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Local edge-connectivity augmentation in hypergraphs is NP-complete

2010
*
Discrete Applied Mathematics
*

We consider a

doi:10.1016/j.dam.2009.12.011
fatcat:spmz3dgom5fu5plhu6teoamjwy
*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. ...##
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Augmenting the Edge-Connectivity of a Hypergraph by Adding a Multipartite Graph

2012
*
Journal of Graph Theory
*

Szigeti,

doi:10.1002/jgt.21643
fatcat:chtwvo3kgfc7vkuwlr4szfvmti
*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*. ...##
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A unifying approach to splitting-off

2012
*
Combinatorica
*

The first

doi:10.1007/s00493-012-2548-8
fatcat:cffekh7minf3vkz2r54gdoleia
*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. ...##
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Contents

2010
*
Discrete Applied Mathematics
*

Jackson

doi:10.1016/s0166-218x(10)00054-5
fatcat:oxwaaoup3besdcn5z7htv7cwsa
*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. ...##
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Fair and Reliable Reconnections for Temporary Disruptions in Electric Distribution Networks using Submodularity
[article]

2022
*
arXiv
*
pre-print

We first show that MRT

arXiv:2104.07631v2
fatcat:reuouxtu6jeavfdrhmfn7ght3m
*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. ...##
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Simultaneous Embeddability of Two Partitions
[chapter]

2014
*
Lecture Notes in Computer Science
*

We show that (i) every pair of partitions has a weak simultaneous embedding, (ii) it

doi:10.1007/978-3-662-45803-7_6
fatcat:4qflfetdxre7tpsafwf3lmi2qm
*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*. ...##
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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 ...##
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Simultaneous Embeddability of Two Partitions
[article]

2014
*
arXiv
*
pre-print

We show that (i) every pair of partitions has a weak simultaneous embedding, (ii) it

arXiv:1408.6019v1
fatcat:ffxzjrahcbdndalpqko45c3yzi
*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*. ...##
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HRNCE grammars — a hypergraph generating system with an eNCE way of rewriting

1999
*
Theoretical Computer Science
*

S-HRNCE languages are

doi:10.1016/s0304-3975(99)00258-3
fatcat:7kulb5wykzegbhonizj5ol6jg4
*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. ...##
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Finding Perfect Matchings in Bipartite Hypergraphs

2015
*
Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms
*

That

doi:10.1137/1.9781611974331.ch126
dblp:conf/soda/Annamalai16
fatcat:i572vgr5cfdwpiimtverqyvumm
*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 ...##
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Tree Transduction Tools for Cdec

2014
*
Prague Bulletin of Mathematical Linguistics
*

A fast, multithreaded implementation of the Cohn and Blunsom (2009) model for extracting compact tree-to-string rules

doi:10.2478/pralin-2014-0011
fatcat:3efseayabbcefgqy22xtcws7qa
*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*. ...##
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Covering symmetric supermodular functions by uniform hypergraphs

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

doi:10.1016/j.jctb.2003.12.004
fatcat:alinr2xocrcbvorpoyasruereq
*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. ...##
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Parsing and Hypergraphs
[chapter]

2004
*
Text, Speech and Language Technology
*

While symbolic parsers can be viewed as deduction systems, this view

doi:10.1007/1-4020-2295-6_18
fatcat:vrpqvsapzrexxdlebjg4qydpe4
*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 ...##
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Finding Perfect Matchings in Bipartite Hypergraphs
[article]

2016
*
arXiv
*
pre-print

That

arXiv:1509.07007v2
fatcat:3ijoqfneonbbxpbjgmujydpq7m
*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*...##
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Towards Structured Modelling with Hyperdag P Systems

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 ...

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