Topological Hole Detection in Wireless Sensor Networks and its Applications Stefan Funke Department of Computer Science, Stanford University, U.S.A. DIAL-M-POMC 2005 Speaker ： Shih-Yun Hsu

DIAL-M-POMC  Discrete Algorithms and Methods for Mobile Computing and Communications  Workshop in conjunction with ACM/SIGMOBILE MobiCom (1997 ～ 2004)  Principles of Mobile Computing  Workshop in conjunction with  ACM/SIGACT and SIGOPS PODC (2001)  ACM/DISC (2002)

Outline  Introduction  Related works  Main methods  Topology hole finding  Coarse Boundary Sampling and Pruning  Applications  Experiment evaluation  Conclusions

Introduction  Due to cost restrictions and to achieve the maximum life-time by energy savings  The characteristics of sensors  Low-capability devices  Temperature  Humidity  Small radio device that allows for communication between nearby sensor nodes  Easy to be deployed by airplanes

Introduction  To achieve the maximum life-time  It is impossible to equip energy-hungry GPS unit  None of the sensor nodes is aware of its geographic location

Introduction  There are many holes in the monitoring region  Fall right into the flames and be destroyed  Plunge into a lake or pond and be unable to perform their monitoring task  Fall from airplane on the grand then break  Detecting the boundaries of such holes in the monitored space created by fire or other phenomena

Related works  GLIDER: Gradient Landmark-Based Distributed Routing for Sensor Networks  Geographic Routing without Location Information  MAP: Medial Axis Based Geometric Routing in Sensor Networks

Main methods  Topology hole finding  Coarse Boundary Sampling and Pruning

Topology hole finding  Basic concept Beacon Euclidean length hole Unit Disk Graph (UDG)

Topology hole finding  Monitoring (connected) region  Beacon  Any points  d p (x) denotes the minimum Euclidean length from p to x  The isolevel (contour of level) of k  The sub-graph of UDG induced by I(k) might be disconnected p x d p (x) I(k) C 1 (k) C 2 (k)

Topology hole finding  Pick a local beacon q  Compute hop-distances h(v’) to q  Mark all nodes v which do not have a 2-hop neighbor v’ with h(v’) > h(v) C 1 (k) q v

Topology hole finding beacon Border nodes

Topology hole finding

 The first beacon was chosen randomly  Maintain a variable CBD(v) (Closest Beacon Distance) storing the (hop-)distance and choose the last 3 beacons as far as possible

Coarse Boundary Sampling and Pruning  A natural way to reduce this number is to compute a maximal independent set (MIS) within all the marked nodes  Maximal independent sets in radio networks  Thomas Moscibroda, Roger Wattenhofer  Department of Computer Engineering and Networks Laboratory, ETH Zurich, Switzerland  ACM Symp. on PODC 2005

Coarse Boundary Sampling and Pruning

Density

Applications  GLIDER: Gradient Landmark-Based Distributed Routing for Sensor Networks  Qing Fang, Jie Gao, Leonidas J. Guibas, Vin de Silva, Li Zhang  Department of Electrical Engineering, Computer Science, Mathematics, Stanford University  Information Dynamics Lab, HP Labs  INFOCOM 2005

Applications -GLIDER- S D

 Paths that share the same subsequence of tiles are kept apart  Load-balance

Applications -GLIDER- GLIDER for random landmark selection GLIDER for topology-aware landmark selection

Applications -GLIDER-  In inter-tile, the GLIDER protocol is also load- balance

Applications -GLIDER-  In intra-tile, the GLIDER protocol could not be load-balance Near Far

Applications -GLIDER-  Load imbalance due to Landmarks being too close to boundaries

Applications -GLIDER-

 Landmarks sends a HELLO message with distance counter 0 which increases at every hop  The value △ (v) is then the minimum counter value over all messages received  d local (p)=min(d(p, q i ))  New position of landmark p’=d local (p)/3  p still in the tile of p’  Any tile will not contain a whole hole  If d(p’, q’)<d local (p) (p and q are closer)  Removed q’ p q1q1 q2q2 q3q3 q4q4 P’

Applications -GLIDER-

Applications  Geographic Routing without Location Information  Ananth Rao, Sylvia Ratnasamy, Christos Papadimitriou, Scott Shenker and Ion Stoica  University of California, Berkeley  INFOCOM 2003

Applications - Geographic Routing -

 Holes might obstruct the shortest paths between nodes of the network and hence their lengths are not a good estimate of the true geometric distance

Applications - Geographic Routing - Truthful distances Not truthful distances

Applications - Geographic Routing -  P is the set of boundary nodes  The distance measured between a pair is truthful, if the respective shortest path in the communication graph from p to q providing this estimate does not contain any as intermediate node

Applications - Geographic Routing -

Applications  MAP: Medial Axis Based Geometric Routing in Sensor Networks  Jehoshua Bruck, Jie Gao, Anxiao (Andrew) Jiang  California Institute of Technology, US  Caltech, US  MobiCom 2005

Applications -MAP-

Near Far to the border

Experiment evaluation  4900 nodes  800×800 square region  Communication range is 15(average degree 5), 20(10), 27(18), 40(39)  The degree is r communication /r sense  Unit disk graphs (UDG)  Random Uniform Distributions  Randomly perturbed Grid  Non-UDG

UDG with Random Uniform Distributions 15(5) 20(10) 27(18) 40(39) Communication Range (Ave. degree)

UDG with Randomly perturbed Grid 15(5) 20(10) 27(18) 40(39) Communication Range (Ave. degree)

Non-UDG With UDG With Non-UDG

Non-UDG Degree 8Degree 16 Degree 20

Conclusions  This paper we have presented a rather simple and straightforward algorithm for detecting holes in a wireless communication network  Location-unaware  Higher density is better  This paper also sketched further applications of hole finding routine, where the knowledge about holes in the network provides for better performance of existing topology-based, location-free protocols

Thank You!!