## Boundary recognition in sensor networks by topological methods (2006)

Venue: | In Proc. of the ACM/IEEE International Conference on Mobile Computing and Networking (MobiCom |

Citations: | 68 - 16 self |

### BibTeX

@INPROCEEDINGS{Wang06boundaryrecognition,

author = {Yue Wang and Jie Gao},

title = {Boundary recognition in sensor networks by topological methods},

booktitle = {In Proc. of the ACM/IEEE International Conference on Mobile Computing and Networking (MobiCom},

year = {2006},

pages = {122--133}

}

### Years of Citing Articles

### OpenURL

### Abstract

Wireless sensor networks are tightly associated with the underlying environment in which the sensors are deployed. The global topology of the network is of great importance to both sensor network applications and the implementation of networking functionalities. In this paper we study the problem of topology discovery, in particular, identifying boundaries in a sensor network. Suppose a large number of sensor nodes are scattered in a geometric region, with nearby nodes communicating with each other directly. Our goal is to find the boundary nodes by using only connectivity information. We do not assume any knowledge of the node locations or inter-distances, nor do we enforce that the communication graph follows the unit disk graph model. We propose a simple, distributed algorithm that correctly detects nodes on the boundaries and connects them into meaningful boundary cycles. We obtain as a byproduct the medial axis of the sensor field, which has applications in creating virtual coordinates for routing. We show by extensive simulation that the algorithm gives good results even for networks with low density. We also prove rigorously the correctness of the algorithm for continuous geometric domains.

### Citations

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Citation Context ...newly added sensors are deployed only in the expected region. A number of networking protocols also exploit geometric intuitions for simplicity and scalability, such as geographical greedy forwarding =-=[2, 17]-=-. Such algorithms based on local greedy advances would fail at local minima if the sensor networks have non-trivial topology. Backup methods, such as face routing on a planar subgraph, can help packet... |

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Citation Context ...newly added sensors are deployed only in the expected region. A number of networking protocols also exploit geometric intuitions for simplicity and scalability, such as geographical greedy forwarding =-=[2, 17]-=-. Such algorithms based on local greedy advances would fail at local minima if the sensor networks have non-trivial topology. Backup methods, such as face routing on a planar subgraph, can help packet... |

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Citation Context ... node whose minimum hop count to nodes in R is locally maximal. To discover extremal nodes, we have the nodes on R synchronize among themselves and start to flood the network at roughly the same time =-=[5]-=- [12]. Each node in the network records the minimum hop count to nodes in the coarse inner boundary R. This is as if we merge the nodes in R to a dummy root σ, and build a shortest path tree T (σ), ro... |

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Citation Context ... often quite irregularly shaped [13]. Algorithms that rely on the unit disk graph model fail in practice (e.g., the extraction of a planar subgraph by the relative neighborhood graph or Gabriel graph =-=[18]-=-). While the unit (or quasi-unit) disk graph assumption is often useful for theoretical analysis, it is preferable to consider algorithms that do not rely on this assumption or that degrade gracefully... |

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Citation Context ...ticularly note that our method works well even in cases of very low average degree, such as less than 10, or even as low as 6 in some models. Degree 6 has been shown to be optimal for mobile networks =-=[22]-=-. 4.1 Effect of node distribution and density For each figure in this part, we show a pink circle in the upper left corner to illustrate the communication range of the sensor field. 4.1.1 Random distr... |

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Citation Context ...chniques: geometric methods, statistical methods and topological methods. Geometric methods for boundary detection use geographical location information. The first paper on this topic, by Fang et al. =-=[6]-=-, assumes that the nodes know their geographical locations and that the communication graph follows the unit-disk graph assumption, where two nodes are connected by an edge if and only if their distan... |

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Citation Context ... paths from points of F ′ to its closest point on R. Due to the properties of wavefront propagation, the extremal points must be either on the boundary or on the medial axis, where wavefronts collide =-=[16, 20]-=-. However, since cycle R is a shortest path cycle surrounding the hole, we argue that the extremal points on the exterior of R must stay on the boundary of F ′ . Lemma 7. The extremal points are exact... |

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Citation Context ...(e.g., experiments reported in this paper use δ1 = δ2 = 0.18d). The condition on whether a node belongs to a cut can be checked locally. Alstrup et al. gave a distributed algorithm to compute the LCA =-=[1]-=-. The idea is to label the nodes of a rooted tree with O(log n) bits such that by using only the labels of two nodes one can calculate the label of their LCA. With this labeling, each pair of neighbor... |

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Citation Context ...eresare a number of routing schemes that address explicitly the importance of topological properties and propose routing with virtual coordinates that are adaptive to the intrinsic geometric features =-=[3, 7]-=-. The construction of these virtual coordinate systems requires the identification of topological features first. Our focus is to develop a distributed algorithm that detects hole boundaries. Thus, a ... |

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Citation Context .... In practice the sensors are not as dense and they are not necessarily deployed uniformly randomly. There are also topological methods to detect insufficient sensor coverage and holes. Ghrist et al. =-=[14]-=- proposed an algorithm that detects holes via homology with no knowledge of sensor locations; however, the algorithm is centralized, with assumptions that both the sensing range and communication rang... |

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Citation Context ...eresare a number of routing schemes that address explicitly the importance of topological properties and propose routing with virtual coordinates that are adaptive to the intrinsic geometric features =-=[3, 7]-=-. The construction of these virtual coordinate systems requires the identification of topological features first. Our focus is to develop a distributed algorithm that detects hole boundaries. Thus, a ... |

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Citation Context ...with no knowledge of sensor locations; however, the algorithm is centralized, with assumptions that both the sensing range and communication range are disks with radii carefully tuned. Kröller et al. =-=[19]-=- presented a new algorithm by searching for combinatorial structures called flowers and augmented cycles. They make less restrictive assumptions on the problem setup, modeling the communication graph ... |

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Citation Context ...ole boundaries and eventually discovers boundary cycles. Statistical methods for boundary detection usually make assumptions about the probability distribution of the sensor deployment. Fekete et al. =-=[9]-=- proposed a boundary detection algorithm for sensors (uniformly) randomly deployed inside a geometric region. The main idea is that nodes on the boundaries have much lower average degrees than nodes i... |

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(Show Context)
Citation Context ...ccess of this algorithm critically depends on the identification of at least one flower structure, which may not always be the case especially in a sparse network. Towards a practical solution, Funke =-=[10]-=- developed a simple heuristic with only connectivity information. The basic idea is to construct iso-contours based on hop count from a root node and identify where the contours are broken. Under the ... |

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Citation Context ...rentiate boundary nodes. Another statistical approach is to compute the “restricted stress centrality” of a vertex v, which measures the number of shortest paths going through v with a bounded length =-=[8]-=-. Nodes in the interior tend to have a higher centrality than nodes on the boundary. With a sufficiently high density, the centrality of the nodes exhibits bi-modal behavior and thus can be used to de... |

18 | Hole detection or: how much geometry hides in connectivity
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Citation Context ... for each point on the geometry boundary the algorithm marks a corresponding sensor node within distance 4.8, and each node marked as boundary is within distance 2.8 from the actual geometry boundary =-=[11]-=-. The simplicity of the algorithm is appealing; however, the algorithm only identifies nodes that are near the boundaries but does not show how they are connected in a meaningful way. The density requ... |

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Citation Context ...r boundary R + ; the correctness of the inner boundary R − can be proved in the same way. By the refinement algorithm, we can find the Voronoi diagram of R by a wavefront propagation algorithm (e.g., =-=[15]-=-). The extremal points are the points that do not stay on the interior of any shortest paths from points of F ′ to its closest point on R. Due to the properties of wavefront propagation, the extremal ... |

16 |
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Citation Context ...ctors and SPM-vertices, B, is often called the cut locus. Our boundary detection algorithm makes use of the properties of the shortest path map. We list below the useful properties that are proved in =-=[20]-=-. Lemma 4 ( [20]). Given a closed polygonal region F in the plane, with k simple polygonal obstacles inside. The shortest path map at an arbitrary root r ∈ F has the following properties. 1. Each bise... |