## Approximately uniform random sampling in sensor networks (2004)

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Venue: | In Proc. of the 1st Workshop on Data Management in Sensor Networks (DMSN ’04 |

Citations: | 24 - 1 self |

### BibTeX

@INPROCEEDINGS{Bash04approximatelyuniform,

author = {Boulat A. Bash and John W. Byers and Jeffrey Considine},

title = {Approximately uniform random sampling in sensor networks},

booktitle = {In Proc. of the 1st Workshop on Data Management in Sensor Networks (DMSN ’04},

year = {2004},

pages = {32--39}

}

### Years of Citing Articles

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### Abstract

Recent work in sensor databases has focused extensively on distributed query problems, notably distributed computation of aggregates. Existing methods for computing aggregates broadcast queries to all sensors and use in-network aggregation of responses to minimize messaging costs. In this work, we focus on uniform random sampling across nodes, which can serve both as an alternative building block for aggregation and as an integral component of many other useful randomized algorithms. Prior to our work, the best existing proposals for uniform random sampling of sensors involve contacting all nodes in the network. We propose a practical method which is only approximately uniform, but contacts a number of sensors proportional to the diameter of the network instead of its size. The approximation achieved is tunably close to exact uniform sampling, and only relies on well-known existing primitives, namely geographic routing, distributed computation of Voronoi regions and von Neumann’s rejection method. Ultimately, our sampling algorithm has the same worst-case asymptotic cost as routing a point-to-point message, and thus it is asymptotically optimal among request/reply-based sampling methods. We provide experimental results demonstrating the effectiveness of our algorithm on both synthetic and real sensor topologies. 1

### Citations

1802 | GPSR: Greedy Perimeter Stateless Routing for Wireless Networks
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(Show Context)
Citation Context ... spatial samples in the expectation. This cost is low since the messaging cost of computing a spatial sample is akin to routing a point-to-point message using a geographic routing method such as GPSR =-=[8]-=-. In the worst case, such a message traverses the diameter of the network. In contrast, the best existing methods for node sampling, which can compute an exactly uniform sample, necessitate contacting... |

1190 | TAG: A tiny aggregation service for ad-hoc sensor networks
- Madden, Franklin, et al.
- 2002
(Show Context)
Citation Context ...g a request/reply model in which a query is broadcast to a region of interest, individual sensors make best-effort replies, and responses are aggregated in-network en route to the origin of the query =-=[3, 11, 20]-=-. In this paper, we argue that there is a rich and relatively under-explored set of classic statistical methods that have not yet been extensively studied in the domain of sensor databases. In particu... |

1171 | An Energy-Efficient Mac Protocol for Wireless Sensor Networks
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- 2002
(Show Context)
Citation Context ...ary to put all small cells to sleep to remove their impact. We note that this approach is similar in spirit to some routing schemes which use sleep for power management, particularly in crowded areas =-=[21]-=-. Because the sensed values from the sleeping nodes are unavailable, this approach may not be appropriate for some applications. Pointers: Another method for increasing the sampling probability of sma... |

1064 |
Computational Geometry: Algorithms and Applications
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- 2000
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Citation Context ... we must also quantify the size of the region of points that are closest to a particular sensor s. Formally, the set of points closer to sensor s than any other sensor is called the Voronoi cell of s =-=[4]-=-. In the planar case which we consider, the Voronoi cell of s is a convex polygon containing s, where each edge of this polygon lies on a perpendicular bisector between s and another sensor. The exact... |

731 |
The art of computer programming, Volume2, Seminumerical algorithms
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(Show Context)
Citation Context ...ch of the early work on random sampling focused on sampling complex distributions, assuming the ability to sample simpler distributions. A well known example of this is von Neumann’s rejection metho=-=d [10, 19]-=-. Suppose we wish to sample from a distribution with probability density function f (i.e. an event t has probability f(t)). If we can sample from a distribution with probability density function g, th... |

388 | The Cougar Approach to In-Network Query Processing in Sensor Networks
- Yao, Gehrke
(Show Context)
Citation Context ...g a request/reply model in which a query is broadcast to a region of interest, individual sensors make best-effort replies, and responses are aggregated in-network en route to the origin of the query =-=[3, 11, 20]-=-. In this paper, we argue that there is a rich and relatively under-explored set of classic statistical methods that have not yet been extensively studied in the domain of sensor databases. In particu... |

369 |
D.E.: Mica: A wireless platform for deeply embedded networks
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Citation Context ...e to failure, are highly resourceconstrained, and must communicate across a lossy network. Sensor networks comprised of small battery-powered motes are a representative instantiation of this scenario =-=[7]-=-. In such an environment, aggregation queries are particularly effective, as they are robust to node and link failures, can be resilient to incorrect or outlying responses, and are amenable to the use... |

326 | Geographic routing without location information
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- 2003
(Show Context)
Citation Context ...rge cell would donate part of its “unused” area to its small neighbor. Virtual coordinates: Instead of using real-world geographic coordinates to map points to sensors, we can use virtual coordina=-=tes [14, 15]-=-, modified to include either a repulsive force between close sensors, or a hard lower bound on the inter-sensor distances. Virtual coordinate spaces also allow the boundaries of the sensor network to ... |

264 |
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Citation Context ...ent and data aggregation problems, we also note that it is an integral component of other useful randomized algorithms that are potentially applicable to sensor networks, including randomized routing =-=[18]-=-. In the context of sensor networks, a natural abstraction is spatial sampling, i.e. sampling from geographical locations within the network uniformly at random. On a 2-D network with bounded spatial ... |

259 | Approximate aggregation techniques for sensor databases
- Considine, Li, et al.
- 2004
(Show Context)
Citation Context ...g a request/reply model in which a query is broadcast to a region of interest, individual sensors make best-effort replies, and responses are aggregated in-network en route to the origin of the query =-=[3, 11, 20]-=-. In this paper, we argue that there is a rich and relatively under-explored set of classic statistical methods that have not yet been extensively studied in the domain of sensor databases. In particu... |

228 | Synopsis diffusion for robust aggregation in sensor networks
- Nath, Gibbons, et al.
(Show Context)
Citation Context ...nsor databases. In particular, we propose a more careful study of random sampling methods, which have long been used in other domains to approximately compute aggregates such as MEDIAN, AVG, and MODE =-=[2, 12, 13]-=-. Random sampling is a particularly good fit for approximate aggregation queries in the sensor network domain in light of the potentially modest messaging cost. While we view random sampling as especi... |

223 |
Various techniques used in connection with random digits
- Neumann
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(Show Context)
Citation Context ...priate k-quantile of Voronoi cell sizes across the network. We argue that these statistics can be updated infrequently and consistently. Ultimately, this application of von Neumann’s rejection metho=-=d [19]-=- results in approximately uniform node samples. As sketched above, our algorithm for generating a random sample has a messaging cost that is typically bounded by the messaging cost of a small constant... |

209 | Min-wise independent permutations
- Broder, Charikar, et al.
- 1998
(Show Context)
Citation Context ...ble. Prior to this work, the following two methods for near-uniform sampling were proposed in the context of sensor and other overlay networks. Min-wise sampling: In [13], the use of min-wise samples =-=[1] was pro-=-posed for sampling a sensor network uniformly at random. Given a hash function h on sensor IDs, they returned the value associated with the ID s such that h(s) is minimal (i.e. ∀s ′ ∈S(h(s) ≤ ... |

139 | Data-Centric Storage in Sensornets with GHT, A Geographic Hash Table. Springer Mobile Networks and Applications
- Ratnasamy, Karp, et al.
(Show Context)
Citation Context ...s have been used previously to weight sensor readings for spatial aggregates [6] and they are easily computable, but it is well known that these areas vary widely when the sensors are placed randomly =-=[16]. -=-This variation leads to a bias in spatial sampling – each sensor is chosen with probability in proportion to A(s), the area of its Voronoi cell. For convenience, we assume the areas are normalized s... |

122 | Approximate medians and other quantiles in one pass and with limited memory
- Manku, Rajagopalan, et al.
- 1998
(Show Context)
Citation Context ...nsor databases. In particular, we propose a more careful study of random sampling methods, which have long been used in other domains to approximately compute aggregates such as MEDIAN, AVG, and MODE =-=[2, 12, 13]-=-. Random sampling is a particularly good fit for approximate aggregation queries in the sensor network domain in light of the potentially modest messaging cost. While we view random sampling as especi... |

116 | Random sampling for histogram construction: how much is enough
- Chaudhuri, Motwani, et al.
- 1998
(Show Context)
Citation Context ...nsor databases. In particular, we propose a more careful study of random sampling methods, which have long been used in other domains to approximately compute aggregates such as MEDIAN, AVG, and MODE =-=[2, 12, 13]-=-. Random sampling is a particularly good fit for approximate aggregation queries in the sensor network domain in light of the potentially modest messaging cost. While we view random sampling as especi... |

105 | Gem: Graph embedding for routing and datacentric storage in sensor networks without geographic information
- NEWSOME, SONG
(Show Context)
Citation Context ...rge cell would donate part of its “unused” area to its small neighbor. Virtual coordinates: Instead of using real-world geographic coordinates to map points to sensors, we can use virtual coordina=-=tes [14, 15]-=-, modified to include either a repulsive force between close sensors, or a hard lower bound on the inter-sensor distances. Virtual coordinate spaces also allow the boundaries of the sensor network to ... |

71 | Coping with Irregular Spatio-temporal Sampling
- Ganesan, Ratnasamy, et al.
- 2004
(Show Context)
Citation Context ...t of sensor nodes with low messaging cost. Since it is well-known that nodes in a sensor network often have highly irregular placements, spatial sampling will produce non-uniform samples of the nodes =-=[5]-=-. Our work relies on spatial sampling as a starting point, but uses practical methods for smoothing, or regularizing, the nonuniform samples to produce approximately uniform node samples. The key idea... |

43 | Choosing a random peer
- King, Saia
- 2004
(Show Context)
Citation Context ...ethods can be applied much more broadly, outside the context of sensor networks. For example, uniform node sampling is also an important problem in structured P2P networks based on coordinate systems =-=[9]-=-. Variants of our methods apply to these P2P scenarios and provide a simpler and more topology-agnostic alternative to existing methods. Acknowledgments We are grateful to Deepak Ganesan and Stanislav... |

5 |
Going beyond nodal aggregates: Spatial average of a physical process in sensor networks
- Han, Ganeriwal, et al.
- 2003
(Show Context)
Citation Context ...coordinate from within the space at random and using geographical routing to route to the node closest to that point. While this is desirable for many applications, such as computing spatial averages =-=[6]-=-, many other applications and database queries prefer to ignore geometry and instead wish to sample uniformly from the set of nodes. Examples include querying average sensor battery life, counting the... |

1 |
Lobcast: Reliable Data Dissemination in Wireless Sensor Networks. Under submission
- Rost, Balakrishnan
(Show Context)
Citation Context ...d return sample t with probability ,wherecis a positive constant. If t is not accepted, it is rejected and the process repeats for f(t) cg(t) 4s(a) MIT sensor testbed. Reproduced with permission from =-=[17]-=- (b) James Reserve sensor network. Reproduced with permission from [5] Figure 1: Maps of real sensor deployments used in our experiments. a new sample t. Assuming that c is chosen so that f(t) cg(t) p... |