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The Existence and Efficient Construction of Large Independent Sets in General Random Intersection Graphs
[chapter]
2004
Lecture Notes in Computer Science
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We investigate the existence and efficient algorithmic construction of close to optimal independent sets in random models of intersection graphs. ...
(c) We then propose and analyse three algorithms for the efficient construction of large independent sets in this model. ...
Karoński and K.B. Singer-Cohen for informing us about their work in random intersection graphs and providing useful material. ...
doi:10.1007/978-3-540-27836-8_86
fatcat:ueopb6wjxbf7rakuevvoa3b4la
Large independent sets in general random intersection graphs
2008
Theoretical Computer Science
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We investigate the existence and efficient algorithmic construction of close to optimal independent sets in random models of intersection graphs. ...
(c) We then propose and analyse three algorithms for the efficient construction of large independent sets in this model. ...
Karoński and K.B. Singer-Cohen for informing us about their work in random intersection graphs and providing useful material. ...
doi:10.1016/j.tcs.2008.06.047
fatcat:nyxt22ij2zccvkgbl5usmmgdym
A spectral algorithm for finding maximum cliques in dense random intersection graphs
[article]
2022
arXiv
pre-print
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In a random intersection graph G_n,m,p, each of n vertices selects a random subset of a set of m labels by including each label independently with probability p and edges are drawn between vertices that ...
, especially in the dense regime, thus suggesting that spectral properties of random intersection graphs may be also used to construct efficient algorithms for other NP-hard graph theoretical problems ...
.: Maximum cliques in graphs with small intersection number and random intersection graphs. ...
arXiv:2210.02121v1
fatcat:jscb3xzpqjfmvlzg2voyjimysa
Random matroids
1980
Proceedings of the twelfth annual ACM symposium on Theory of computing - STOC '80
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We introduce a new random structure generalizing matroids. These random matroid8 allow us to develop general techniques for solving hard combinatorial optimization problems with random inputs. i. ...
Acknowledgments We wish to thank Andy Langer, Allen Emerson, and Christos Papadimitriou for their helpful suggestions and spirited discussions on these topics.
Bibliography ...
In contrast, ~itney matro~ds are not cZos~d under intersection. The problem of constructing a maximal independent set in the intersection of k. ...
doi:10.1145/800141.804688
dblp:conf/stoc/ReifS80
fatcat:2zw67byzu5gezhummh7vlvtfhu
Computing convex quadrangulations
2012
Discrete Applied Mathematics
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We use projected Delaunay tetrahedra and a maximum independent set approach to compute large subsets of convex quadrangulations on a given set of points in the plane. ...
On the other hand, quadrangulations may be the mesh of choice in certain applications, including finite-element generation [14, 18] and scattered bivariate data analysis [15] . ...
(3D) Delaunay tetrahedra [1, 9] , and then construct an independent set [12] in their intersection graph. ...
doi:10.1016/j.dam.2011.11.002
pmid:22389540
pmcid:PMC3277885
fatcat:33x3qbctkncejosivwcdmwtvae
Page 1285 of Mathematical Reviews Vol. , Issue 99b
[page]
1991
Mathematical Reviews
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Further, we give an efficient algorithm for constructing such decision trees when the models are given as a set of polygons in the plane. ...
We first study the expected size of the intersection between a random Voronoi diagram and a generic geometric object that consists of a finite collection of line segments in the plane. ...
Randomness and Pseudo-Randomness in Discrete Mathematics
[chapter]
1998
PROGRESS IN MATHEMATICS
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In several cases the probabilistic proof provides such a randomized efficient algorithm, and in other cases the task of finding such an algorithm requires additional ideas. ...
Once an efficient randomized algorithm is found, it is sometimes possible to derandomize it and convert it into an efficient deterministic one. ...
Another Ramsey-type question mentioned in subsection 1.2 deals with the existence of large triangle-free graphs with no large independent sets. ...
doi:10.1007/978-3-0348-8974-2_1
fatcat:j6bavkgixvbspapsnbt47hf75m
Maximum Cliques in Graphs with Small Intersection Number and Random Intersection Graphs
[article]
2012
arXiv
pre-print
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In particular, we consider the maximum clique problem for graphs with small intersection number and random intersection graphs (a model in which each one of m labels is chosen independently with probability ...
This theorem generalizes and strengthens other related results in the state of the art, but also broadens the range of values considered. ...
Other applications include oblivious resource sharing in a (general) distributed setting, efficient and secure communication in sensor networks [16] , interactions of mobile agents traversing the web ...
arXiv:1204.4054v1
fatcat:suktbu7vkvcvhftkkfbakepv2i
Random Forest Clustering and Application to Video Segmentation
2009
Procedings of the British Machine Vision Conference 2009
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This paper considers the problem of clustering large data sets in a high-dimensional space. Using a random forest, we first generate multiple partitions of the same input space, one per tree. ...
The proposed algorithm is able to capture non-convex structure while being computationally efficient, capable of dealing with large data sets. ...
An example of intersection (compact partition) is shown in green. quent graph construction allows the application of efficient graph clustering methods, which in the case of video segmentation needs to ...
doi:10.5244/c.23.100
dblp:conf/bmvc/PerbetSM09
fatcat:ob2ll4lkyvcwjnsl7wviuya7sy
Communication aspects of networks based on geometric incidence relations
1989
Theoretical Computer Science
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Stated in graph-theoretic terms it is the (d, D&graph problem: how many vertices can a (8, D) For a survey on methods for the construction of large (d, D) -graphs refer to [20] . ...
and A is a set of elements in some level s and A* the set of elements connected to A in the next level. ...
Brebner and Valiant [25] prove it in a general setting using only the following network properties: Obliviousness, Symmetry and Non-Repetitiveness. For our case Symmetry was established in Lemma 2. ...
doi:10.1016/0304-3975(89)90099-6
fatcat:evz6lbq3lvaw3kegqronq32gse
Efficiently covering complex networks with cliques of similar vertices
2006
Theoretical Computer Science
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We describe a polynomial time algorithm for covering graphs with cliques, prove its asymptotic optimality in a random intersection graph model and present experimental results on complex real-world networks ...
Note added in proof Our greedy algorithm can also be used to suggest a value for the size of the largest clique in a random intersection graph. ...
Acknowledgements We would like to thank the authors of [4, 7, 9] for generous access to their databases. ...
doi:10.1016/j.tcs.2005.12.005
fatcat:i523bnizsng6lgxebypslyy5se
Maximum Cliques in Graphs with Small Intersection Number and Random Intersection Graphs
[chapter]
2012
Lecture Notes in Computer Science
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In particular, we consider the maximum clique problem for graphs with small intersection number and random intersection graphs (a model in which each one of m labels is chosen independently with probability ...
This theorem generalizes and strengthens other related results in the state of the art, but also broadens the range of values considered (see e.g. [21] and [4]). ...
Other applications include oblivious resource sharing in a (general) distributed setting, efficient and secure communication in sensor networks [17] , interactions of mobile agents traversing the web ...
doi:10.1007/978-3-642-32589-2_63
fatcat:3qws5xyrrre5fgoxak5sy3ftga
A Dichotomy for Local Small-Bias Generators
2015
Journal of Cryptology
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As a secondary contribution, we give evidence in support of the view that small bias is a good measure of pseudorandomness for local functions with large stretch. ...
Following the works of Cryan and Miltersen (MFCS '01) and by Mossel et al (FOCS '03), we ask: which graphs and predicates yield "small-bias" generators (that fool linear distinguishers)? ...
Fooling Heavy Tests In this section we show that if the predicate P is non-linear and the graph G has large sets of "independent" hyperedges, the function f G,P fools linear tests of weight larger than ...
doi:10.1007/s00145-015-9202-8
fatcat:fg5ccijdujhlvaza6hi7z34iyu
A Dichotomy for Local Small-Bias Generators
[chapter]
2012
Lecture Notes in Computer Science
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The file type is application/pdf.
As a secondary contribution, we give evidence in support of the view that small bias is a good measure of pseudorandomness for local functions with large stretch. ...
Following the works of Cryan and Miltersen (MFCS '01) and by Mossel et al (FOCS '03), we ask: which graphs and predicates yield "small-bias" generators (that fool linear distinguishers)? ...
Fooling Heavy Tests In this section we show that if the predicate P is non-linear and the graph G has large sets of "independent" hyperedges, the function f G,P fools linear tests of weight larger than ...
doi:10.1007/978-3-642-28914-9_34
fatcat:5oncloneerh3xik5lo5la3bjiy
The Exact Complexity of Pseudorandom Functions and Tight Barriers to Lower Bound Proofs
[article]
2021
IACR Cryptology ePrint Archive
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Perhaps surprisingly, we prove extremely tight upper and lower bounds in various circuit models. • In general B 2 circuits, assuming the existence of PRFs, PRFs can be constructed in 2n + o(n) size, simplifying ...
We show that such construction is almost optimal by giving an unconditional 2n − O(1) lower bound. • In logarithmic depth circuits, assuming the existence of NC 1 PRFs, PRFs can be constructed in 2n + ...
Acknowledgement We are greatly thankful to Yilei Chen for his support throughout this project and providing lots of useful comments. We also thank Lijie Chen and Ryan Williams for useful discussion. ...
dblp:journals/iacr/FanL021
fatcat:6k5d5ucoizh3bjbydxhlpwqvw4
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