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## Local approximation schemes for ad hoc and sensor networks (2005)

Venue: | In Proc. 3rd Joint Workshop on Foundations of Mobile Computing (DialM-POMC |

Citations: | 38 - 9 self |

### Citations

1995 | Energy-efficient communication protocol for wireless microsensor networks
- Heinzelman, Chandrakasan, et al.
(Show Context)
Citation Context ...e literature, numerous proposals to structure wireless networks have been presented. The main purposes of such structures are to provide the communication between adjacent nodes (MAC layer protocols, =-=[32, 31, 14]-=-) and between distant nodes (routing protocols, [34, 2, 36, 33, 35]), to improve the energy efficiency of the network [10], or to enable a proper initialization of the network [18, 27]. As diverse as ... |

373 | On calculating connected dominating set for efficient routing in ad hoc wireless networks
- Wu, Li
- 1999
(Show Context)
Citation Context ...rks have been presented. The main purposes of such structures are to provide the communication between adjacent nodes (MAC layer protocols, [32, 31, 14]) and between distant nodes (routing protocols, =-=[34, 2, 36, 33, 35]-=-), to improve the energy efficiency of the network [10], or to enable a proper initialization of the network [18, 27]. As diverse as the different structures may be, there are a few key primitives on ... |

370 |
Approximation Algorithms for NP-complete problems in planar graphs
- Baker
- 1994
(Show Context)
Citation Context ...ersection graphs, especially in disk graphs, have been studied in great detail. However, most approaches that yield a PTAS exploit the representation, and then apply a shifting strategy introduced in =-=[4, 15]-=-. In [11], a PTAS for the Maximum Independent Set problem on general disk graphs is described, and in [13], the Minimum Dominating Set problem is considered for unit disk graphs together with other pr... |

335 | Garcia-Luna-Aceves, “Energy-Efficient, collision-Free medium access control for wireless sensor networks
- Rajendran, Obraczka, et al.
- 2003
(Show Context)
Citation Context ...e literature, numerous proposals to structure wireless networks have been presented. The main purposes of such structures are to provide the communication between adjacent nodes (MAC layer protocols, =-=[32, 31, 14]-=-) and between distant nodes (routing protocols, [34, 2, 36, 33, 35]), to improve the energy efficiency of the network [10], or to enable a proper initialization of the network [18, 27]. As diverse as ... |

307 |
Unit disk graphs
- Clark, Colbourn, et al.
- 1990
(Show Context)
Citation Context ...ith maximum cardinality. Note that while a MIS can easily be computed using a greedy approach, finding a maximum independent set is a strongly NP-hard problem, even when restricting the input to UDGs =-=[8]-=-. For any two vertices u, v ∈ V , we denote by d(u, v) the shortest hop-distance between u and v. Using this, we call Γr(v) the (closed) r-neighborhood of v, that is, for any r ≥ 0, and v ∈ V , we def... |

269 | Distributed construction of connected dominating set in wireless ad hoc networks
- Wang, Alzoubi, et al.
- 2002
(Show Context)
Citation Context ...rks have been presented. The main purposes of such structures are to provide the communication between adjacent nodes (MAC layer protocols, [32, 31, 14]) and between distant nodes (routing protocols, =-=[34, 2, 36, 33, 35]-=-), to improve the energy efficiency of the network [10], or to enable a proper initialization of the network [18, 27]. As diverse as the different structures may be, there are a few key primitives on ... |

256 |
Complexity of Network Synchronization
- Awerbuch
- 1985
(Show Context)
Citation Context ... to send a message to all of its neighbors. However, note that at the cost of higher message complexity, our algorithms can also be employed in asynchronous settings using the notion of synchronizers =-=[3]-=-. In each communication round, a node can send a message to each of its neighbors in the graph. In other words, we study the classic message-passing model which abstracts away collisions. In a graph G... |

243 | Approximation schemes for covering and packing problems in image processing and VLSI
- Hochbaum, Maass
- 1985
(Show Context)
Citation Context ...ersection graphs, especially in disk graphs, have been studied in great detail. However, most approaches that yield a PTAS exploit the representation, and then apply a shifting strategy introduced in =-=[4, 15]-=-. In [11], a PTAS for the Maximum Independent Set problem on general disk graphs is described, and in [13], the Minimum Dominating Set problem is considered for unit disk graphs together with other pr... |

206 | E.: Scheduling algorithms for multihop radio networks
- Ramanathan, Lloyd
- 1993
(Show Context)
Citation Context ...e literature, numerous proposals to structure wireless networks have been presented. The main purposes of such structures are to provide the communication between adjacent nodes (MAC layer protocols, =-=[32, 31, 14]-=-) and between distant nodes (routing protocols, [34, 2, 36, 33, 35]), to improve the energy efficiency of the network [10], or to enable a proper initialization of the network [18, 27]. As diverse as ... |

170 | Finding nearest neighbors in growth-restricted metrics
- Karger, Ruhl
- 2002
(Show Context)
Citation Context ...e relationship between these definitions. Especially in the context of P2P networks, polynomial growth means that the number of nodes at distance r from any given node depends polynomially on r (e.g. =-=[1, 17]-=-). In our definition, however, we use the term for the purpose of modeling the wireless nature of communication in radio networks. Particularly, our definition does not restrict the number of nodes lo... |

150 | Simple heuristics for unit disk graphs
- Marathe, Breu, et al.
- 1995
(Show Context)
Citation Context ...ng is a constant approximation for minimum vertex coloring. These simple observations suffice to obtain efficient sequential and distributed constant approximation algorithms for those three problems =-=[26]-=-. In the sequential scenario, however, even better solutions are known. Particularly, polynomial approximation schemes (PTAS) are known for various combinatorial optimization problems in unit disk gra... |

138 |
Deterministic coin tossing with applications to optimal parallel list ranking, Information and Control 70
- Cole, Vishkin
- 1986
(Show Context)
Citation Context ...t I can be created, e.g., by a local algorithm presented in [21]. The resulting cluster graph G then has bounded degree (Lemma 3.2), which allows for an efficient (∆G+1)-coloring by a local algorithm =-=[9]-=-. This structure is then exploited to simultaneously create local independent sets in the neighborhoods of central vertices with the same color. These local independent sets are constructed taking int... |

138 | Ad-hoc networks beyond unit disk graphs,” Proc. joint workshop on Foundations of mobile computing citation
- Kuhn, Wattenhofer, et al.
- 2003
(Show Context)
Citation Context ...adius of the neighborhoods only. Most intersection graphs used to model wireless adhoc networks, including (Quasi) Unit Disk and Coverage Area Graphs satisfy the polynomially bounded growth condition =-=[25, 28]-=-. Consider a subset W ⊆ V of vertices called clusterheads. A clustergraph G of radius c is then given by introducing edges in the c-hop neighborhoods around w ∈ W . In this context, the vertices in W ... |

136 | R.: What Cannot Be Computed Locally
- Kuhn, Moscibroda, et al.
- 2004
(Show Context)
Citation Context ...er the last years. As for the minimum dominating set problem in general graphs, algorithms with provably efficient time-complexity and approximation guarantees have been given in [16, 24], whereas in =-=[19]-=-, distributed time-lower bounds have been proven. For the unit disk graph, a multiplicity of algorithms have been proposed in the wireless networking community. Unfortunately, most of them have the pr... |

133 | R.: Constant-Time Distributed Dominating Set Approximation
- Kuhn, Wattenhofer
- 2005
(Show Context)
Citation Context ...tudied intensively over the last years. As for the minimum dominating set problem in general graphs, algorithms with provably efficient time-complexity and approximation guarantees have been given in =-=[16, 24]-=-, whereas in [19], distributed time-lower bounds have been proven. For the unit disk graph, a multiplicity of algorithms have been proposed in the wireless networking community. Unfortunately, most of... |

116 | NC-Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs
- Hunt, Marathe, et al.
- 1998
(Show Context)
Citation Context ...on with an approximation ratio of 1+ ε. If a representation (coordinates in R2) of the UDG is known, polynomial-time approximation schemes for minimum dominating set and maximum independent set exist =-=[13]-=-. That is, for an arbitrary constant ε > 0, a (1 + ε)-approximation can be computed in polynomial time. In [30, 29], a PTAS which does not rely on coordinate information has been presented. Unfortunat... |

113 | Unit Disk Graph Recognition is NPhard
- Breu, Kirkpatrick
- 1998
(Show Context)
Citation Context ...ring centralized approaches, the case when there is no geometric representation of a (unit) disk graph given is significantly different: Computing a corresponding representation is an NP-hard problem =-=[6]-=-, in fact, it does not even admit a PTAS [22]. For this case, there also exist approximation schemes that do not rely on coordinates of the vertices given in [30] and [29]. 3. MODEL AND DEFINITIONS A ... |

108 | Message-optimal connected dominating sets in mobile ad hoc networks,” in MobiHoc
- Alzoubi, Wan, et al.
(Show Context)
Citation Context ...rks have been presented. The main purposes of such structures are to provide the communication between adjacent nodes (MAC layer protocols, [32, 31, 14]) and between distant nodes (routing protocols, =-=[34, 2, 36, 33, 35]-=-), to improve the energy efficiency of the network [10], or to enable a proper initialization of the network [18, 27]. As diverse as the different structures may be, there are a few key primitives on ... |

101 | Polynomial-time approximation schemes for geometric graphs
- Erlebach, Jansen, et al.
- 2001
(Show Context)
Citation Context ...aphs, especially in disk graphs, have been studied in great detail. However, most approaches that yield a PTAS exploit the representation, and then apply a shifting strategy introduced in [4, 15]. In =-=[11]-=-, a PTAS for the Maximum Independent Set problem on general disk graphs is described, and in [13], the Minimum Dominating Set problem is considered for unit disk graphs together with other problems fo... |

97 | Enhancing Ad Hoc Routing with Dynamic Virtual Infrastructures
- Sinha, Sivakumar, et al.
- 2001
(Show Context)
Citation Context |

94 | Suel R: An Efficient Distributed Algorithm for Constructing Small Dominating Sets
- Jia, Rajaraman
(Show Context)
Citation Context ...tudied intensively over the last years. As for the minimum dominating set problem in general graphs, algorithms with provably efficient time-complexity and approximation guarantees have been given in =-=[16, 24]-=-, whereas in [19], distributed time-lower bounds have been proven. For the unit disk graph, a multiplicity of algorithms have been proposed in the wireless networking community. Unfortunately, most of... |

84 | Polynomial-Time Approximation Scheme for Minimum Connected Dominating Set
- Cheng, Huang, et al.
- 2003
(Show Context)
Citation Context ...blem on general disk graphs is described, and in [13], the Minimum Dominating Set problem is considered for unit disk graphs together with other problems for which the shifting strategy is viable. In =-=[7]-=-, a PTAS for the Minimum Connected Dominating Set problem is given. 98 Approaches based on the shifting strategy are inherently central and cannot efficiently be adapted to work in a distributed conte... |

83 | The price of being near-sighted
- Kuhn, Moscibroda, et al.
- 2006
(Show Context)
Citation Context ...ributed approximation schemes were given for covering and packing linear programs where solutions may be fractional and hence, the problem becomes easier because no symmetries have to be broken, e.g. =-=[5, 23]-=-. The remainder of this paper is organized as follows. An overview of relevant previous work in given in Section 2. We formally introduce the model of computation in Section 3. Section 4 introduces th... |

69 | D: Global Optimization Using Local Information with Applications to Flow Control
- Bartal, JW, et al.
- 1997
(Show Context)
Citation Context ...ributed approximation schemes were given for covering and packing linear programs where solutions may be fractional and hence, the problem becomes easier because no symmetries have to be broken, e.g. =-=[5, 23]-=-. The remainder of this paper is organized as follows. An overview of relevant previous work in given in Section 2. We formally introduce the model of computation in Section 3. Section 4 introduces th... |

63 | Initializing Newly Deployed Ad Hoc and Sensor Networks
- Kuhn, Moscibroda, et al.
- 2004
(Show Context)
Citation Context ... protocols, [32, 31, 14]) and between distant nodes (routing protocols, [34, 2, 36, 33, 35]), to improve the energy efficiency of the network [10], or to enable a proper initialization of the network =-=[18, 27]-=-. As diverse as the different structures may be, there are a few key primitives on which most of them are built. The most important such primitives are classical graph-theoretic objects such as domina... |

61 |
On the locality of bounded growth
- Kuhn, Moscibroda, et al.
- 2005
(Show Context)
Citation Context ...n [21], a MIS can be computed deterministically in time TMIS ∈ O(log∆ log∗n) in growth-bounded graphs, hence yielding an O(log∆ log∗n+log∗n/εO(1)) time algorithm in combination with our algorithm. In =-=[20]-=-, the UDG definition has been extended to arbitrary metric spaces, resulting in the notion of unit ball graphs (UBG). The nodes of a unit ball graph are assumed to be points of a metric space and two ... |

61 | Unit disk graph approximation
- Kuhn, Moscibroda, et al.
- 2004
(Show Context)
Citation Context ...here is no geometric representation of a (unit) disk graph given is significantly different: Computing a corresponding representation is an NP-hard problem [6], in fact, it does not even admit a PTAS =-=[22]-=-. For this case, there also exist approximation schemes that do not rely on coordinates of the vertices given in [30] and [29]. 3. MODEL AND DEFINITIONS A wireless ad-hoc network is modeled by a graph... |

51 | Distributed Low-Cost Backbone Formation for Wireless Ad Hoc Networks
- Wang, Wang, et al.
- 2005
(Show Context)
Citation Context |

47 | Fast deterministic distributed maximal independent set computation on growth-bounded graphs
- Kuhn, Moscibroda, et al.
- 2005
(Show Context)
Citation Context ...rhood is at most polynomial in r. Note that the growth of a UDG, is at most quadratic in r and hence, every UDG is growth-bounded. Our results carry over to general growth-bounded graphs. As shown in =-=[21]-=-, a MIS can be computed deterministically in time TMIS ∈ O(log∆ log∗n) in growth-bounded graphs, hence yielding an O(log∆ log∗n+log∗n/εO(1)) time algorithm in combination with our algorithm. In [20], ... |

44 | R.: Maximal Independent Sets in Radio Networks
- Moscibroda, Wattenhofer
- 2005
(Show Context)
Citation Context ... protocols, [32, 31, 14]) and between distant nodes (routing protocols, [34, 2, 36, 33, 35]), to improve the energy efficiency of the network [10], or to enable a proper initialization of the network =-=[18, 27]-=-. As diverse as the different structures may be, there are a few key primitives on which most of them are built. The most important such primitives are classical graph-theoretic objects such as domina... |

35 | Name independent routing for growth bounded networks
- Abraham, Malkhi
- 2005
(Show Context)
Citation Context ...e relationship between these definitions. Especially in the context of P2P networks, polynomial growth means that the number of nodes at distance r from any given node depends polynomially on r (e.g. =-=[1, 17]-=-). In our definition, however, we use the term for the purpose of modeling the wireless nature of communication in radio networks. Particularly, our definition does not restrict the number of nodes lo... |

17 | A PTAS for the minimum dominating set problem in unit disk graphs
- Nieberg, Hurink
- 2005
(Show Context)
Citation Context ...-time approximation schemes for minimum dominating set and maximum independent set exist [13]. That is, for an arbitrary constant ε > 0, a (1 + ε)-approximation can be computed in polynomial time. In =-=[30, 29]-=-, a PTAS which does not rely on coordinate information has been presented. Unfortunately, similar results are not known in distributed settings, where each node has to base its decision on information... |

15 | On the Node-Scheduling Approach to Topology Control
- Deb, Nath
- 2005
(Show Context)
Citation Context ...rovide the communication between adjacent nodes (MAC layer protocols, [32, 31, 14]) and between distant nodes (routing protocols, [34, 2, 36, 33, 35]), to improve the energy efficiency of the network =-=[10]-=-, or to enable a proper initialization of the network [18, 27]. As diverse as the different structures may be, there are a few key primitives on which most of them are built. The most important such p... |

10 |
A robust PTAS for maximum independent sets in unit disk graphs
- Nieberg, Hurink, et al.
- 2004
(Show Context)
Citation Context ...-time approximation schemes for minimum dominating set and maximum independent set exist [13]. That is, for an arbitrary constant ε > 0, a (1 + ε)-approximation can be computed in polynomial time. In =-=[30, 29]-=-, a PTAS which does not rely on coordinate information has been presented. Unfortunately, similar results are not known in distributed settings, where each node has to base its decision on information... |

6 |
Distributed Algorithms for Coloring and Connected Domination in Wireless Ad Hoc Networks
- Gandhi, Parthasarathy
- 2004
(Show Context)
Citation Context ...ed in the wireless networking community. Unfortunately, most of them have the property that in the worst case, they have either linear running time [34, 2, 35] or no approximation guarantees [36]. In =-=[12]-=-, an algorithm was recently proposed that computes a constant approximation to the connected dominating set problem in polylogarithmic time in a model that accounts for possible collisions of messages... |

5 | Wireless communication graphs
- Nieberg, Hurink
- 2004
(Show Context)
Citation Context ...adius of the neighborhoods only. Most intersection graphs used to model wireless adhoc networks, including (Quasi) Unit Disk and Coverage Area Graphs satisfy the polynomially bounded growth condition =-=[25, 28]-=-. Consider a subset W ⊆ V of vertices called clusterheads. A clustergraph G of radius c is then given by introducing edges in the c-hop neighborhoods around w ∈ W . In this context, the vertices in W ... |