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Efficient Algorithm for Embedding Hypergraphs in a Cycle [chapter]

Qian-Ping Gu, Yong Wang
2003 Lecture Notes in Computer Science  
We give 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.  ... 
doi:10.1007/978-3-540-24596-4_10 fatcat:hzxhxcy7encirjyxdgbop4galy

On minimizing the maximum congestion for Weighted Hypergraph Embedding in a Cycle

SingLing Lee, Hann-Jang Ho
2003 Information Processing Letters  
The problem of Weighted Hypergraph 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.  ... 
doi:10.1016/s0020-0190(03)00297-7 fatcat:f2jdxjoaszaqnlc3oxrd2n747e

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

Jianping Li, Weidong Li, Lusheng Wang
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.  ... 
doi:10.1007/s10878-011-9387-1 fatcat:h6t6o7hgmfgfthmhaw4zd6euje

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

Kang Li, Lusheng Wang
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.  ... 
doi:10.1016/j.ipl.2005.10.008 fatcat:2v35wtoqwjckfc3mslo562agxi

On packing and coloring hyperedges in a cycle

Jianping Li, Lusheng Wang, Hao Zhao
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  ... 
doi:10.1016/j.dam.2007.05.037 fatcat:ws2jgvvrsjegrfz7crlq7kxjem

Multilevel Hypergraph Partitioning [chapter]

George Karypis
2003 Combinatorial Optimization  
Our multilevel hypergraph partitioning 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.  ... 
doi:10.1007/978-1-4757-3748-6_3 fatcat:wwyxaliwwfapflj5boubsbedhq

On the Approximability of Partial VC Dimension [chapter]

Cristina Bazgan, Florent Foucaud, Florian Sikora
2016 Lecture Notes in Computer Science  
We study the 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  ... 
doi:10.1007/978-3-319-48749-6_7 fatcat:niczarrae5d2dnozkgp5qjr25e

Planar Feedback Vertex Set and Face Cover: Combinatorial Bounds and Subexponential Algorithms

Athanassios Koutsonas, Dimitrios M. Thilikos
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.  ... 
doi:10.1007/s00453-010-9390-4 fatcat:ke7s3hjrcbejtfpyyrsjqikjc4

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

Athanassios Koutsonas, Dimitrios M. Thilikos
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.  ... 
doi:10.1007/978-3-540-92248-3_24 fatcat:m5uq75uwwvc4df2vwkd53oxe64

Approximating max-min linear programs with local algorithms

Patrik Floreen, Petteri Kaski, Topi Musto, Jukka Suomela
2008 Proceedings, International Parallel and Distributed Processing Symposium (IPDPS)  
To contrast the negative results, we present 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.  ... 
doi:10.1109/ipdps.2008.4536235 dblp:conf/ipps/FloreenKMS08 fatcat:ws4e6pge4zdujcxr7aq6qjs56q

Hypergraph Partitioning With Embeddings [article]

Justin Sybrandt, Ruslan Shaydulin, Ilya Safro
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.  ... 
arXiv:1909.04016v5 fatcat:wfpycc6sirdsnasocgyp72375a

Parameterized and approximation complexity of Partial VC Dimension

Cristina Bazgan, Florent Foucaud, Florian Sikora
2019 Theoretical Computer Science  
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  ... 
doi:10.1016/j.tcs.2018.09.013 fatcat:7f62vhskhbetbawvjngdjae4oi

Parameterized and Approximation Complexity of Partial VC Dimension [article]

Cristina Bazgan, Florent Foucaud, Florian Sikora
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  ... 
arXiv:1609.05110v2 fatcat:nj2nim5duvchxa36bq6kzvlyx4

Block Crossings in Storyline Visualizations [chapter]

Thomas C. van Dijk, Martin Fink, Norbert Fischer, Fabian Lipp, Peter Markfelder, Alexander Ravsky, Subhash Suri, Alexander Wolff
2016 Lecture Notes in Computer Science  
Our main results is 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.  ... 
doi:10.1007/978-3-319-50106-2_30 fatcat:vzlpknzcffhzxih7drn67svtq4

Fast Parameterized Algorithms for Graphs on Surfaces: Linear Kernel and Exponential Speed-Up [chapter]

Fedor V. Fomin, Dimitrios M. Thilikos
2004 Lecture Notes in Computer Science  
(ii) Using such 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.  ... 
doi:10.1007/978-3-540-27836-8_50 fatcat:l66jjmhyyff4rjblksq5ea4xgy
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