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Perfectf-matchings andf-factors in hypergraphs—A combinatorial approach

Isabel Beckenbach, Robert Scheidweiler
2017 Discrete Mathematics  
Keywords: perfect f -matchings in hypergraphs, f -factors in hypergraphs, mengerian hypergraph, balanced hypergraph, perfect hypergraph, Hall's Theorem  ...  We prove characterizations of the existence of perfect f -matchings in uniform mengerian and perfect hypergraphs. Moreover, we investigate the f -factor problem in balanced hypergraphs.  ...  to the perfect f -matching problem in balanced hypergraphs we had f (v) ≤ 4 for all v ∈ V .  ... 
doi:10.1016/j.disc.2017.05.005 fatcat:5dff6egarbfqbmwwyd57h37i2i

A combinatorial, primal-dual approach to semidefinite programs

Sanjeev Arora, Satyen Kale
2007 Proceedings of the thirty-ninth annual ACM symposium on Theory of computing - STOC '07  
For a number of problems, such as Sparsest Cut and Balanced Separator in undirected and directed weighted graphs, and the Min UnCut problem, this yields combinatorial approximation algorithms that are  ...  We develop a general primal-dual approach to solve SDPs using a generalization of the well-known multiplicative weights update rule to symmetric matrices.  ...  Vijay Vazirani suggested several years ago that primal-dual methods be investigated in the SDP context.  ... 
doi:10.1145/1250790.1250823 dblp:conf/stoc/AroraK07 fatcat:vejflz5yercrtcoaflkn2wizom

A Combinatorial, Primal-Dual Approach to Semidefinite Programs

Sanjeev Arora, Satyen Kale
2016 Journal of the ACM  
For a number of problems, such as Sparsest Cut and Balanced Separator in undirected and directed weighted graphs, and the Min UnCut problem, this yields combinatorial approximation algorithms that are  ...  We develop a general primal-dual approach to solve SDPs using a generalization of the well-known multiplicative weights update rule to symmetric matrices.  ...  Vijay Vazirani suggested several years ago that primal-dual methods be investigated in the SDP context.  ... 
doi:10.1145/2837020 fatcat:66pm5wv4hzgmjavsjowgbgpb7m

Computing the Partition Function for Perfect Matchings in a Hypergraph

ALEXANDER BARVINOK, ALEX SAMORODNITSKY
2011 Combinatorics, probability & computing  
We also discuss applications to counting of perfect and nearly perfect matchings in hypergraphs.  ...  When the weights w S are positive and within a constant factor, fixed in advance, of each other, we present a simple polynomial time algorithm to approximate the sum within a polynomial in m factor.  ...  The research of the authors was also partially supported by a United States -Israel BSF grant 2006377. Typeset by A M S-T E X  ... 
doi:10.1017/s0963548311000435 fatcat:kgg6u57hprbircrdmd5y4roz6u

Computing the partition function for perfect matchings in a hypergraph [article]

Alexander Barvinok, Alex Samorodnitsky
2011 arXiv   pre-print
We also discuss applications to counting of perfect and nearly perfect matchings in hypergraphs.  ...  When the weights w_S are positive and within a constant factor, fixed in advance, of each other, we present a simple polynomial time algorithm to approximate the sum within a polynomial in m factor.  ...  Typeset by A M S-T E X Acknowledgment The authors are grateful to Jeff Kahn for helpful discussions.  ... 
arXiv:1009.2397v3 fatcat:l54q6qgld5adpgwotodalvzrba

Kinematic Structure Correspondences via Hypergraph Matching

Hyung Jin Chang, Tobias Fischer, Maxime Petit, Martina Zambelli, Yiannis Demiris
2016 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)  
In this paper, we present a novel framework for finding the kinematic structure correspondence between two objects in videos via hypergraph matching.  ...  Our main contributions can be summarised as follows: (i) casting the kinematic structure correspondence problem into a hypergraph matching problem, incorporating multi-order similarities with normalising  ...  Acknowledgement: This work was supported in part by EU FP7 project WYSIWYD under Grant 612139. We thank Dr. Minsu Cho for fruitful discussions.  ... 
doi:10.1109/cvpr.2016.457 dblp:conf/cvpr/ChangFPZD16 fatcat:iwrlf634hfblrmtdigdm6ft22q

Dynamic load-balancing with variable number of processors based on graph repartitioning

Clement Vuchener, Aurelien Esnard
2012 2012 19th International Conference on High Performance Computing  
These approaches can be very inefficient, especially in terms of resource consumption.  ...  In this paper, we present a new graph repartitioning algorithm which accepts to dynamically change the number of processors, assuming the load is already balanced.  ...  A very common approach to solve the load-balancing problem (static or dynamic) is based on graph (or hypergraph) model [1] .  ... 
doi:10.1109/hipc.2012.6507501 dblp:conf/hipc/VuchenerE12 fatcat:x4fgmwaxbjhgnnktcj2k6kmldy

Page 6465 of Mathematical Reviews Vol. , Issue 96k [page]

1996 Mathematical Reviews  
The section starts with a hierarchy of hypergraph properties and a short consideration of the polyhedral approach.  ...  These hypergraph classes generalize several graph classes (bipartite graphs and trees) or correspond to some combinatorial structure patterns (paths of a graph, branching, etc.).  ... 

The Tight Cut Decomposition of Matching Covered Uniformable Hypergraphs [article]

Isabel Beckenbach, Meike Hatzel, Sebastian Wiederrecht
2019 arXiv   pre-print
The perfect matching polytope, i.e. the convex hull of (incidence vectors of) perfect matchings of a graph is used in many combinatorial algorithms.  ...  Moreover, we show how the tight cut decomposition leads to a decomposition of the perfect matching polytope of uniformable hypergraphs and that the recognition problem for tight cuts in uniformable hypergraphs  ...  We will add a new characterisation of balanced hypergraphs in terms of their perfect matching polytope.  ... 
arXiv:1812.05461v3 fatcat:li2ksb3xsfbehik44jbqjvcv2y

Hypergraph matchings and designs [article]

Peter Keevash
2018 arXiv   pre-print
We survey some aspects of the perfect matching problem in hypergraphs, with particular emphasis on structural characterisation of the existence problem in dense hypergraphs and the existence of designs  ...  [18, 71] ), and it appears naturally in combinatorial existence problems, as in dense hypergraphs almost perfect matchings and fractional matchings tend to appear at the same threshold.  ...  perfect matchings in any regular uniform hypergraph with small codegrees.  ... 
arXiv:1807.05752v1 fatcat:dj4eawinsrg5plbc4ekxydvnpe

Learning Kinematic Structure Correspondences Using Multi-Order Similarities

Hyung Jin Chang, Tobias Fischer, Maxime Petit, Martina Zambelli, Yiannis Demiris
2017 IEEE Transactions on Pattern Analysis and Machine Intelligence  
In this paper, we present a novel framework for finding the kinematic structure correspondences between two articulated objects in videos via hypergraph matching.  ...  We use hypergraph matching with normalised weight terms to simultaneously consider structural topology, kinematic correlation and combinatorial motion.  ...  Note that a subgraph of G which is isomorphic to G may not have the same number of edges per node as G, but may contain more edges; in other words, a subgraph isomorphism might not be a perfect match.  ... 
doi:10.1109/tpami.2017.2777486 pmid:29989982 fatcat:e55c5eqe7jeh5i2pnmw5y5nvea

On the Varshamov–Tenengolts construction on binary strings

Ankur A. Kulkarni, Negar Kiyavash, R. Sreenivas
2014 Discrete Mathematics  
Moreover, we show for any n the smallest of these sets is within n 2 −n n 2 −3n+4− 4 2 n of the smallest cover of this hypergraph and that each of these sets is a perfect matching.  ...  We show that these sets are also responsible for the (near) solution of several combinatorial problems on a certain hypergraph. Furthermore our results are valid for any string length.  ...  However this also means these hypergraphs are, in general, not balanced (recall from Berge [3] that a hypergraph is said to be balanced if its incidence matrix is balanced).  ... 
doi:10.1016/j.disc.2013.11.003 fatcat:6ftyt3ynp5hhtcrffn3wsdnvra

Page 287 of Mathematical Reviews Vol. , Issue 81A [page]

1981 Mathematical Reviews  
The optimum perfect matching problem may be viewed as a linear programming problem over the polytope whose extreme points are incidence vectors of perfect matchings in G; the primal algorithm is used to  ...  The primal algorithm also provides new means for establishing known lower bounds on the number of perfect matchings in G when G is k-connected.  ... 

Bayesian evolutionary hypergraph learning for predicting cancer clinical outcomes

Soo-Jin Kim, Jung-Woo Ha, Byoung-Tak Zhang
2014 Journal of Biomedical Informatics  
The proposed model represents the interactions of prognostic genes as a combinatorial space.  ...  The proposed learning approach effectively balances performance and parsimony of the model using information-theoretic dependency and complexity-theoretic regularization priors.  ...  Fig. 4 describes the evolving process of hypergraph classifiers learned by the Bayesian approach.  ... 
doi:10.1016/j.jbi.2014.02.002 pmid:24524888 fatcat:o5mod3y56reihfx7kwxbxgy3bq

Finding Perfect Matchings in Bipartite Hypergraphs

Chidambaram Annamalai
2015 Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms  
That is, when Haxell's condition holds it forces the existence of a perfect matching in the bipartite hypergraph.  ...  We prove the existence of an efficient algorithm to find perfect matchings in bipartite hypergraphs whenever a stronger version of Haxell's condition holds.  ...  This condition is sufficient to force the existence of a perfect matching in the hypergraph.  ... 
doi:10.1137/1.9781611974331.ch126 dblp:conf/soda/Annamalai16 fatcat:i572vgr5cfdwpiimtverqyvumm
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