1. Written by Wei Shi, Joaquin Garcia-Alfaro, Jean-Pierre Corriveau Mengfei Peng Searching for a Black Hole in Interconnected Networks using Mobile Agents and Tokens

2. Assumption Agents: asynchronous, co-located/dispersed, carry a map of the network. Not assume FIFO on either nodes or links (first-in first-out) Network: un-oriented, asynchronous Hypercube, Torus, Complete network. Model: Token model

4. Agent Black hole

5. Token model Port Shared memory on a nodeagent Node 1 Node 2 Node 3

6. Token model Port Shared memory on a nodeagent How can we use a token? Cautious walk 1,when the agent leaves the port, It puts a token at the port----this means “I’m going to the next node” Node 1 Node 2 Node 3 A B C D E F 2,when the agent comes back, It picks up the token----that means ”I come back safely” This port is dangerous, I don’t go into it. I can stay here waiting or go to another way. I come back and the next node is safe.

7. A piece of software Maybe A died here, it’s a dangerous port. I won’t go into it.

8. Whiteboard model Port Shared memory on a node agent Node 1 Node 2 Node 3

9. Whiteboard model Port Shared memory on a node agent How can we use a whiteboard? Cautious walk 1,when the agent leaves the port, It writes “I’m going to the next node” on the whiteboard Node 1 Node 2 Node 3 A BC D E F 2,when the agent comes back, It writes--”I come back safely” A: I’m going to the next node A: I come back safely and the next node is safe

10. Synchronous agents Let’s meet at 11:00 OK, 11:00 Asynchronous agents Let’s meet When? Whenever you can come Sure, I will try to come early 5 kilometers cost 50 minutes. 6 kilometers cost 60 minutes. 8 kilometers cost 80 minutes. 77 kilometers cost 770 minutes. 5 kilometers cost 5 minutes. 6 kilometers cost 150 minutes. 8 kilometers cost 999 minutes. 8 kilometers cost 3 minutes. 1 time unit 4 time unit 100 time units

11. Co-located agents

12. Dispersed agents

13. S S S Bypass technique 1,use cautious walk to find a safe ring----no black hole in the ring Dangerous ring Safe ring

14. S SS S 2,agent A is exploring the dangerous ring, and leave a token at port J2 Dangerous ring Safe ring

15. S S S S 3,agent B comes and sees A’s token, and moves A’s token to a safe port J1. Dangerous ring Safe ring

16. S S S S 3,agent B goes to the safe ring and continues exploration. Dangerous ring Safe ring

17. S S S S 3,agent B leaves its token at port P3, and explores the next node L Dangerous ring Safe ring

18. S S S S Question 1: what happens if there is an agent C comes? Dangerous ring Safe ring

19. S S S S S Answer: Dangerous ring Safe ring

20. Question: When can we use the bypass technique? In a interconnected network, after finding a safe ring. What’s the purpose of bypass technique? Allow more than one agent to explore the same ring at the same time.

21. Main results prove that, in the context of the Bhs problem in an asynchronous network with co-located agents, the token model can support the same cost as in the whiteboard model Solutions to the Bhs problem for asynchronous torus, and complete network using tokens a complete network, each node is linked to every other node by an edge.

22. complexity 2 co-located agents,edge labeled, n nodes Dispersed agents HypercubeAlgorithm Two Rings, Two tokens O(n) ɵ (n) exploring TorusAlgorithm Cross Rings, 5 tokens O(n) ɵ (n) 3 agents, 7 tokens, oriented torus O(n) k (k > 3) agents,1 token per agent, oriented torus O(k 2 n 2 ) Complete Network algorithm Take Turn,1 token ɵ (n) N agents, 1 token per agent,an un-oriented complete network Kn. O(n 2 )