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Efficient Algorithm for Embedding Hypergraphs in a Cycle
[chapter]

2003
*
Lecture Notes in Computer Science
*

We give

doi:10.1007/978-3-540-24596-4_10
fatcat:hzxhxcy7encirjyxdgbop4galy
*a*1.8-*approximation**algorithm**for*the problem. This*improves*the previous 2-*approximation*results. The*algorithm*has the optimal O(mn) time*for*the hypergraph with m*hyperedges*and n nodes. ... The problem of Minimum Congestion Hypergraph*Embedding**in**a**Cycle*(MCHEC) is to embed the*hyperedges*of*a*hypergraph as paths*in**a**cycle*such that the maximum congestion (the maximum number of paths that ... Step Concluding remarks*A*1.8-*approximation**algorithm*is given*for*the MCHEC problem. This*improves*the previous 2-*approximation*results. ...##
###
On minimizing the maximum congestion for Weighted Hypergraph Embedding in a Cycle

2003
*
Information Processing Letters
*

The problem of Weighted Hypergraph

doi:10.1016/s0020-0190(03)00297-7
fatcat:f2jdxjoaszaqnlc3oxrd2n747e
*Embedding**in**a**Cycle*(WHEC) is to embed the weighted*hyperedges*of*a*hypergraph as the paths*in**a**cycle*, such that the maximum congestion of any physical link*in*the ...*A*simpler version of this problem is the Weighted Graph*Embedding**in**a**Cycle*(WGEC) that embeds the weighted edges of*a*normal graph as the paths*in**a**cycle*. ... Gonzalez*for*the helpful discussions. ...##
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A polynomial time approximation scheme for embedding a directed hypergraph on a weighted ring

2011
*
Journal of combinatorial optimization
*

*In*this paper, we design

*a*polynomial time

*approximation*scheme

*for*this problem. ...

*A*family of polynomial time

*approximation*

*algorithms*with performance guarantee 1 +

*for*all fixed > 0 is called

*a*polynomial time

*approximation*scheme (PTAS). ...

*For*the Minimum Congestion Hypergraph

*Embedding*

*in*

*a*

*Cycle*problem (MCHEC,

*for*short), the

*hyperedges*of the hypergraph and the links

*in*

*a*

*cycle*are undirected. ...

##
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A polynomial time approximation scheme for embedding a directed hypergraph on a ring

2006
*
Information Processing Letters
*

*In*this paper, we design

*a*polynomial time

*approximation*scheme

*for*this problem. ... Given

*a*directed hypergraph H = (V , E H ), we consider the problem of

*embedding*all directed

*hyperedges*on

*a*weighted ring. ...

*For*the Minimum Congestion Hypergraph

*Embedding*

*in*

*a*

*Cycle*problem (MCHEC,

*for*short), the

*hyperedges*of the hypergraph and the links

*in*

*a*

*cycle*are undirected. ...

##
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On packing and coloring hyperedges in a cycle

2007
*
Discrete Applied Mathematics
*

*In*this paper, we prove that the MPPCHC problem is NP-hard and then present an

*algorithm*with

*approximation*ratio 2

*for*this problem. ...

*For*the special case where each

*hyperedge*has the same profit 1 and each link e j has same capacity k, we propose an

*algorithm*with

*approximation*ratio 3 2 . ... Acknowledgments The authors are very grateful to an anonymous referee whose helpful comments and suggestions have led to

*a*substantially

*improved*presentation of the paper. Jianping ...

##
###
Multilevel Hypergraph Partitioning
[chapter]

2003
*
Combinatorial Optimization
*

Our multilevel hypergraph partitioning

doi:10.1007/978-1-4757-3748-6_3
fatcat:wwyxaliwwfapflj5boubsbedhq
*algorithm*scales very well*for*large hypergraphs. Hypergraphs with over 100,000 vertices can be bisected*in**a*few minutes on today's workstations. ...*In*this paper, we present*a*new hypergraph partitioning*algorithm*that is based on the multilevel paradigm.*In*the multilevel paradigm,*a*sequence of successively coarser hypergraphs is constructed. ... Figure 8 : 8 Multilevel Partitioning followed by*a*V-*cycle*. Figure 9 : 9 Multilevel Partitioning with two*embedded*v-*cycles*. ...##
###
On the Approximability of Partial VC Dimension
[chapter]

2016
*
Lecture Notes in Computer Science
*

We study the

doi:10.1007/978-3-319-48749-6_7
fatcat:niczarrae5d2dnozkgp5qjr25e
*approximation*complexity of Max Partial VC Dimension on general hypergraphs and on more restricted instances,*in*particular, neighborhood hypergraphs of graphs. ...*hyperedge*-intersections with C has size at least ℓ. ... Any α-*approximation**algorithm**for*Max Partial Double Hitting Set on hypergraphs without 4-*cycles**in*its bipartite incidence graph can be used to obtain*a*4α-*approximation**algorithm**for*Max Partial VC Dimension ...##
###
Planar Feedback Vertex Set and Face Cover: Combinatorial Bounds and Subexponential Algorithms

2010
*
Algorithmica
*

*In*this paper we

*improve*the

*algorithmic*analysis of both problems by proving

*a*series of combinatorial results relating the branchwidth of planar graphs with their face cover. ... As

*a*consequence, it follows that Planar Feedback Vertex Set and Face Cover can be solved

*in*O(2 15.11· √ k + n 2 ) and O(2 10.1· √ k + n 2 ) steps, respectively. ... Acknowledgements We wish to thank the two anonymous referees

*for*their helpful comments. ...

##
###
Planar Feedback Vertex Set and Face Cover: Combinatorial Bounds and Subexponential Algorithms
[chapter]

2008
*
Lecture Notes in Computer Science
*

*In*this paper we

*improve*the

*algorithmic*analysis of both problems by proving

*a*series of combinatorial results relating the branchwidth of planar graphs with their face cover. ... As

*a*consequence, it follows that Planar Feedback Vertex Set and Face Cover can be solved

*in*O(2 15.11· √ k + n 2 ) and O(2 10.1· √ k + n 2 ) steps, respectively. ... Acknowledgements We wish to thank the two anonymous referees

*for*their helpful comments. ...

##
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Approximating max-min linear programs with local algorithms

2008
*
Proceedings, International Parallel and Distributed Processing Symposium (IPDPS)
*

To contrast the negative results, we present

doi:10.1109/ipdps.2008.4536235
dblp:conf/ipps/FloreenKMS08
fatcat:ws4e6pge4zdujcxr7aq6qjs56q
*a*local*approximation**algorithm*which achieves good*approximation*ratios if we can bound the relative growth of the vertex neighbourhoods*in*H. ...*In*the distributed setting, each agent v is responsible*for*choosing the value of x_v, and the communication network is*a*hypergraph H where the sets V_k and V_i constitute the*hyperedges*. ... Acknowledgments We thank Marja Hassinen*for*discussions and comments. ...##
###
Hypergraph Partitioning With Embeddings
[article]

2020
*
arXiv
*
pre-print

*A*hypergraph is

*a*generalization of

*a*traditional graph wherein "

*hyperedges*" may connect any number of nodes. As

*a*result, hypergraph partitioning is an NP-Hard problem to both solve or

*approximate*. ...

*In*this work we propose using graph

*embeddings*of the initial hypergraph

*in*order to ensure that coarsened problem instances retrain key structural features. ... We would like to thank Sebastian Schlag from the Karlsruhe Institute of Technology

*for*helping us to understand KaHyPar. We would also like to thank our editor and reviewers. ...

##
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Parameterized and approximation complexity of Partial VC Dimension

2019
*
Theoretical Computer Science
*

⋆

doi:10.1016/j.tcs.2018.09.013
fatcat:7f62vhskhbetbawvjngdjae4oi
*A*preliminary version of this work containing the*approximation*complexity results appeared*in*[8] . ...*hyperedge*-intersections with C has size at least ℓ. ... Any α-*approximation**algorithm**for*Max Partial Double Hitting Set can be used to obtain*a*4α-*approximation**algorithm**for*Max Partial VC Dimension on hypergraphs without 4-*cycles**in*their bipartite incidence ...##
###
Parameterized and Approximation Complexity of Partial VC Dimension
[article]

2016
*
arXiv
*
pre-print

*hyperedge*-intersections with C has size at least ℓ. ... We study the

*algorithmic*complexity of Partial VC Dimension and Max Partial VC Dimension both on general hypergraphs and on more restricted instances,

*in*particular, neighborhood hypergraphs of graphs. ... Any α-

*approximation*

*algorithm*

*for*Max Partial Double Hitting Set can be used to obtain

*a*4α-

*approximation*

*algorithm*

*for*Max Partial VC Dimension on hypergraphs without 4-

*cycles*

*in*their bipartite incidence ...

##
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Block Crossings in Storyline Visualizations
[chapter]

2016
*
Lecture Notes in Computer Science
*

Our main results is

doi:10.1007/978-3-319-50106-2_30
fatcat:vzlpknzcffhzxih7drn67svtq4
*a*constant-factor*approximation**algorithm**for*meetings of bounded size. ... The*algorithm*is based on (*approximately*) solving*a**hyperedge*deletion problem on hypergraphs that may be of independent interest. ...*Improvements**for*2-SBCM. By using specific structures*for*2-character meetings we can*improve**approximation*factor and runtime; note that the general*algorithm*yields*a*36-*approximation*. ...##
###
Fast Parameterized Algorithms for Graphs on Surfaces: Linear Kernel and Exponential Speed-Up
[chapter]

2004
*
Lecture Notes in Computer Science
*

(ii) Using such

doi:10.1007/978-3-540-27836-8_50
fatcat:l66jjmhyyff4rjblksq5ea4xgy
*a*kernel we*improve*the best so far*algorithm**for*k-dominating set on graphs of genus (iii) Applying tools from the topological graph theory, we*improve*drastically the best so far combinatorial ... Our new bound provides further exponential speed-up of our*algorithm**for*the k-dominating set and we prove that the same speed-up applies*for**a*wide category of parameterized graph problems such as k-vertex ...*For**a*nicely D-dominated Σ-*embedded*graph G and the set C(G) of all maximal D-*cycles*of G, we define hypergraph H(G) is obtained from G by adding*hyperedges*corresponding to maximal D-*cycles*of G. ...
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