1. Topology Control Murat Demirbas SUNY Buffalo Uses slides from Y.M. Wang and A. Arora

2. Why Control Communications Topology • High density deployment is common • Even with minimal sensor coverage, we get a high density communication network (radio range > typical sensor range) • Energy constraints • When not easily replenished • High interference • Many nodes in communication range • We will look at selecting high-quality links as part of routing!

3. Problem Statement(s) • Choose a transmit-power level whereby network is connected • per node or same for all nodes • with per node there is the issue of avoiding asymmetric links • cone-based algorithm: • node u transmits with the minimum power ρu s.t. there is at least one neighbor in every cone of angle x centered at u • Find an MCDS, i.e. a minimum subset of nodes that is both: • Set cover • Connected

4. Problem Statement(s) • Find a minimum subset of nodes that provides some density • in each geographic region  connectivity • we’ll look at the examples of SPAN, GAF, CEC Sub-problems: • Prune asymmetric links • Tolerate node perturbations • Load balance

5. Outline • Cone-based algorithm • SPAN • GAF-CEC

6. Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M. Wang, and R. Wattenhofer Microsoft Research, Redmond

7. OUTLINE • Motivation • Bigger Picture and Related Work • Basic Cone-Based Algorithm • Summary of Two Main Results • Properties of the Basic Algorithm • Optimizations • Properties of Asymmetric Edge Removal • Performance Evaluation

8. Motivation for Topology Control • Example of No Topology Control with maximum transmission radius R(maximum connected node set) • High energy consumption • High interference • Low throughput

9. Example of No Topology Control with smaller transmission radius • Network may partition

10. Example of Topology Control • Global connectivity • Low energy consumption • Low interference • High throughput

11. Bigger Picture and Related Work Routing Topology Control Selective Node Shutdown [Hu 1993] [Ramanathan & Rosales-Hain 2000] [Rodoplu & Meng 1999] [Wattenhofer et al. 2001] [GAF] [Span] MAC / Power-controlled MAC [MBH 01] [WTS 00] Relative Neighborhood Graphs, Gabriel graphs, Sphere-of-Influence graphs, -graphs, etc. Computational Geometry

12. Basic Cone-Based Algorithm (INFOCOM 2001) • Assumption: receiver can determine the direction of sender • Directional antenna community: Angle of Arrival problem • Each node u broadcasts “Hello” with increasing power (radius) • Each discovered neighbor v replies with “Ack”.

13.  No! There’s an -gap! Cone-Based Algorithm with Angle  Need a neighbor in every -cone. Can I stop?

14. Notation • E = { (u,v)  V x V: vis a discovered neighbor by node u} • G= (V, E) • E may not be symmetric • (B,A) in E but (A,B) not in E

15. Two symmetric sets • E+ = { (u,v): (u,v)  E or (v,u)  E } • Symmetric closure of E • G+ = (V, E+ ) • E- = { (u,v): (u,v)  E and (v,u)  E } • Asymmetric edge removal • G- = (V, E- )

16. Summary of Two Main Results • Let GR= (V, ER), ER= { (u,v): d(u,v)  R } • Connectivity Theorem • If   150, thenG+ preserves the connectivity of GR and the bound is tight. • Asymmetric Edge Theorem • If   120, thenG- preserves the connectivity of GR and the bound is tight.

17. The Why-150 Lemma 150 = 90 + 60

18. Properties of the Basic Algorithm • Counterexample for  = 150 + 

19. Counterexample for  = 150 + 

20. Counterexample for  = 150 + 

21. For   150 ( 5/6 ) • Connectivity Lemma • if d(A,B) = d R and (A,B) E+,there must be a pair of nodes, oneredand onegreen, with distance less than d(A,B).

22. Connectivity Theorem • Order the edges in ERby length and induction on the rank in the ordering • For every edge inER, there’s a corresponding path in G+ . • If   150, thenG+ preserves the connectivity of GR and the bound is tight.

23. Optimizations • Shrink-back operation • “Boundary nodes” can shrink radius as long as not reducing cone coverage • Asymmetric edge removal • If  120, remove all asymmetric edges • Pairwise edge removal • If  < 60, remove longer edge e2 B e1  A e2 C

24. Properties of Asymmetric Edge Removal • Counterexample for  = 120 + 

25. For   120 ( 2/3 ) • Asymmetric Edge Lemma • if d(A,B)  R and (A,B) E,there must be a pair of nodes, W or Xand node B, with distance less than d(A,B).

26. Asymmetric Edge Theorem • Two-step inductions on ER and then on E • For every edge in ER , if it becomes an asymmetric edge in G , then there’s a corresponding path consisting of only symmetric edges. • If   120, thenG- preserves the connectivity of GR and the bound is tight.

27. Performance Evaluation • Simulation Setup • 100 nodes randomly placed on a 1500m-by-1500m grid. Each node has a maximum transmission radius 500m. • Performance Metrics • Average Radius • Average Node Degree

28. Average Radius

29. Average Node Degree

30. Reconfiguration • In response to mobility, failures, and node additions • Based on Neighbor Discovery Protocol (NDP) beacons • Joinu(v)event: may allow shrink-back • Leaveu(v)event: may resume “Hello” protocol • AngleChangeu(v)event: may allow shrink-back or resume “Hello” protocol • Careful selection of beacon power

31. Summary • Distributed cone-based topology control algorithm that achieves maximum connected node set • If we treat all edges as bi-directional • 150-degree tight upper bound • If we remove all unidirectional edges • 120-degree tight upper bound • Simulation results show that average radius and node degree can be significantly reduced

32. Outline • Cone-based algorithm • SPAN • GAF-CEC

33. SPAN • Goal: preserve fairness and capacity & still provide energy savings • SPAN elects “coordinators” from all nodes to create backbone topology • Other nodes remain in power-saving mode and periodically check if they should become coordinators • Tries to minimize # of coordinators while preserving network capacity • Depends on an ad-hoc routing protocol to get list of neighbors & the connectivity matrix between them • Runs above the MAC layer and “alongside” routing

35. Coordinator Election & Announcement • Rule: if 2 neighbors of a non-coordinator node cannot reach each other (either directly or via 1 or 2 coordinators), node becomes coordinator • Announcement contention is resolved by delaying coordinator announcements with a randomized backoff delay • delay = ((1 – Er/Em) + (1 – Ci/(Ni pairs)) + R)*Ni*T Er/Em: energy remaining/max energy Ni: number of neighbors for node i Ci: number of connected nodes through node i R: Random[0,1] T: RTT for small packet over wireless link

36. Coordinator Withdrawal • Each coordinator periodically checks if it should withdraw as a coordinator • A node withdraws as coordinator if each pair of its neighbors can reach each other directly of via some other coordinators • To ensure fairness, after a node has been a coordinator for some period of time, it withdraws if every pair of nodes can reach each other through other neighbors (even if they are not coordinators) • After sending a withdraw message, the old coordinator remains active for a “grace period” to avoid routing loses until the new coordinator is elected

38. Performance Results

39. Outline • Cone-based algorithm • SPAN • GAF-CEC

40. GAF/CEC: Geographical Adaptive Fidelity • Each node uses location information (provided by some orthogonal mechanism) to associate itself to a virtual grid • All nodes in a virtual grid must be able to communicate to all nodes in an adjacent grid • Assumes a deterministic radio range, a global coordinate system and global starting point for grid layout • GAF is independent of the underlying ad-hoc routing protocol

41. Virtual Grid Size Determination • r: grid size, R: deterministic radio range • r2 + (2r)2 <= R2 • r <= R/sqrt(5)

42. Parameters settings • enat: estimated node active time • enlt: estimated node lifetime • Td,Ta, Ts: discovery, active, and sleep timers • Ta = enlt/2 • Ts = [enat/2, enat] • Node ranking: • Active > discovery (only one node active per grid) • Same state, higher enlt --> higher rank (longer expected time first) • Node ids to break ties

43. Performance Results

44. CEC • Cluster-based Energy Conservation • Nodes are organized into overlapping clusters • A cluster is defined as a subset of nodes that are mutually reachable in at most 2 hops

45. Cluster Formation • Cluster-head Selection: longest lifetime of all its neighbors (breaking ties by node id) • Gateway Node Selection: • primary gateways have higher priority • gateways with more cluster-head neighbors have higher priority • gateways with longer lifetime have higher priority

46. Network Lifetime