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Local edge-connectivity augmentation in hypergraphs is NP-complete

Zoltán Király, Ben Cosh, Bill Jackson
2010 Discrete Applied Mathematics  
We consider a local connectivity hypergraph augmentation problem. Specifically, we are given a hypergraph G = (V, E) and a subpartition of V .  ...  Using a transformation from the bin-packing problem, we show that the associated decision problem is NP-complete when k = 2.  ...  Acknowledgement: We would like to thank András Frank for organizing the workshop on connectivity problems, held in Bonn in June 1999, where the inspiration for our main result struck.  ... 
doi:10.1016/j.dam.2009.12.011 fatcat:spmz3dgom5fu5plhu6teoamjwy

Augmenting the Edge-Connectivity of a Hypergraph by Adding a Multipartite Graph

Attila Bernáth, Roland Grappe, Zoltán Szigeti
2012 Journal of Graph Theory  
Szigeti, Edge-connectivity augmentation with partition constraints, SIAM J. Discrete Math. Vol. 12, No. 2 (1999) 160-207) and edge-connectivity augmentation of hypergraphs by adding graph edges (J.  ...  This problem is a common generalization of the following two problems: edge-connectivity augmentation of graphs with partition constraints (J. Bang-Jensen, H. Gabow, T. Jordán, Z.  ...  The problem Hypergraph Local Edge-Connectivity Augmentation by a Graph is NP-complete.  ... 
doi:10.1002/jgt.21643 fatcat:chtwvo3kgfc7vkuwlr4szfvmti

A unifying approach to splitting-off

Attila Bernáth, Tamás Király
2012 Combinatorica  
The first is local edge-connectivity augmentation of undirected hypergraphs. The second is global arc-connectivity augmentation of mixed hypergraphs with undirected hyperedges.  ...  This hard problem is a natural generalization of many solved connectivity augmentation problems, such as local edge-connectivity augmentation of graphs, global arcconnectivity augmentation of mixed graphs  ...  Further applications Local edge-connectivity augmentation of hypergraphs In this section we consider the local edge-connectivity augmentation of hypergraphs without increasing the rank.  ... 
doi:10.1007/s00493-012-2548-8 fatcat:cffekh7minf3vkz2r54gdoleia

Contents

2010 Discrete Applied Mathematics  
Jackson Local edge-connectivity augmentation in hypergraphs is NP-complete 723 doi:10.1016/S0166-218X(10)00054-5 R.B. Ellis and J.P.  ...  Sher Eigenvalue assignments and the two largest multiplicities in a Hermitian matrix whose graph is a tree 681 J.S.-T. Juan, D.D.-F. Liu and L.-Y.  ... 
doi:10.1016/s0166-218x(10)00054-5 fatcat:oxwaaoup3besdcn5z7htv7cwsa

Fair and Reliable Reconnections for Temporary Disruptions in Electric Distribution Networks using Submodularity [article]

Cyrus Hettle, Swati Gupta, Daniel Molzahn
2022 arXiv   pre-print
We first show that MRT is a special case of the well-known minimum linear ordering problem from submodular optimization literature and that MRT is also NP-hard.  ...  We therefore consider optimizing multiple metrics simultaneously using local search methods that reconfigure the system's base tree to optimize service disruptions, reconnection times, and energy losses  ...  These complete hypergraphs can be efficiently covered by a fractional LP solution, which completely covers each complete hypergraph in turn, moving from largest to smallest.  ... 
arXiv:2104.07631v2 fatcat:reuouxtu6jeavfdrhmfn7ght3m

Simultaneous Embeddability of Two Partitions [chapter]

Jan Christoph Athenstädt, Tanja Hartmann, Martin Nöllenburg
2014 Lecture Notes in Computer Science  
We show that (i) every pair of partitions has a weak simultaneous embedding, (ii) it is NP-complete to decide the existence of a strong simultaneous embedding, and (iii) the existence of a full simultaneous  ...  Each element of the set is mapped to a point in the plane and each block of either of the two partitions is mapped to a region that contains exactly those points that belong to the elements in the block  ...  Our NP-completeness result implies that vertex-planarity testing of 2-regular hypergraphs is also NP-complete.  ... 
doi:10.1007/978-3-662-45803-7_6 fatcat:4qflfetdxre7tpsafwf3lmi2qm

Page 9759 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
A network connecting a given set of points in /! space is called locally minimal if no aux- iliary vertex of the network can be moved to decrease the total length.  ...  The authors prove that both minimum and maximum traveling salesman problems on complete graphs with edge-distances either 1 or 2 (denoted by min_ TSP12 and max_ TSP12, respectively) are approximable within  ... 

Simultaneous Embeddability of Two Partitions [article]

Jan Christoph Athenstädt, Tanja Hartmann, Martin Nöllenburg
2014 arXiv   pre-print
We show that (i) every pair of partitions has a weak simultaneous embedding, (ii) it is NP-complete to decide the existence of a strong simultaneous embedding, and (iii) the existence of a full simultaneous  ...  Each element of the set is mapped to a point in the plane and each block of either of the two partitions is mapped to a region that contains exactly those points that belong to the elements in the block  ...  Our NP-completeness result implies that vertex-planarity testing of 2-regular hypergraphs is also NP-complete.  ... 
arXiv:1408.6019v1 fatcat:ffxzjrahcbdndalpqko45c3yzi

HRNCE grammars — a hypergraph generating system with an eNCE way of rewriting

Changwook Kim, Tae Eui Jeong
1999 Theoretical Computer Science  
S-HRNCE languages are in NP and there is an NP-complete linear HRNCE (Lin-HRNCE) language satisfying any two of the following conditions: connected; degree-bounded; and rankbounded.  ...  HRNCE grammars without edge erasing can generate PSPACE-complete languages.  ...  Clearly, L(G') is NP-complete and consists of connected and rank-bounded hypergraphs only. Similarly, consider G" obtained from G as follows.  ... 
doi:10.1016/s0304-3975(99)00258-3 fatcat:7kulb5wykzegbhonizj5ol6jg4

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.  ...  Unlike in graphs, however, there is no known polynomial time algorithm to find the hypergraph perfect matching that is guaranteed to exist when Haxell's condition is satisfied.  ...  For a given collection of edges F ⊆ E, define τ (F ) to be the cardinality of the smallest subset of B that hits 2 all the edges in F . 1 For a definition of this NP-complete problem see, for example  ... 
doi:10.1137/1.9781611974331.ch126 dblp:conf/soda/Annamalai16 fatcat:i572vgr5cfdwpiimtverqyvumm

Tree Transduction Tools for Cdec

Matthews Austin, Baltescu Paul, Blunsom Phil, Lavie Alon, Dyer Chris
2014 Prague Bulletin of Mathematical Linguistics  
A fast, multithreaded implementation of the Cohn and Blunsom (2009) model for extracting compact tree-to-string rules is also included.  ...  The implementation of the tree composition algorithm used by cdec is described, and translation quality and decoding time results are presented.  ...  previous work, we introduce one more type of hypergraph augmentation.  ... 
doi:10.2478/pralin-2014-0011 fatcat:3efseayabbcefgqy22xtcws7qa

Covering symmetric supermodular functions by uniform hypergraphs

Tamás Király
2004 Journal of combinatorial theory. Series B (Print)  
These results include as a special case a formula on the minimum number of r-hyperedges whose addition to an initial hypergraph will make it k-edge-connected. r  ...  We consider the problem of finding a uniform hypergraph that satisfies cut demands defined by a symmetric crossing supermodular set function.  ...  Let l H ðu; vÞ denote the local edge-connectivity between u and v in a hypergraph H; i.e. NP-completeness was proved by Cosh, Jackson, and Kira´ly for the following special case.  ... 
doi:10.1016/j.jctb.2003.12.004 fatcat:alinr2xocrcbvorpoyasruereq

Parsing and Hypergraphs [chapter]

Dan Klein, Christopher D. Manning
2004 Text, Speech and Language Technology  
While symbolic parsers can be viewed as deduction systems, this view is less natural for probabilistic parsers.  ...  We present a view of parsing as directed hypergraph analysis which naturally covers both symbolic and probabilistic parsing.  ...  2 DT NN NP NP DT¡¬ NP ¡ « PP ¡ AE [NN+ NP DT¡«] µ NP Passive Edges Active Edges Traversals × ÓÖ ´ µ does not change × ÓÖ ´ µ ¼ is discovered is finished no traversal  ... 
doi:10.1007/1-4020-2295-6_18 fatcat:vrpqvsapzrexxdlebjg4qydpe4

Finding Perfect Matchings in Bipartite Hypergraphs [article]

Chidambaram Annamalai
2016 arXiv   pre-print
That is, when Haxell's condition holds it forces the existence of a perfect matching in the bipartite hypergraph.  ...  Unlike in graphs, however, there is no known polynomial time algorithm to find the hypergraph perfect matching that is guaranteed to exist when Haxell's condition is satisfied.  ...  Finally, in 1 For a definition of this NP-complete problem see, for example, [Cyg13] . 2 A subset S ⊆ B hits all the edges in F if for each e ∈ F , S ∩ e = ∅. constrast to the graph case, the proof is  ... 
arXiv:1509.07007v2 fatcat:3ijoqfneonbbxpbjgmujydpq7m

Towards Structured Modelling with Hyperdag P Systems

Michael J. Dinneen, Yun-Bum Kim, Radu Nicolescu
2010 International Journal of Computers Communications & Control  
In this paper, we propose and define a new model called hyperdag P systems, in short, hP systems, which extend the definition of conventional P systems, by allowing dags, interpreted as hypergraphs, instead  ...  Modelling these as tree-based systems, while theoretically possible, is not very appealing, because it typically needs artificial extensions that introduce additional complexities, inexistent in the originals  ...  In contrast, any formal systems that use graph edges (or digraph arcs) to model 1:1 communication channels will need n(n − 1) separate edges (or 2n(n − 1) arcs) to model the associated complete subgraph  ... 
doi:10.15837/ijccc.2010.2.2477 fatcat:losz4niiube2lmd4xe6pap2z54
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