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D94725004 許明宗 R97725039 林世昌

An Algorithmic Approach to Geographic Routing in Ad Hoc and Sensor Networks - IEEE/ACM Trans. on Networking, Vol 16, Number 1, February 2008. D94725004 許明宗 R97725039 林世昌. Authors. Fabian Kuhn Member, IEEE. Roger Wattenhofer. Aaron Zollinger Member, IEEE. Outline. Introduction

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D94725004 許明宗 R97725039 林世昌

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  1. An Algorithmic Approach to Geographic Routingin Ad Hoc and Sensor Networks- IEEE/ACM Trans. on Networking, Vol 16, Number 1, February 2008 D94725004 許明宗 R97725039 林世昌

  2. Authors Fabian Kuhn Member, IEEE Roger Wattenhofer Aaron Zollinger Member, IEEE ACNs 2009 Spring

  3. Outline ACNs 2009 Spring Introduction Related Work Models and Preliminaries Geographic Routing Conclusion

  4. Introduction (1/2) ACNs 2009 Spring • Wireless Ad Hoc Networks • Emergency and rescue operations, disaster relief efforts • Wireless Sensor Networks • Monitoring space, things, and the interactions of things with each other and the encompassing space • Routing Challenges in Wireless Ad Hoc Networks • Energy conservation • Low link communication reliability • Mobility

  5. Introduction (2/2) ACNs 2009 Spring • Geographic Routing (directional, location-based, position-based, geometric routing) • Each node knows its own position and position of neighbors • Source knows the position of the destination • Why “Geographic Routing”? • No routing tables stored in nodes • Independence of remotely occurring topology changes

  6. Related Work ACNs 2009 Spring

  7. Models and Preliminaries (1/3) ACNs 2009 Spring • Definition 3.1: (Unit Disk Graph) • Let V⊂ R2 be a set of points in the two-dimensional plane. The graph with edges between all nodes with distance at most 1 is called the unit disk graph of V. • Definition 3.2: (Cost Function): • A cost function c:]0,1] R+ is a nondecreasing function which maps any possible edge length d (0<d ≦1) to a positive real value c(d) such that d’ > d c(d’) ≧ c(d). For the cost of an edge e ∈ E we also use the shorter form c(e) := c(d(e)).

  8. Models and Preliminaries (2/3) ACNs 2009 Spring • Definition 3.3: (Ω(1)-Model): • If the distance between any two nodes is bounded from below by a term of order Ω(1), i.e., there is a positive constant d0 such that d0 is a lower bound on the distance between any two nodes, this is referred to as the Ω(1)-model. • For the routing algorithms in the paper, the network graph is required to be planar. • In order to achieve planarity on the unit disk graph , the Gabriel Graph is employed.

  9. Models and Preliminaries (3/3) ACNs 2009 Spring • Definition 3.4: (Geographic Ad Hoc Routing Algorithm) • Let G =(V,E)be a Euclidean graph. The task of a geographic ad hoc routing algorithm A is to transmit a message from a source S∈ V to a destination D∈ V by sending packets over the edges of while complying with the following conditions: • All nodes v∈ V know their geographic positions as well as the geographic positions of all their neighbors in G. • The source S is informed about the position of the destination D. • The control information which can be stored in a packet is limited by O(log n) bits. • Except for the temporary storage of packets before forwarding, a node is not allowed to maintain any information.

  10. Geographic Routing ACNs 2009 Spring • Greedy Routing • Face Routing • Planar Graph • GreedyOther Adaptive Face Routing (GOAFR) • OFR, OBFR, and OAFR • GOAFR+

  11. Greedy Routing (1/2) G.G. Finn ‘87 • Nodes learn 1-hop neighbors’ positions from beaconing • A node forwards packets to its neighbor closest to D A stateless and scalable routing for Wireless Ad Hoc (Sensor) Networks • Lemma 4.1: • If GR reaches D, it does so withO(d2)cost, whereddenotes the Euclidean distance between S and D. • pf: the disk with center D and radius d contains at most O(d2) nodes with pairwise distance at least 1. ACNs 2009 Spring

  12. Greedy Routing (2/2) Greedy Routing not always possible! x is a local minimum(dead end) to D; w and y are far from D ACNs 2009 Spring

  13. Face Routing (1/2) E. Kranakis, H. Singh, and J. Urrutia ‘99 Well-known graph traversal: the right-hand rule • (1) Traverse a face • (2) Requires only neighbors’ positions Fails when there are cross links in the graph!  planar graph, e.g., RNG, GG z y x ACNs 2009 Spring

  14. Face Routing (2/2) Face (Perimeter) traversal on a planar graph Two primitives: (1) the right-hand rule (2) face-changes D F4 F3 a F2 Walking sequence: F1 -> F2 -> F3 -> F4 F1 S • With O(n) messages • Many existing algorithms like GFG, GPSR, GOAFR+, and etc. combine greedy routing with face routing. ACNs 2009 Spring

  15. Planar Graph(1/2) • Given a radio graph, make a planar sub-graph in which every cross-edge is eliminated. w w u v u v Gabriel Graph Relative Neighborhood Graph GG (Gabriel Graph) Relative Neighborhood Graph (RNG) ACNs 2009 Spring

  16. Planar Graph (2/2) RNGSub-graph Full Radio Graph GG Sub-graph  Important assumptions - Unit-disk graph & Accurate localization How well do planarization techniques work in real-world? ACNs 2009 Spring

  17. GOAFR- Other Face Routing D • Lemma 5.1: • OFR always terminates in O(n) steps, where n is the number of nodes. If S and D are connected, OFR reaches D; otherwise, disconnection will be detected. F2 P2 F1 P1 S ACNs 2009 Spring

  18. GOAFR–Other Bounded Face Routing (1/2) S D ACNs 2009 Spring

  19. GOAFR–Other Bounded Face Routing (2/2) The shortest path between S and D ACNs 2009 Spring • Lemma 5.2: • If the length of the major axis of ε is at least the length of a—with respect to the Euclidean metric—shortest path between S and D, OBFR reaches the destination. Otherwise OBFR reports failure to the source. In any case, OBFR expends cost at most .

  20. GOAFR–Other Adaptive Face Routing (1/2) ACNs 2009 Spring • OAFR ( Other Adaptive Face Routing ) 0) Initialize to be the ellipse with foci and the length of whose major axis is . 1) Start OBFR with ε. 2) If the destination has not been reached, double the length of ε’s major axis and go to step 1.

  21. GOAFR–Other Adaptive Face Routing (2/2) ACNs 2009 Spring • Theorem 5.3 • OAFR reaches the destination with cost O(c2(p*)), p* is an optimal path • Theorem 6.1 • Any deterministic (randomized) geographic ad hoc routing algorithm has (expected) cost Ω(c2) • Theorem 6.2 • Let c be the cost of an optimal path on a unit disk graph. In the worst case, the cost for applying OAFR to find a route from the source to the destination is Θ(C2). This is asymptotically optimal.

  22. GOAFR greedy fails OAFR Greedy Routing greedy works After First Face Traversal ACNs 2009 Spring

  23. GPSR greedy fails Perimeter Routing Greedy Routing greedy fails greedy works A location closer than where greedy routing failed ACNs 2009 Spring

  24. Early Fallback to Greedy Routing? We could fall back to greedy routing as soon as we are closer to Dthan the local minimum But: Face Greedy ACNs 2009 Spring

  25. GOAFR+ • Counter p: closer to Dthan u • Counterq: farther from Dthan u • Fall back to greedy routing if p >  q ACNs 2009 Spring

  26. Performance Network Connectivity Greedy Success Rate FR AFR OAFR GFG/GPSR GOAFR+ ACNs 2009 Spring

  27. Conclusion (1/2) ACNs 2009 Spring • GOAFR+ • Combination of the greedy forwarding and face routing approaches • Using greedy forwarding, the algorithm also becomes efficient in average-case networks • Average-case efficiency, correctness, and asymptotic worst-case optimality • Bounded searchable area and a counter technique • Proved to require at most O(c2) steps

  28. CorrectRouting Worst-CaseOptimal Avg-CaseEfficient ComprehensiveSimulation Conclusion (2/2) ACNs 2009 Spring

  29. Thanks for Your Listening ACNs 2009 Spring

  30. Discussion ACNs 2009 Spring • Lemma 3.3: • The shortest p ath for cost function intersected with the unit disk graph is only longer than the shortest path on the unit disk graph for the respective metric.

  31. ACNs 2009 Spring

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