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Improved non-approximability results for minimum vertex cover with density constraints

Andrea E.F. Clementi, Luca Trevisan
1999 Theoretical Computer Science  
We provide new non-approximabili~ results for the restrictjons of the MIN VERTEX COVER problem to bounded-degree, sparse and dense graphs.  ...  Then, we consider sparse graphs with no dense components (i.e. everywhere sparse graphs), and we show a similar result but with a better trade-off between non-approximability and spars&y.  ...  VERTEX COVER problem with density constraints.  ... 
doi:10.1016/s0304-3975(97)00226-0 fatcat:4o2gvwapxzgrjlg4w2jixvhv44

The Probabilistic Method for Solving Minimum Vertex Cover Problem Using Systems of Non-linear Equations

Listrovoy Sergey Vladimirovich, Motsnyi Stanislav Vladimirovich
2015 International Journal of Information Technology and Computer Science  
In this paper the probabilistic method is presented for solving the minimum vertex cover problem using systems of non-linear equations that are formed on the basis of a neighborhood relationship of a particular  ...  The experiment results show that our method has significantly better time complexity and much smaller frequency of the approximation errors in comparison with one of the most currently efficient algorithms  ...  The results of our method (the non-linear equations method) were compared with one of the most optimized methods (the frequency method) for the minimum vertex cover on the random graphs in heterogeneous  ... 
doi:10.5815/ijitcs.2015.11.01 fatcat:ry55rlg7bfd6hhzvti6i3icgaa

A New Multilayered PCP and the Hardness of Hypergraph Vertex Cover [article]

Irit Dinur, Venkatesan Guruswami, Subhash Khot, Oded Regev
2003 arXiv   pre-print
This enables us to prove that Ek-Vertex-Cover is NP-hard to approximate within factor (k-1-ϵ) for any k ≥ 3 and any ϵ>0.  ...  The result is essentially tight as this problem can be easily approximated within factor k.  ...  Acknowledgements We would like to thank Noga Alon for his help with s-wise t-intersecting families.  ... 
arXiv:cs/0304026v1 fatcat:qvy625a3wbecfcird4z7ncjaci

Crowdsensing in Opportunistic Mobile Social Networks: A Context-aware and Human-centric Approach [article]

Phuong Nguyen, Klara Nahrstedt
2017 arXiv   pre-print
Since finding the optimal solution for minimum vertex cover problem is NP-complete, approximation algorithms have to be used.  ...  In this paper, we propose the notions of node observability and coverage utility score and design a new context-aware approximation algorithm to find vertex cover that is tailored for crowd-sensing task  ...  In the next section, we discuss the constrained version of the two well-known approximation algorithms for minimum vertex cover problem with our modification to comply with the constraint on the maximum  ... 
arXiv:1704.08598v1 fatcat:ti2my54hgvaohk3rztjmtco4sm

Page 1301 of Mathematical Reviews Vol. , Issue 2002B [page]

2002 Mathematical Reviews  
(I-ROME-IS; Rome); Trevisan, Luca (CH-GENV-CI; Geneva) Improved non-approximability results for minimum vertex cover with density constraints. (English summary) Theoret. Comput.  ...  The current paper improves the known lower bounds on approximating the minimum vertex cover problem. Previously, J. T.  ... 

A Constrained Resampling Strategy for Mesh Improvement

Ahmed Abdelkader, Ahmed H. Mahmoud, Ahmad A. Rushdi, Scott A. Mitchell, John D. Owens, Mohamed S. Ebeida
2017 Computer graphics forum (Print)  
In this paper, we describe a versatile strategy for mesh improvement by interpreting quality objectives as spatial constraints on resampling and develop a toolbox of local operators to improve the mesh  ...  The conflicting nature of such objectives makes it challenging to establish similar guarantees for each combination, e.g., angle bounds and vertex count.  ...  Acknowledgements The authors would like to thank Dong-Ming Yan, Kaimo Hu [HYB * 16] and Jianwei Guo [AGY * 16] for providing valuable input and helping run some additional tests, and Darren Engwirda for  ... 
doi:10.1111/cgf.13256 fatcat:4uhvhfan2vfpbglbsiq53lauqa

Near-Optimal Budgeted Data Exchange for Distributed Loop Closure Detection [article]

Yulun Tian, Kasra Khosoussi, Matthew Giamou, Jonathan P. How and Jonathan Kelly
2018 arXiv   pre-print
We approach this problem from different perspectives and leverage existing results on monotone submodular maximization to provide efficient approximation algorithms with performance guarantees.  ...  However, even with the most resource-efficient techniques, the resources available onboard may be insufficient for verifying every potential loop closure.  ...  ACKNOWLEDGEMENT This work was supported in part by the NASA Convergent Aeronautics Solutions project Design Environment for Novel Vertical Lift Vehicles (DELIVER), by the Northrop Grumman Corporation,  ... 
arXiv:1806.00188v1 fatcat:mx6ex6ysqrba3ht6znpilbwuom

A new multilayered PCP and the hardness of hypergraph vertex cover

Irit Dinur, Venkatesan Guruswami, Subhash Khot, Oded Regev
2003 Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03  
This enables us to prove that Ek-Vertex-Cover is NP-hard to approximate within a factor of (k − 1 − ε) for arbitrary constants ε > 0 and k ≥ 3.  ...  The result is nearly tight as this problem can be easily approximated within factor k.  ...  Acknowledgements We would like to thank Noga Alon for his help with s-wise t-intersecting families. We would also like to thank Luca Trevisan and the anonymous referees for useful comments.  ... 
doi:10.1145/780542.780629 dblp:conf/stoc/DinurGKR03 fatcat:3ajruolnovcjzhqe64zqfrb3x4

A New Multilayered PCP and the Hardness of Hypergraph Vertex Cover

Irit Dinur, Venkatesan Guruswami, Subhash Khot, Oded Regev
2005 SIAM journal on computing (Print)  
This enables us to prove that Ek-Vertex-Cover is NP-hard to approximate within a factor of (k − 1 − ε) for arbitrary constants ε > 0 and k ≥ 3.  ...  The result is nearly tight as this problem can be easily approximated within factor k.  ...  Acknowledgements We would like to thank Noga Alon for his help with s-wise t-intersecting families. We would also like to thank Luca Trevisan and the anonymous referees for useful comments.  ... 
doi:10.1137/s0097539704443057 fatcat:inqeesj45bh67eceuqk2ml2wii

A new multilayered PCP and the hardness of hypergraph vertex cover

Irit Dinur, Venkatesan Guruswami, Subhash Khot, Oded Regev
2003 Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03  
This enables us to prove that Ek-Vertex-Cover is NP-hard to approximate within a factor of (k − 1 − ε) for arbitrary constants ε > 0 and k ≥ 3.  ...  The result is nearly tight as this problem can be easily approximated within factor k.  ...  Acknowledgements We would like to thank Noga Alon for his help with s-wise t-intersecting families. We would also like to thank Luca Trevisan and the anonymous referees for useful comments.  ... 
doi:10.1145/780627.780629 fatcat:4xze7f5zpbhgxntemkq4hlq32e

LP-based algorithms for multistage minimization problems [article]

Evripidis Bampis, Bruno Escoffier, Alexander Kononov
2019 arXiv   pre-print
In this paper, we study the multistage variants of some important discrete minimization problems (including Minimum Cut, Vertex Cover, Set Cover, Prize-Collecting Steiner Tree, Prize-Collecting Traveling  ...  For several polynomial-time solvable problems, such as Minimum Cost Perfect Matching, the multistage variant becomes hard to approximate (even for two time steps for Minimum Cost Perfect Matching).  ...  In addition, the proposed 2-approximations are the best results that one can hope for these problems, unless there is a better approximation for Vertex Cover.  ... 
arXiv:1909.10354v1 fatcat:lizmu5xlgzefla3rtdmivz7hfe

A Branch-and-Bound Algorithm for the Knapsack Problem with Conflict Graph

Andrea Bettinelli, Valentina Cacchiani, Enrico Malaguti
2017 INFORMS journal on computing  
The goal of the KPCG is to select the maximum profit set of compatible items while satisfying the knapsack capacity constraint.  ...  We study the Knapsack Problem with Conflict Graph (KPCG), an extension of the 0-1 Knapsack Problem, in which a conflict graph describing incompatibilities between items is given.  ...  Results aggregated by density.  ... 
doi:10.1287/ijoc.2016.0742 fatcat:sdgpczmhirhrxnwjgz5sjnvcl4

An O(logn) Approximation Ratio for the Asymmetric Traveling Salesman Path Problem [chapter]

Chandra Chekuri, Martin Pál
2006 Lecture Notes in Computer Science  
We consider a variant of the traveling salesman problem (TSP): Given a directed graph G = (V, A) with non-negative arc lengths : A → R + and a pair of vertices s,t, find an s-t walk of minimum length that  ...  Although an O(log n) approximation ratio has long been known for ATSP, the best known ratio for ATSPP is O( √ n).  ...  Acknowledgments: We thank Fumei Lam for an enlightening conversation, for sending us a copy of the manuscript [19] and for pointing out [2] . We thank Moses Charikar for pointing out [18] .  ... 
doi:10.1007/11830924_11 fatcat:mf6yvlrvqvhpjgarw32b3h2nbm

Near-Optimal Budgeted Data Exchange for Distributed Loop Closure Detection

Yulun Tian, Kasra Khosoussi, Matthew Giamou, Jonathan How, Jonathan Kelly
2018 Robotics: Science and Systems XIV  
We approach this problem from different perspectives and leverage existing results on monotone submodular maximization to provide efficient approximation algorithms with performance guarantees.  ...  However, even with the most resource-efficient techniques, the resources available onboard may be insufficient for verifying every potential loop closure.  ...  ACKNOWLEDGEMENT This work was supported in part by the NASA Convergent Aeronautics Solutions project Design Environment for Novel Vertical Lift Vehicles (DELIVER), by the Northrop Grumman Corporation,  ... 
doi:10.15607/rss.2018.xiv.071 dblp:conf/rss/TianKGHK18 fatcat:bteb5pn3njaare7i7vnhctheme

Preface of Special Issue on Theoretical Aspects of Computer Science

Christoph Dürr, Thomas Schwentick
2013 Theory of Computing Systems  
Compared with the original extended abstracts the articles have been strongly revised and extended by full proofs and additional results.  ...  These extended abstracts were among the top papers of those that were chosen for presentation at STACS 2011 in a highly competitive peer-review process (after which only 54 papers out of 271 submission  ...  Bodlaender present a cubic-vertex kernel for the NP-hard Vertex Cover problem with respect to the non-standard parameter size of a minimum feedback vertex set of the input graph.  ... 
doi:10.1007/s00224-013-9467-y fatcat:47u6phttwjfyhmd63fuwo5mo4y
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