Networking Sensors, II

Transcription

1 Networking Sensors, II Sensing Networking Leonidas Guibas Stanford University Computation CS321 ZG Book, Ch. 3 1

2 Class Administration Paper presentation preferences due today, by class time Project info Start thinking and discussing topics Can form teams up to two people each Project proposals due Monday, October 24 Projects due Wednesday, November 30 Class project presentations during the week of December 5 2

3 Projects Implementation on real hardware 5 stargates, 16 motes available Ex., implement power-aware greedy geographic routing Simulation of a large sensor network application Qing Fang lecture on network simulators, Friday, October 14 Ex., maintaining escape routes from a fast moving fire Theoretical study Ex., Approximation algorithms for minimum energy broadcast 3

4 Virtual Coordinates 4

5 Virtual Coordinates Estimate distances between a sufficient number of pairs of nodes Compute an embedding of these nodes in the plane, while preserving these distances as much as possible Usually a global process, via a spring relaxation step [Rao, Ratnasamy, Papadimitriou, Shenker, Stoica 2003] 5

6 Virtual Coordinate Simulation 3200 Nodes, Uniformly Distributed in a 200x200 area. 8 unit range, 16 Neighbors on Avg. 6

7 Perimeter Nodes w. Known Locations 7

8 10 iterations 100 Iterations 1000 Iterations 8

9 Clustering Nodes 9

10 Clusters and Other Hierarchies Node clustering is extremely common in sensor networks It is natural in settings where nodes of different capabilities are available 10

11 Clustering is Useful Even in Homogeneous Networks Clusters are usually of size comparable with the node communication range Clusters allow better resource utilization Each cluster elects a node as its clusterhead Nodes belonging to multiple clusters can function as gateways 11

12 Clusterhead Election Assume each node has a unique ID Each node nominates the highest ID node it can hear to become a clusterhead All nominated nodes become clusterheads -- and form a cluster with their nominators 12

13 A Two-Level Communication Network Local traffic: within a cluster, directly or via the clusterhead Long-distance traffic: via clusteheads and gateways Clustering can even out node density in a network 13

14 Naming and Routing via Hierarchical Clustering [Funke, Guibas, Nguyen, Wang 2005] Generalized quadtree Required properties: Clusters in level i of the decomposition have diameters at most α 2 i, where α is a constant Each cluster in level i+1 contains a small number of clusters in level i 14

15 Examples of HDs A quad-tree induces a HD when the sensor field is dense and node coordinates are available. DCH tree (Discrete Center Hierarchy) Nodes in levels i are at least 2 i hops apart Each node in level i is within 2 i+1 hops from some node in level i+1 15

16 Addressing Scheme A HD yields an IP-type addressing scheme for nodes Clusters are also assigned addresses 16

17 The Importance of Sideways Links 17

18 Routing Tables Def: A cluster L at level k is a neighboring cluster of a node v if dist(v, L) α 2 k+1 L α 2 k+1 v Routing table stored at each node: hop distances to all its neighboring clusters Under mild assumptions, each node has O(log n) neighboring clusters diam(l) α 2 k 18

19 Routing Scheme Each node w forwards packages for v toward the smallest cluster containing v in w s routing table. u w v Routing quality: Efficient: path(u,v) 4 d uv Balance: No node artificially gets more load; hierarchy is not used in the routing Robust: the failure of any given link does not affect many paths 19

20 Implementation DCH: can be constructed in log n rounds Initially all nodes are in level 0 Nodes in level i initiates a restricted flooding with distance 2 i Discovering nearby nodes in level i Establishing routing paths between nodes in level i Nodes in level i nominate a subset of themselves to level i+1 Routing table: each cluster initiates a restricted flooding with distance α 2 i+1 where i is the cluster level Nodes being flooded over record an entry to their routing table The communication and storage cost at each node is O(log n) 20

21 HD Names and Routes Summary HD effectively discovers the intrinsic geometry of the network Provides a hierarchy-based scheme with provable approximation quality on the routing paths Naming by structure discovery, vs. naming by embedding and inheritance 21

22 Beyond Point-to-Point Connections 22

23 Trajectory-Based Forwarding Path follows a Sine wave Useful for dense sensor networks Requires position information Sensors follow a parametric path No routing tables or routing information Local computation to find next hop Highly scalable 23

24 Energy Minimizing Broadcast [ We have a network of n nodes with known positions A special node, the source s, wishes to transmit a packet so that it is received by all other nodes Intermediate nodes can act as relays for the packet Transmission power attenuates as O(1/r ) The objective is to minimize the total energy used The result is realized by a optimal broadcast tree B 24

25 Energy Minimizing Broadcast Relay solutions may be more efficient r s r The wireless multicast advantage 25

26 A Simple Example: Two Schedules A. s transmits, reaching both v 1 and v 2 B. s transmits to reach only v 1, then v 1 transmits to reach v 2 simplifies to if =2 26

27 A Combinatorial Problem In the general case, the number of possible broadcast strategies is exponential in n; in fact, the minimum energy broadcast problem has been shown to be NP-complete Thus at best we can hope for an approximation algorithm, or a greedy algorithm that works well in practice 27

28 But, in the Wired Setting... The same problem is classical and easy The Minimum Spanning Tree (MST) Problem: Connect n nodes in pairs, so that all n nodes are connected together, and the total cost of all connections is minimized. 28

29 The MST is a Constant-Factor The MST minimizes Approximation! Also, for α 2 radius of a set of nodes For an optimal broadcast tree B not so good, Wan, Calinescu, Li, Frieder, Infocom 2001 for relay node p, T p is the MST of its children and itself, r p its broadcast radius U, the union of the T p s is a spanning tree of all nodes 29

30 if 2 L L 30

31 Broadcast Incremental Power (BIP) Algorithm Like in the Prim-Jarnik MST algorithm, add nodes one at a time to the tree At each step, choose the node that has the minimal incremental cost to be connected to one of the existing nodes No theoretical guarantees, but works well in practice 31

32 Energy-Aware Routing to a Region Broadcast a packet to all nodes within a geographic region get the packet to the region distribute the packet within the region minimize energy use Yu, Govindan, Estrin,

33 Learning Real-Time A* Algorithm Choose a destination d within the desired region R Each node y maintains a learned cost h(y,d) to the destination d Initially h(y,d) is set as follows: straight-line distance to d energy left at y balance route cost and energy reserves 33

34 The GEAR Routing Protocol Greedy neighbor selection: if neighbors exist closer to the destination (Euclidean sense), choose the one of smallest learned cost otherwise choose the neighbor of smallest learned cost (among all neighbors) Relaxation: periodically broadcast learned cost to neighbors: y sends to x where 34

35 An Example Initially s chooses b over c, but in time learns that c is actually a better choice 35

36 LRTA* Properties The algorithm will eventually converge to a a locally minimal path Convergence can be slow (quadratic in the number of nodes) Behaves reasonably well in practice Leads to better network lifetimes that GPSR 36

37 Distribution within the Region R Recursive subdivision and forwarding Restricted flooding can be wasteful 37

38 The End 38