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## Unit Disk Graph Approximation (2004)

Venue: | In Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (DIAL-M |

Citations: | 62 - 10 self |

### Citations

14082 |
Computers and Intractability: A Guide to the Theory of NP-Completeness
- Garey, Johnson
- 1979
(Show Context)
Citation Context ...es from the graph's connectivity properties only. The proof is based on a reduction from an instance of 3SAT. Without loss of generality, we can assume that each variable appears in at most 3 clauses =-=[6]-=-. We give a polynomial time construction of a graph GC = (VC , EC ) from an instance C of SAT, such that the following holds: . C is satisfiable # GC is realizable as UDG . C is not satisfiable # GC i... |

849 | Routing with guaranteed delivery in ad hoc wireless networks,”
- Bose, Morin, et al.
- 2001
(Show Context)
Citation Context ...proaches lies in the area of routing where virtual coordinates represent a simple way to embody the topology of the network. Based on virtual coordinates, geometric routing algorithm such as GFG/GPSR =-=[2]-=- or GOAFR [7] can be applied. Other than for routing algorithms in multi-hop radio networks, virtual coordinates have found prominent application in the context of Internet mapping [5, 11]. Here, the ... |

631 | Predicting Internet network distance with coordinates-based approaches
- Ng, Zhang
(Show Context)
Citation Context ...uch as GFG/GPSR [2] or GOAFR [7] can be applied. Other than for routing algorithms in multi-hop radio networks, virtual coordinates have found prominent application in the context of Internet mapping =-=[5, 11]-=-. Here, the goal is to derive topological information about the Internet graph in order to improve anycast and peer-to-peer systems. The paper is organized as follows. After introducing various defini... |

387 | Geographic Routing without Location Information,"
- Rao, Ratnasamy, et al.
- 2003
(Show Context)
Citation Context ...isk graph with d # 1/ # 2 may be of independent interest. Our lower bound results are of particular interest in the light of recent work on virtual coordinates for wireless ad hoc and sensor networks =-=[12, 13, 10]-=-. The reason is that the problems of finding a good embedding of a unit disk graph in the plane, and assigning virtual coordinates to nodes in wireless multi-hop networks -- when being modelled as a u... |

367 | Localization from mere connectivity,”
- Shang, Ruml, et al.
- 2003
(Show Context)
Citation Context ...isk graph with d # 1/ # 2 may be of independent interest. Our lower bound results are of particular interest in the light of recent work on virtual coordinates for wireless ad hoc and sensor networks =-=[12, 13, 10]-=-. The reason is that the problems of finding a good embedding of a unit disk graph in the plane, and assigning virtual coordinates to nodes in wireless multi-hop networks -- when being modelled as a u... |

317 | Geometric ad-hoc routing: Of theory and practice.
- Kuhn, Wattenhofer, et al.
- 2003
(Show Context)
Citation Context ... in the area of routing where virtual coordinates represent a simple way to embody the topology of the network. Based on virtual coordinates, geometric routing algorithm such as GFG/GPSR [2] or GOAFR =-=[7]-=- can be applied. Other than for routing algorithms in multi-hop radio networks, virtual coordinates have found prominent application in the context of Internet mapping [5, 11]. Here, the goal is to de... |

140 | Ad-hoc networks beyond unit disk graphs.
- KUHN, WATTENHOFER, et al.
- 2003
(Show Context)
Citation Context ...t as # 3/2-#, where # tends to 0 as the number of nodes n goes to infinity. This inapproximability lower bound comes along with another impossibility result, namely, given a d-quasi unit disk graph G =-=[8]-=- with parameter d # 1/ # 2, it is NP -hard to find a realization (an embedding fulfilling all requirements of the quasi unit disk graph) of G. In a quasi unit disk graph, two nodes are connected by an... |

114 | Unit disk graph recognition is NP-hard.
- Breu, Kirkpatrick
- 1998
(Show Context)
Citation Context ...aph have at least distance 1. In other words, we would like to embed a given unit disk graph in the plane. Unfortunately, it can be shown that this is impossible in polynomial time unless P = NP . In =-=[3]-=-, Breu and Kirkpatrick show that given a graph G, deciding whether G is a unit disk graph is NP -complete. Finding a realization of a unit disk graph, that is, finding an embedding which fulfils all u... |

94 | Robust position-based routing in wireless ad hoc networks with unstable transmission ranges,” pp.
- ere, Fraigniaud, et al.
- 2001
(Show Context)
Citation Context ...works as a quasi unit disk graph (as opposed to a unit disk graph) has the advantage of being significantly closer to reality, while still being concise enough to permit stringent theoretical results =-=[8, 1]-=-. From a computational geometry point of view, the impossibility of finding a realization for a d-quasi unit disk graph with d # 1/ # 2 may be of independent interest. Our lower bound results are of p... |

58 | Virtual coordinates for ad hoc and sensor networks,” in
- Moscibroda, O’Dell, et al.
- 2004
(Show Context)
Citation Context ...isk graph with d # 1/ # 2 may be of independent interest. Our lower bound results are of particular interest in the light of recent work on virtual coordinates for wireless ad hoc and sensor networks =-=[12, 13, 10]-=-. The reason is that the problems of finding a good embedding of a unit disk graph in the plane, and assigning virtual coordinates to nodes in wireless multi-hop networks -- when being modelled as a u... |

10 | Range-Free Ranking in Sensors Networks and Its Applications to Localization, in
- Lotker, Albeniz, et al.
- 2004
(Show Context)
Citation Context ...mial time approximation scheme (PTAS) for the problem. Independently, Lotker et. al. also showed that no PTAS exists for the problem of assigning virtual coordinates to the nodes of a unit disk graph =-=[9]-=-. However, in [9], no actual lower bound on the approximability of the problem is given. The primary application of virtual coordinate approaches lies in the area of routing where virtual coordinates ... |