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## Constant-Time Distributed Dominating Set Approximation (2003)

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Venue: | In Proc. of the 22 nd ACM Symposium on the Principles of Distributed Computing (PODC |

Citations: | 133 - 22 self |

### Citations

13826 |
Computers and Intractability, A Guide to the Theory of NP-completeness (Freeman
- Garey, Johnson
- 1968
(Show Context)
Citation Context ...e Swiss National Science Foundation under grant number 5005-67322. minimum size. MDS and the closely related minimum set cover problem are two of the first problems that have been shown to be NP-hard =-=[8, 12]-=-. In this paper, we present a distributed approximation algorithm for MDS. In computer networks it is often desirable to have a dominating set in order to enable a hierarchical structure in which the ... |

1934 |
Reducibility among combinatorial problems
- Karp
- 1972
(Show Context)
Citation Context ...e Swiss National Science Foundation under grant number 5005-67322. minimum size. MDS and the closely related minimum set cover problem are two of the first problems that have been shown to be NP-hard =-=[8, 12]-=-. In this paper, we present a distributed approximation algorithm for MDS. In computer networks it is often desirable to have a dominating set in order to enable a hierarchical structure in which the ... |

820 |
Approximation Algorithms for Combinatorial Problems
- Johnson
- 1974
(Show Context)
Citation Context ...nsively been studied over the last 30 years. The problem of finding a minimum dominating set has been proven to be NP-hard in [8, 12]. The best known approximation is achieved by the greedy algorithm =-=[11, 14, 18]-=-. As long as there are uncovered nodes, the greedy algorithm picks a node which covers the biggest number of uncovered nodes and puts it into the dominating set. It achieves an approximation ratio of ... |

765 | A threshold of ln n for approximating set cover
- Feige
- 1998
(Show Context)
Citation Context ...imation ratio of ln # where # is the highest degree in the graph. Unless the problems of NP can be solved by deterministicsn O(log log n) algorithms, this is the best possible up to lower order terms =-=[6]-=-. For the related problem of finding small connected dominating sets, a similar approach is shown to be a (ln #+ O(1))-approximation in [9]. For the distributed construction of dominating sets, severa... |

373 | On calculating connected dominating set for efficient routing in ad hoc wireless networks
- Wu, Li
- 1999
(Show Context)
Citation Context ...distributed construction of dominating sets, several algorithms have been developed. In [13] an algorithm which calculates a dominating set of size at most n/2 in O(log ∗ n) rounds has been proposed. =-=[19]-=- presents a (connected) dominating set algorithm which runs in a constant number of rounds. None of those algorithms achieves a nontrivial asymptotic bound on the approximation ratio. Note that O(∆) i... |

368 | Randomized rounding: A technique for provably good algorithms and algorithmic proofs - Raghavan, Thompson - 1987 |

365 | Approximation Algorithms for Connected Dominating Sets
- Guha, Khuller
- 1996
(Show Context)
Citation Context ...lgorithms, this is the best possible up to lower order terms [6]. For the related problem of finding small connected dominating sets, a similar approach is shown to be a (ln #+ O(1))-approximation in =-=[9]-=-. For the distributed construction of dominating sets, several algorithms have been developed. In [13] an algorithm which calculates a dominating set of size at most n/2 in O(log # n) rounds has been ... |

318 |
On the ratio of optimal integral and fractional covers
- Lovasz
- 1975
(Show Context)
Citation Context ...nsively been studied over the last 30 years. The problem of finding a minimum dominating set has been proven to be NP-hard in [8, 12]. The best known approximation is achieved by the greedy algorithm =-=[11, 14, 18]-=-. As long as there are uncovered nodes, the greedy algorithm picks a node which covers the biggest number of uncovered nodes and puts it into the dominating set. It achieves an approximation ratio of ... |

159 | Topology Control and Routing in Ad hoc Networks: A Survey
- Rajaraman
- 2002
(Show Context)
Citation Context ... the unit disk graph the problem is known to remain NP-hard; however, constant factor approximations are possible in this case. For a recent survey on ad-hoc routing and related problems, we refer to =-=[17]-=-. 3. NOTATION AND PRELIMINARIES In this section we introduce notations as well as some mathematical theorems which are used in the paper. The subject of this paper is the distributed construction of d... |

120 | A tight analysis of the greedy algorithm for set cover
- Slavík
- 1996
(Show Context)
Citation Context ...ensively been studied over the last 30 years. The problem of finding a minimum dominating set has been proven to be NPhard in [8, 12]. The best known approximation is achieved by the greedy algorithm =-=[11, 14, 18]-=-. As long as there are uncovered nodes, the greedy algorithm picks a node which covers the biggest number of uncovered nodes and puts it into the dominating set. It achieves an approximation ratio of ... |

108 | Message-optimal connected dominating sets in mobile ad hoc networks,” in MobiHoc
- Alzoubi, Wan, et al.
(Show Context)
Citation Context ...r program. For ad-hoc networks, the (connected) dominating set problem has also been studied for special graphs. In particular for the unit disk graph a number of publications have been written (e.g. =-=[1, 7]-=-). For the unit disk graph the problem is known to remain NP-hard; however, constant factor approximations are possible in this case. For a recent survey on ad-hoc routing and related problems, we ref... |

94 | Suel R: An Efficient Distributed Algorithm for Constructing Small Dominating Sets
- Jia, Rajaraman
(Show Context)
Citation Context ...cal algorithms) . So far, the only algorithm which achieves a nontrivial approximation ratio---o(#)---in a nontrivial number of rounds---o(diam(G))---for MDS was developed by Jia, Rajaraman, and Suel =-=[10]-=-. In expectation, their algorithm achieves an O(log #)-approximation while the number of rounds is O(log n log #) with high probability. In this paper, we present the first distributed MDS algorithm w... |

92 | Zhang L, Zhu A: Discrete Mobile Centers
- Gao, Guibas, et al.
(Show Context)
Citation Context ...r program. For ad-hoc networks, the (connected) dominating set problem has also been studied for special graphs. In particular for the unit disk graph a number of publications have been written (e.g. =-=[1, 7]-=-). For the unit disk graph the problem is known to remain NP-hard; however, constant factor approximations are possible in this case. For a recent survey on ad-hoc routing and related problems, we ref... |

84 | A parallel approximation algorithm for positive linear programming
- Luby, Nisan
- 1993
(Show Context)
Citation Context ...ted in [5], recently. In our algorithm, we first solve the LP relaxation---a positive linear program---of MDS. Parallel and distributed algorithms for positive linear programming have been studied in =-=[15]-=- and [2], respectively. In polylogarithmic time they both achieve a (1 + #)-approximation for the linear program. For ad-hoc networks, the (connected) dominating set problem has also been studied for ... |

71 | Fast Distributed Algorithms for (Weakly) Connected Dominating Sets and Linear-Size Skeletons
- Dubhashi, Mei, et al.
- 2003
(Show Context)
Citation Context ...ylogarithmic time. For the connected dominating set problem, a distributed algorithm which also achieves an approximation ratio of O(log #) in a polylogarithmic number of rounds has been presented in =-=[5]-=-, recently. In our algorithm, we first solve the LP relaxation---a positive linear program---of MDS. Parallel and distributed algorithms for positive linear programming have been studied in [15] and [... |

69 | D: Global Optimization Using Local Information with Applications to Flow Control
- Bartal, JW, et al.
- 1997
(Show Context)
Citation Context ...], recently. In our algorithm, we first solve the LP relaxation---a positive linear program---of MDS. Parallel and distributed algorithms for positive linear programming have been studied in [15] and =-=[2]-=-, respectively. In polylogarithmic time they both achieve a (1 + #)-approximation for the linear program. For ad-hoc networks, the (connected) dominating set problem has also been studied for special ... |

64 | Fast distributed construction of small k-dominating sets and applications
- Kutten, Peleg
- 1998
(Show Context)
Citation Context ...small connected dominating sets, a similar approach is shown to be a (ln #+ O(1))-approximation in [9]. For the distributed construction of dominating sets, several algorithms have been developed. In =-=[13]-=- an algorithm which calculates a dominating set of size at most n/2 in O(log # n) rounds has been proposed. [19] presents a (connected) dominating set algorithm which runs in a constant number of roun... |

64 | On the ratio of optimal integral and fractional covers. Discrete mathematics - Lovász - 1975 |

42 |
Vazirani V: Primal-Dual RNC Approximation Algorithms for Set Cover and Covering Integer Programs
- Rajagopalan
- 1998
(Show Context)
Citation Context ...n ratio is asymptotically optimal---O(log #)---and the algorithm terminates after O(log n log #) rounds with high probability. The algorithm of [10] is related to the parallel set cover algorithms in =-=[3, 16]-=-, which achieve O(log #) approximations in polylogarithmic time. For the connected dominating set problem, a distributed algorithm which also achieves an approximation ratio of O(log #) in a polylogar... |

37 |
P: Efficient NC Algorithms for Set Cover with Applications to Learning and Geometry
- Berger, Rompel, et al.
- 1994
(Show Context)
Citation Context ...n ratio is asymptotically optimal---O(log #)---and the algorithm terminates after O(log n log #) rounds with high probability. The algorithm of [10] is related to the parallel set cover algorithms in =-=[3, 16]-=-, which achieve O(log #) approximations in polylogarithmic time. For the connected dominating set problem, a distributed algorithm which also achieves an approximation ratio of O(log #) in a polylogar... |

30 | DS: Computers and Intractability, A Guide to the Theory of NP-Completeness. W.H - MR, Johnson |

23 | Combinatorial Optimization: A - Grotschel, Lovasz - 1993 |

21 | Reducibility among combinatorial problems - RM - 1972 |

7 |
On calculating connected dominating sets for ecient routing in ad hoc wireless networks
- Wu, Li
- 1999
(Show Context)
Citation Context ...distributed construction of dominating sets, several algorithms have been developed. In [13] an algorithm which calculates a dominating set of size at most n/2 in O(log # n) rounds has been proposed. =-=[19]-=- presents a (connected) dominating set algorithm which runs in a constant number of rounds. None of those algorithms achieves a non-trivial asymptotic bound on the approximation ratio. Note that O(#) ... |

2 | Nisan N: A ParallelApproximationAlgorithm for Positive Linear Programming - Luby - 1993 |

1 |
A Tight Analysis of the Greedy Algorithm for Set Cover
- ik
- 1996
(Show Context)
Citation Context ...nsively been studied over the last 30 years. The problem of finding a minimum dominating set has been proven to be NP-hard in [8, 12]. The best known approximation is achieved by the greedy algorithm =-=[11, 14, 18]-=-. As long as there are uncovered nodes, the greedy algorithm picks a node which covers the biggest number of uncovered nodes and puts it into the dominating set. It achieves an approximation ratio of ... |

1 | Panconesi A, Radhakrishnan J, Srinivasan A: Fast Distributed Algorithms for (Weakly) Connected Dominating Sets and Linear-Size Skeletons - Dubhashi, Mei |

1 | Moscibroda T, Wattenhofer R: What Cannot Be Computed Locally - Kuhn |