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Finding large independent sets of hypergraphs in parallel

Hadas Shachnai, Aravind Srinivasan
2001 Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures - SPAA '01  
A basic problem in hypergraphs is that of finding a large independent set-one of guaranteed size-in a given hypergraph.  ...  Understanding the parallel complexity of this and related independent set problems on hypergraphs is a fundamental open issue in parallel computation. Caro and Tuza (J.  ...  We would like to develop a parallel algorithm that finds an IS of size α k (H) for k-uniform hypergraphs with any k ≥ 2. We also aim to find large independent sets in non-uniform hypergraphs.  ... 
doi:10.1145/378580.378622 dblp:conf/spaa/ShachnaiS01 fatcat:qmf5q65itbgu5gurwp3j7xdwxu

Exploiting a Hypergraph Model for Finding Golomb Rulers [chapter]

Manuel Sorge, Hannes Moser, Rolf Niedermeier, Mathias Weller
2012 Lecture Notes in Computer Science  
In particular, we consider a natural hypergraph characterization of rulers and investigate the construction and structure of the corresponding hypergraphs.  ...  Apart from providing missing proofs, the major changes in this article are extended observations on the structure of the considered hypergraphs, a partial improvement in the running time of the data reduction  ...  Acknowledgments We thank Falk Hüffner for assistance with Subsection 3.3 and we are grateful to anonymous referees for their valuable feedback leading to significant improvements of the presentation.  ... 
doi:10.1007/978-3-642-32147-4_33 fatcat:pn622gag6jb7rgjir4swxrfcl4

Exploiting a hypergraph model for finding Golomb rulers

Manuel Sorge, Hannes Moser, Rolf Niedermeier, Mathias Weller
2014 Acta Informatica  
In particular, we consider a natural hypergraph characterization of rulers and investigate the construction and structure of the corresponding hypergraphs.  ...  Apart from providing missing proofs, the major changes in this article are extended observations on the structure of the considered hypergraphs, a partial improvement in the running time of the data reduction  ...  Acknowledgments We thank Falk Hüffner for assistance with Subsection 3.3 and we are grateful to anonymous referees for their valuable feedback leading to significant improvements of the presentation.  ... 
doi:10.1007/s00236-014-0202-1 fatcat:rf3trewv3fcy5nx6ibrr43zh4i

Scalable Graph Algorithms [article]

Christian Schulz
2019 arXiv   pre-print
In order to find these patterns, massive amounts of data have to be acquired and processed.  ...  In general, this research is based on four pillars: multilevel algorithms, practical kernelization, parallelization and memetic algorithms that are highly interconnected.  ...  While the grants are acknowledged in the individual papers, we also acknowledge them here.  ... 
arXiv:1912.00245v1 fatcat:mop2e6pqtnbr7irkrakraael6a

A global parallel algorithm for enumerating minimal transversals of geometric hypergraphs

Khaled Elbassioni, Imran Rauf, Saurabh Ray
2019 Theoretical Computer Science  
We apply this decomposition framework to get incremental polynomial-time algorithms for finding minimal hitting sets and minimal set covers for a number of hypergraphs induced by a set of points and a  ...  A distinguishing feature of the algorithms we obtain is that they admit an efficient global parallel implementation, in the sense that all minimal hitting sets can be generated in polylogarithmic time  ...  3/2 ) processors to compute a maximal independent set (complement of a minimal transversal, in the case of explicitly given hypegraphs) of an independence system given by an oracle on n vertices.  ... 
doi:10.1016/j.tcs.2018.09.027 fatcat:wrb6l5li6fdtpeeoekpzf5pave

Distributed Algorithms for Matching in Hypergraphs [article]

Oussama Hanguir, Clifford Stein
2020 arXiv   pre-print
In this paper we are interested in the problem of finding matchings in hypergraphs in the massively parallel computation (MPC) model that is a common abstraction of MapReduce-style computation.  ...  We study the d-Uniform Hypergraph Matching (d-UHM) problem: given an n-vertex hypergraph G where every hyperedge is of size d, find a maximum cardinality set of disjoint hyperedges.  ...  In this work, we are interested in the problem of finding matchings in very large hypergraphs, large enough that we cannot solve the problem on one computer.  ... 
arXiv:2009.09605v1 fatcat:v7y2ldxi4fgbbjegtcubsjnzia

AN EFFICIENT INCREMENTAL ALGORITHM FOR GENERATING ALL MAXIMAL INDEPENDENT SETS IN HYPERGRAPHS OF BOUNDED DIMENSION

E. BOROS, V. GURVICH, K. ELBASSIONI, L. KHACHIYAN
2000 Parallel Processing Letters  
We show that for hypergraphs of bounded edge size, the problem of extending a given list of maximal independent sets is N C-reducible to the computation of an arbitrary maximal independent set for an induced  ...  Our objective in this note is to show that for hypergraphs of bounded dimension, problem M IS(A, I) can be efficiently solved in parallel: Theorem 1 M IS(A, I) ∈ N C for dim(A) ≤ 3, and M IS(A, I) ∈ RN  ...  Introduction Let A ⊆ 2 V be a hypergraph (set family) on a finite vertex set V. A vertex set I ⊆ V is called independent if I contains no hyperedge of A.  ... 
doi:10.1142/s0129626400000251 fatcat:yg6gg7zjsvcgxazmwctrr73pk4

On Computing Maximal Independent Sets of Hypergraphs in Parallel [article]

Ioana O. Bercea, Navin Goyal, David G. Harris, Aravind Srinivasan
2014 arXiv   pre-print
Whether or not the problem of finding maximal independent sets (MIS) in hypergraphs is in (R)NC is one of the fundamental problems in the theory of parallel computing.  ...  It is known that the problem is in RNC when the edges of the hypergraph have constant size.  ...  Harris and Aravind Srinivasan were supported in part by NSF Award CNS-1010789.  ... 
arXiv:1405.1133v2 fatcat:u7agcq4xurextoltyc3ld6bvae

COMPUTATIONAL COMPLEXITY OF THE PERFECT MATCHING PROBLEM IN HYPERGRAPHS WITH SUBCRITICAL DENSITY

MAREK KARPIŃSKI, ANDRZEJ RUCIŃSKI, EDYTA SZYMAŃSKA
2010 International Journal of Foundations of Computer Science  
In addition, we consider parallel complexity of the problem, which could be also of independent interest.  ...  In this paper we consider the computational complexity of deciding the existence of a perfect matching in certain classes of dense k-uniform hypergraphs.  ...  The properties of these algorithms are presented in the following theorems. The first of them provides a parallel algorithm which finds an r-deficient matching for large r, but relatively small δ.  ... 
doi:10.1142/s0129054110007635 fatcat:abk4o645onhyjfgdp2fom3xobe

Exact and approximate route set generation for resilient partial observability in sensor location problems

Marco Rinaldi, Francesco Viti
2017 Transportation Research Part B: Methodological  
Thanks to the route sets found by our approach, we are able to find full observability solutions characterized by a small number of sensors, while yet being efficient also in terms of partial observability  ...  In particular, we propose exact and heuristic solutions for identifying the optimal route sets such that no other route would include any additional information for finding optimal full and partial observability  ...  an increasing amount of links, up to a value of | | 12 L  , beyond which memory requirements become too large to be accommodated with the available hardware (parallelization of hypergraph construction  ... 
doi:10.1016/j.trb.2017.08.007 fatcat:axlpfegibze5znwi7satitihxm

On computing maximal independent sets of hypergraphs in parallel

Ioana O. Bercea, Navin Goyal, David G. Harris, Aravind Srinivasan
2014 Proceedings of the 26th ACM symposium on Parallelism in algorithms and architectures - SPAA '14  
Whether or not the problem of finding maximal independent sets (MIS) in hypergraphs is in (R)NC is one of the fundamental problems in the theory of parallel computing.  ...  It is known that the problem is in RNC when the edges of the hypergraph have constant size.  ...  Harris and Aravind Srinivasan were supported in part by NSF Award CNS-1010789. We thank the anonymous SPAA reviewers for useful and extensive comments on a previous version of this paper.  ... 
doi:10.1145/2612669.2612670 dblp:conf/spaa/BerceaGHS14 fatcat:qyggg2nszncghojuwwlb7qbwmy

On Computing Maximal Independent Sets of Hypergraphs in Parallel

Ioana O. Bercea, Navin Goyal, David G. Harris, Aravind Srinivasan
2017 ACM Transactions on Parallel Computing  
Whether or not the problem of finding maximal independent sets (MIS) in hypergraphs is in (R)NC is one of the fundamental problems in the theory of parallel computing.  ...  It is known that the problem is in RNC when the edges of the hypergraph have constant size.  ...  Harris and Aravind Srinivasan were supported in part by NSF Award CNS-1010789. We thank the anonymous SPAA reviewers for useful and extensive comments on a previous version of this paper.  ... 
doi:10.1145/2938436 fatcat:zr3agjy575fezipofl4nimu3fe

On the dualization of hypergraphs with bounded edge-intersections and other related classes of hypergraphs

Leonid Khachiyan, Endre Boros, Khaled Elbassioni, Vladimir Gurvich
2007 Theoretical Computer Science  
Furthermore, combining this result with the currently known algorithms for finding a single maximally independent set of a hypergraph, we obtain efficient parallel algorithms for incrementally generating  ...  We consider the problem MIS(A, I): given a hypergraph A, and a subfamily I ⊆ I(A) of its maximal independent sets (MIS) I(A), either extend this subfamily by constructing a new MIS I ∈ I(A) \ I or prove  ...  In fact, we shall present below an algorithm that, for any given constant δ, will keep generating in incremental polynomial time (and in fact efficiently in parallel) maximal independent sets of A, and  ... 
doi:10.1016/j.tcs.2007.03.005 fatcat:dqxb6av6drbfniklmyuvzdxyky

Efficient NC algorithms for set cover with applications to learning and geometry

Bonnie Berger, John Rompel, Peter W. Shor
1994 Journal of computer and system sciences (Print)  
In addition, we give a linear-processor NC algorithm for a variant of the set cover problem first proposed by Chazelle and Friedman and use it to obtain NC algorithms for several problems in computational  ...  In this paper we give the first NC approximation algorithms for the unweighted and weighted set cover problems.  ...  The basic technique used in [7] is: first, construct a hypergraph that captures the behavior of the randomized algorithm. Next, find a balanced set cover for this hypergraph.  ... 
doi:10.1016/s0022-0000(05)80068-6 fatcat:pxhmqyr4frhz5imskbukzqf56e

NP-Hardness of Coloring 2-Colorable Hypergraph with Poly-Logarithmically Many Colors

Amey Bhangale, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
In terms of NP-hardness, it improves the result of Guruswam, Håstad and Sudani [SIAM Journal on Computing, 2002], combined with Moshkovitz-Raz [Journal of the ACM, 2010], by an 'exponential' factor.  ...  The second result improves the result of Saket [Conference on Computational Complexity (CCC), 2014] which shows quasi-NP-hardness of coloring a 2-colorable 4-uniform hypergraph with O (log γ n) colors  ...  15:10 Hypergraph Coloring hardness of approximation as well as in other areas which use the Long Code or similar objects. We conclude with a couple of obvious interesting open problems: 1.  ... 
doi:10.4230/lipics.icalp.2018.15 dblp:conf/icalp/Bhangale18 fatcat:mgbf47aqozgf5dbcg6a33wvnba
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