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Hardness and Approximation Results for Black Hole Search in Arbitrary Networks

Hardness and Approximation Results for Black Hole Search in Arbitrary Networks. Klasing , R., Markou , E. & Radzik , T. (2007). Hardness and approximation results for Black Hole Search in arbitrary networks . Theor . Comput . Sci., 384 (2-3), 201-221 . Mengfei Peng. Assumptions. Network:

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Hardness and Approximation Results for Black Hole Search in Arbitrary Networks

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  1. Hardness and Approximation Results for Black Hole Search in Arbitrary Networks Klasing, R., Markou, E. & Radzik, T. (2007). Hardness and approximation results for Black Hole Search in arbitrary networks. Theor. Comput. Sci., 384 (2-3), 201-221. MengfeiPeng

  2. Assumptions Network: giving map; starting node is known to be safe; connected undirected graph. Agent: Two agent; synchronous, communicate only when in the same node(no token or whiteboard)

  3. Basic idea Two agents Each agent explores half of the graph Explore one node then go together exchange information. Not realistic. Question: Compare to token model and whiteboard,what do you think of this idea? Is it a good agent model?

  4. Rendezvous of Mobile Agents in Unknown Graphs with Faulty Links Chalopin, J., Das, S. & Santoro, N. (2007). Rendezvous of mobile agents in unknown graphs with faulty links. Proceedings of the 21st international conference on Distributed Computing, D33 (15), 108-122. Mengfeipeng

  5. Purpose: agent gathering—all survive agents meet at a safe node. Faulty link: an agent which goes into faulty links will disappear. K agents, R faulty links, so no more than k-r agents can rendezvous. Assumptions: Network size is unknown but given an upper bound bidirectional graph, edge-labeled, asynchronous, strongly connected symmetric graph. Agents: identical, dispersed Whiteboard model FIFO: first-in first-out

  6. Algorithm Result: Rendezvous k-r agents in total O(m(m+k)) moves, m is edge number. Use tree to add new nodes. If a node the agent arrives has been visited before, the node becomes an edge.

  7. Algorithm 1, Agents from the same node are in one team; if when an agent wakes up, its homebase already visited by someone else, then the agent just join the team. 2, Agents start to explore the graph(cautious walk), and traversal as many links as it can; 3, The team which explored more than half links in the graph becomes the leader, then all the other agents rendezvous at the leader’s homebase.

  8. Questions What’s the difference between black hole and faulty links? All links lead to one node are faulty, then the node is a black hole. What’s the main idea of the second algorithm? Find a leader team, and gather all survive agents in its homebase.

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