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The relation of Connected Set Cover and Group Steiner Tree

Khaled Elbassioni, Slobodan Jelić, Domagoj Matijević
2012 Theoretical Computer Science  
Based on that we obtain the first algorithm for CSC with polylogarithmic approximation guarantee as well as the first approximation algorithms for the weighted version of the problem and the version with  ...  We report that the Connected Set Cover (CSC) problem is just a special case of the Group Steiner Tree (GST) problem.  ...  [9] raise an interesting question whether there exist a polynomial algorithm for an on-line variant of the (weighted) CSC problem with a polylogarithmic approximation guarantee.  ... 
doi:10.1016/j.tcs.2012.02.035 fatcat:rjkf3ivm7fdw5owilh4osvwzzy

Efficient Construction of Dominating Set in Wireless Networks [article]

Xiaohua Xu, Xiang-Yang Li
2012 arXiv   pre-print
The objective is to find a min-weight subset D'⊆ D of disks such that each node is covered at least K disks in D'. We propose a novel two-approximation algorithm for this problem.  ...  Assume each node has a disparate communication range and is associated with a positive weight, we present a randomized algorithm to find a min-weight dominating set.  ...  Theorem 4: Suppose that there exists a polynomial aapproximation algorithm for the Minimum Geometric Hitting Set and there exists a polynomial b-approximation algorithm for the Minimum Disk Cover, then  ... 
arXiv:1208.5738v1 fatcat:v7kbyz2hczfkvn2hubcegbhc2m

Neighbourhood Evaluation Criteria for Vertex Cover Problem [article]

Kaustubh K Joshi
2020 arXiv   pre-print
Neighbourhood Evaluation Criteria is a heuristical approximate algorithm that attempts to solve the Minimum Vertex Cover. degree count is kept in check for each vertex and the highest count based vertex  ...  is included in our cover set.  ...  In such a case the NEC algorithm will pick up any node since all of them are equivalent and do not have any tiebreaker for providing a benefit for selection.  ... 
arXiv:2005.05065v1 fatcat:7tbejfmrvzgvxgulussuwspaay

An Improved Approximation Bound for Spanning Star Forest and Color Saving [chapter]

Stavros Athanassopoulos, Ioannis Caragiannis, Christos Kaklamanis, Maria Kyropoulou
2009 Lecture Notes in Computer Science  
We present a simple algorithm for the maximum spanning star forest problem.  ...  Although the algorithm is purely combinatorial, our analysis defines a linear program that uses a parameter f and which is feasible for values of the parameter f not smaller than the approximation ratio  ...  In this case, set cover is equivalent to graph coloring (i.e., the problem of coloring the nodes of a graph so that no two adjacent nodes are assigned the same color and the number of colors is minimized  ... 
doi:10.1007/978-3-642-03816-7_9 fatcat:zwinj6ydsnfltegw5oun2xchru

Page 1588 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews  
An algorithm is a differential 6- approximation for 6 € [0, 1] if the solution achieves a ratio at least O for all instances.  ...  algorithms for projective clustering.  ... 

Covering Graphs Using Trees and Stars [chapter]

G. Even, N. Garg, J. Könemann, R. Ravi, A. Sinha
2003 Lecture Notes in Computer Science  
In this paper, we provide constant factor approximation algorithms for finding tree and star covers of graphs, in the rooted and un-rooted versions. paths, walks, or stars.  ...  Most of their approximation algorithms deal with minimizing the number of covering objects (e.g. paths) subject to a constraint on the cost of each covering object.  ...  Acknowledgments We would like to thank Asaf Levin for sending us a copy of [1] and for his improved bi-criteria approximation algorithm for the unrooted k-star problem.  ... 
doi:10.1007/978-3-540-45198-3_3 fatcat:4mggqkonpjgezlpciyqsgqqrq4

Manipulating MDD Relaxations for Combinatorial Optimization [chapter]

David Bergman, Willem-Jan van Hoeve, John N. Hooker
2011 Lecture Notes in Computer Science  
We introduce a new compilation method for constructing such MDDs, as well as algorithms that manipulate the MDDs to obtain stronger relaxations and hence provide stronger lower bounds.  ...  We apply our methodology to set covering problems, and evaluate the strength of MDD relaxations to relaxations based on linear programming.  ...  For set covering problems we do this by equating a set covering instance with its equivalent logic formula.  ... 
doi:10.1007/978-3-642-21311-3_5 fatcat:qugl7k7cqjbfpigkkdy5d3cgzi

Towards a general principle of evaluation for approximate algorithms

A. Aiello, E. Burattini, A. Massarotti, F. Ventriglia
1979 RAIRO Informatique théorique  
Therefore, we can assert that if there is a "good" approximate algorithm for NODE-COVER there must be a "good" one for CLIQUE and vice versa.  ...  "good" algorithm for SET-COVERING.  ...  EVALUATION FOR APPROXIMATE ALGORITHMS 239 For this two last problems, the adoption of the relative measure (7) has induced Sahni [6] to achieve just the opposite results.  ... 
doi:10.1051/ita/1979130302271 fatcat:f2a37idqibdwxnp3kez3xqw7ne

Wireless coverage with disparate ranges

Peng-Jun Wan, Xiaohua Xu, Zhu Wang
2011 Proceedings of the Twelfth ACM International Symposium on Mobile Ad Hoc Networking and Computing - MobiHoc '11  
We present two algorithms: Ellipsoid Algorithm (EA) and Price-Directive Algorithm (PDA), and prove that by applying our algorithmic results on disk cover, the approximation ratios for EA and PDA are 2  ...  Given a set of nodes and a set of disks of disparate radii, the problem Minimum Disk Cover seeks a disk cover of all nodes with minimum cardinality.  ...  Then, all the equivalence classes for P induce a partition of P. Note that, if a set D ′ at least log L-cover one node in an equivalence class, then they at least log L-cover all nodes in that class.  ... 
doi:10.1145/2107502.2107517 dblp:conf/mobihoc/WanXW11 fatcat:jzxdbfr2xbhvrohr34divw5ib4

A (1 + ln 2)-Approximation Algorithm for Minimum-Cost 2-Edge-Connectivity Augmentation of Trees with Constant Radius [chapter]

Nachshon Cohen, Zeev Nutov
2011 Lecture Notes in Computer Science  
Tree Augmentation is equivalent to the problem of finding a minimumcost edge-cover ⊆ of a laminar set-family.  ...  We give a (1 + ln 2)-approximation algorithm for trees of constant radius. Our algorithm is based on a new decomposition of problem solutions, which may be of independent interest.  ...  Proof of the Theorem A local replacement algorithm for Set-Cover We start by describing a generic local-replacement algorithm for the following well known problem.  ... 
doi:10.1007/978-3-642-22935-0_13 fatcat:2uejkjkgsbhqxklydgahc66cla

Sink location to find optimal shelters in evacuation planning

P. Heßler, H. W. Hamacher
2015 EURO Journal on Computational Optimization  
It turns out that latter class algorithms are superior to the former ones.  ...  transported to the nodes in W .  ...  Algorithm 3 states the resulting O(A)-approximation for the n| |0 sink location problem. Here a cov (S) is for any S ⊆ V p the demand that can be covered by using only nodes in S as sinks.  ... 
doi:10.1007/s13675-015-0054-7 fatcat:u5dnw2xfgjgglj3htwlwexqk6u

Optimization of mobile backbone networks: Improved algorithms and approximation

Emily M. Craparo, Jonathan P. How, Eytan Modiano
2008 2008 American Control Conference  
An approximation algorithm is also developed that is appropriate for largescale problems.  ...  This paper presents new algorithms for throughput optimization in mobile backbone networks.  ...  level.problem instance Average time, seconds (on a log scale) Time required for exact MILP Time required for approximation algorithm (b) Computation time of the approximation algorithm and the exact (  ... 
doi:10.1109/acc.2008.4586789 dblp:conf/amcc/CraparoHM08 fatcat:vqhkilgbofgvfdqg56zdmri4je

Approximating minimum-power edge-covers and 2,3-connectivity

Guy Kortsarz, Zeev Nutov
2009 Discrete Applied Mathematics  
We give a 3/2-approximation algorithm for MPEC, improving over the 2-approximation by [M.T. Hajiaghayi, G. Kortsarz, V.S. Mirrokni, Z.  ...  Finally, we give a 4r max -approximation algorithm for the Minimum-Power Steiner Network (MPSN) problem: find a minimum-power subgraph that contains r(u, v) pairwise edgedisjoint paths for every pair u  ...  Acknowledgment We thank two anonymous referees for useful comments.  ... 
doi:10.1016/j.dam.2008.12.001 fatcat:w5xpaffknvbf7dub5angnfxjku

Maximum Lifetime Scheduling in Wireless Sensor Networks [chapter]

Akshaye Dhawan
2012 Wireless Sensor Networks - Technology and Protocols  
Acknowledgements The author would like to thank his wife Kelli for her support while working on this chapter.  ...  Using the (1 + ) Garg-Könemann approximation algorithm [21] , they provide a (1 + )(1 + 2lnn) approximation of the problem.  ...  The approximation ratios are presented for each of these algorithms. [8] also deal with the target coverage problems.  ... 
doi:10.5772/48575 fatcat:2mvtsgelljf4pkbcz6qp6k7u5a

The Generalized Deadlock Resolution Problem [chapter]

Kamal Jain, MohammadTaghi Hajiaghayi, Kunal Talwar
2005 Lecture Notes in Computer Science  
When all processes are writers (AND nodes), we give an O(log n log log n) approximation for this problem. Finally we give an LP-rounding approach and discuss some other natural variants. *  ...  On the positive side, we give algorithms which work well when the number of writers (AND nodes) or the number of readers (OR nodes) are small.  ...  The first author would also like to thanks Joseph Cheriyan and Laci Lovasz for many initial and fruitful discussions. He would also like to thank David Shmoys for a very short but helpful discussion.  ... 
doi:10.1007/11523468_69 fatcat:7bf62puakva35jcxyof3aykzqy
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