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## Topology Control

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**Topology Control**Murat Demirbas SUNY Buffalo Uses slides from Y.M. Wang and A. Arora**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!**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**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**Outline**• Cone-based algorithm • SPAN • GAF-CEC**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**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**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**Example of No Topology Control with smaller transmission**radius • Network may partition**Example of Topology Control**• Global connectivity • Low energy consumption • Low interference • High throughput**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**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”.****No! There’s an -gap! Cone-Based Algorithm with Angle Need a neighbor in every -cone. Can I stop?**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**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- )**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.**The Why-150 Lemma**150 = 90 + 60**Properties of the Basic Algorithm**• Counterexample for = 150 + **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).**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.**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**Properties of Asymmetric Edge Removal**• Counterexample for = 120 + **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).**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.**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**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**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**Outline**• Cone-based algorithm • SPAN • GAF-CEC**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**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**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**Outline**• Cone-based algorithm • SPAN • GAF-CEC**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**Virtual Grid Size Determination**• r: grid size, R: deterministic radio range • r2 + (2r)2 <= R2 • r <= R/sqrt(5)**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**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**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