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Mobile Search for a Black Hole in an Anonymous Ring

Mobile Search for a Black Hole in an Anonymous Ring. Dobrev , S., Flocchini , P., Prencipe , G., & Santoro, N . ( 2007).  Mobile Search for a Black Hole in an Anonymous Ring . Mengfei Peng. Network :. Ring : a loop network of identical nodes ,

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Mobile Search for a Black Hole in an Anonymous Ring

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  1. Mobile Search for a Black Hole in an Anonymous Ring Dobrev, S., Flocchini, P., Prencipe, G., & Santoro, N. (2007).  Mobile Search for a Black Hole in an Anonymous Ring. MengfeiPeng

  2. Network: • Ring: a loop network of identical nodes, • Whiteboard: Each node has a bounded amount of storage(whiteboard), agents can write or read information from the whiteboard, O(log n) bits are sufficient. • n is known(where n is the size of the ring) • Nodes are anonymous: no special marks on any node.

  3. Agents: • computing capability; • bound of storage; • obey the same protocol; • Asynchronous; • Identical;

  4. Result: co-located agents • two agents are necessary and sufficient to locate the black hole • Moves: O (n log n) moves and it is optimal • Time complexity: 2n-4 units of time using n- 1 agents Result: dispersed agents • If the ring is oriented, two dispersed agents are still necessary and sufficient. Moves: (θ (n log n)). • If the ring is un-oriented, three agents are necessary and sufficient; Moves: (θ (n log n)).

  5. Algorithm: • measure of complexity: • Size: the number of agents; • Cost: the number of moves; • Time: the amount of time elapsed until termination • ----ideal time (i.e., assuming synchronous execution where a move can be made in one time unit)----\time" complexity is “ideal time" complexity. • Cautious Walk

  6. Co-located:2 agents time complexity of Algorithm Divide is also 2n log n + O(n).

  7. n-1 agents to locate BH • Algorithm Optimal Time lets n -1 co-located agents find the black hole in 2n -4time. Why 2n-4: if n-1 is BH, a agent must come to n-2, and come back to 0, so 2(n-2)

  8. Dispersed agents: • initially there is at most one agent at any given location • If k is known, cost in oriented rings: Ω(n log(n-k)). • If k of agents is unknown, cost in oriented rings: Ω (n log n). Algorithm: • Dispersed, oriental ring, k ≥ 2 • Three phases: pairing, elimination, and resolution.

  9. K is known • When arriving at a node already visited by another agent, it proceeds to the right via • the safe port. If there is no safe port, it tests how many agents are at this node; if the • number of agents at the node is k- 1, the algorithm terminates.

  10. K is unknown

  11. A:status:alone

  12. D:status:paired-left

  13. C sees D’s “jion me” mark and terminates. status:paired-right

  14. Questions:1, How (n-1) co-located agents explored the ring?

  15. Questions:2, How k dispersed agents explored the ring while k is known?

  16. Questions:3, How k dispersed agents explored the ring while k is unknown?

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