 3-uniform hypergraphs asserts that every large hypergraph can be decomposed into a bounded number of quasi-random structures consisting of a sub-hypergraph and a sparse underlying  ...  In this paper we show that in such a quasi-random structure most pairs of the edges of the graph can be connected by hyperpaths of length at most twelve. Some applications are also given.  ...  Another simple consequence of Fact 2.3 deals with the distances in a quasi-random bipartite graph (see [7, 8] ).  ... 
doi:10.1016/j.jctb.2005.12.002 fatcat:3ddqr5xjs5adtikaic24etxj34

Quasi-Randomness and Algorithmic Regularity for Graphs with General Degree Distributions

Noga Alon, Amin Coja-Oghlan, Hiêp Hàn, Mihyun Kang, Vojtěch Rödl, Mathias Schacht
2010 SIAM journal on computing (Print)  
Regarding quasi-randomness, we present a new spectral characterization of low discrepancy, which extends to sparse graphs.  ...  Moreover, a regular partition approximates a given graph by a bounded number of quasi-random graphs.  ...  Related Work Quasi-random graphs. Quasi-random graphs with general degree distributions were first studied by Chung and Graham [7] .  ... 
doi:10.1137/070709529 fatcat:frpc7uxhbbhh5k3ivqubotj57y

Szemerédi's Regularity Lemma for Sparse Graphs [chapter]

Y. Kohayakawa
1997 Foundations of Computational Mathematics  
The quest for an equally powerful variant of this lemma for sparse graphs has not yet been successful, but some progress has been achieved recently.  ...  A remarkable lemma of Szemerédi asserts that, very roughly speaking, any dense graph can be decomposed into a bounded number of pseudorandom bipartite graphs.  ...  We hope that the above applications of the regularity lemma for sparse graphs reveal the potential of such variants of Szemerédi's lemma.  ... 
doi:10.1007/978-3-642-60539-0_16 fatcat:4kqy2jga5baylj6qhxsw53nxr4

A Interlaced Filling Algorithm in Deterministic Constructing Compressed Sensing Matrix

Yang Nie, Xin-Le Yu, Zhan-Xin Yang
2016 International Journal of Signal Processing, Image Processing and Pattern Recognition  
A complete random sensing matrix has the drawbacks of large storage and high complexity in its implementation.  ...  In this paper, we propose an interlaced filling algorithm to construct the sensing matrix, which has a quasi-cyclic structure for efficient hardware implementation.  ...  Sparse random matrix is constructed with a random way and its column weight is 5 and 6 respectively. We adopt interlaced filling algorithm to construct the sensing matrix.  ... 
doi:10.14257/ijsip.2016.9.10.13 fatcat:5nsswbzh6bfy7krthr3uvuxhei

Page 2341 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
quasi-random graphs.  ...  The generally accepted notion of quasi-randomness in graphs of density p, namely that the discrepancy |e(G[S]) — p('s!)  ... 

From Quasirandom graphs to Graph Limits and Graphlets [article]

Fan Chung
2013 arXiv   pre-print
We generalize the notion of quasirandom which concerns a class of equivalent properties that random graphs satisfy.  ...  We then consider several families of graphlets and, in particular, we characterize graphlets with low ranks for both dense and sparse graphs.  ...  Quasi-random graphlets Originally, quasi-randomness is an equivalent class of graph properties that are shared by random graphs (see [19] ).  ... 
arXiv:1203.2269v7 fatcat:tjzv34u22zduxix7hd2fzasqau

From quasirandom graphs to graph limits and graphlets

Fan Chung
2014 Advances in Applied Mathematics  
We generalize the notion of quasirandomness which concerns a class of equivalent properties that random graphs satisfy.  ...  We then consider several families of graphlets and, in particular, we characterize quasirandom graphlets with low ranks for both dense and sparse graphs.  ...  Quasi-random graphlets Originally, quasi-randomness is an equivalent class of graph properties that are shared by random graphs (see [19] ).  ... 
doi:10.1016/j.aam.2013.10.002 fatcat:m4g64y7kwzhozefurjixtxi3xu

Massive Quasi-Clique Detection [chapter]

James Abello, Mauricio G. C. Resende, Sandra Sudarsky
2002 Lecture Notes in Computer Science  
We describe techniques that are useful for the detection of dense subgraphs (quasi-cliques) in massive sparse graphs whose vertex set, but not the edge set, fits in RAM.  ...  The algorithms rely on efficient semi-external memory algorithms used to preprocess the input and on greedy randomized adaptive search procedures (GRASP) to extract the dense subgraphs.  ...  We present here an approach for discovering large dense subgraphs (quasi-cliques) in such large sparse multi-digraphs with millions of vertices and edges.  ... 
doi:10.1007/3-540-45995-2_51 fatcat:olursfbshzdnnlfipb2qk2rlzm

Convex Formulation for Planted Quasi-Clique Recovery [article]

Sakirudeen A. Abdulsalaam, M. Montaz Ali
2021 arXiv   pre-print
We propose a convex formulation using nuclear norm minimization for planted quasi-clique recovery.  ...  The maximum quasi-clique problem is applicable in community detection, information retrieval and biology.  ...  Table 5 : 5 Quasi-cliqe recovery from random graph  ... 
arXiv:2109.08902v1 fatcat:atrpuikipfa5pktcgts75kfcba

Page 9596 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
This paper extends the above work to sparse quasi-random graphs, i.e. random graphs in which every edge exists with the probability p = o(1).  ...  Thus, any of these properties can be used to define a quasi-random graph, 1.e. a graph that possesses many of the properties of almost all graphs.  ... 

Page 5298 of Mathematical Reviews Vol. , Issue 94i [page]

1994 Mathematical Reviews  
[Stewart, David Edward] (5-ANUM-AD; Canberra) An efficient procedure for computing quasi-stationary distributions of Markov chains with sparse transition structure. (English summary) Ady. in Appl.  ...  The emphasis is on random walks whose transition probabilities are adapted to the graph’s structure, random walks on (the Cayley graph of) groups being treated as a special case.  ... 

Measurement Matrix Construction Algorithm for Compressed Sensing based on QC-LDPC Matrix

NIE Yang, JING Li-li
2016 International Journal of Grid and Distributed Computing  
In this paper, we use the sparse characteristic of parity-check matrix of LDPC codes, construct measurement matrix based on QC-LDPC (Quasi-cyclic low-density parity-check) matrix, which is a structural  ...  and sparse deterministic measurement matrix.  ...  In this paper, we propose a construction method of deterministic measurement matrix for compressed sensing by the sparse and quasi-cycle of QC-LDPC parity check matrix.  ... 
doi:10.14257/ijgdc.2016.9.2.11 fatcat:iyg465vqwzd4hgaa4icc6zpafy

Empirical Evaluation of Approximation Algorithms for Generalized Graph Coloring and Uniform Quasi-Wideness

Wojciech Nadara, Marcin Pilipczuk, Roman Rabinovich, Felix Reidl, Sebastian Siebertz, Marc Herbstritt
2018 Symposium on Experimental and Efficient Algorithms  
ACM Subject Classification Theory of computation → Graph algorithms analysis Keywords and phrases Empirical Evaluation of Algorithms, Sparse Graph Classes, Generalized Coloring Numbers, Uniform Quasi-Wideness  ...  of being uniformly quasi-wide.  ...  Random planar graphs.  ... 
doi:10.4230/lipics.sea.2018.14 dblp:conf/wea/NadaraPRRS18 fatcat:rgg7eula4vc3nateu6opp3t34i

Robust Sparse Recovery with Sparse Bernoulli matrices via Expanders [article]

Pedro Abdalla
2022 arXiv   pre-print
In particular, random matrices formed by i.i.d Bernoulli p random variables are of practical relevance in the context of nonnegative sparse recovery.  ...  Sparse binary matrices are of great interest in the field of compressed sensing.  ...  Moreover, if G is a random graph sampled uniformly at random among all left dregular bipartite graphs with n left nodes and m right vertices, then with probability 1 − ε, G is a (s, d, θ)-lossless expander  ... 
arXiv:2112.14148v2 fatcat:l62pyces45hybm3wfvwfnbg6iy
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