Using Scattered Mobile Agents to Locate a Black Hole in an Un-oriented Ring with Tokens Stefan Dobrev, Nicola Santoro, Wei Shi Mengfei Peng

Assumptions: Agents: identical, asynchronous, scattered,obey the same rule; Identical: all agents are the same Scattered(dispersed): each agent initially start at different node Network: ring (n is known), anonymous, un-oriented, Anonymous: every node is the same. FIFO; Token model Un-oriented Oriented W EEE WW

Shadow Check 1, Upon waking up, an agent becomes a Junior Explorer(JE) 2, agents start to explore the ring using Cautious Walk. H H H H

3, When 2 agents meet, they both become Senior Explorer(SE) H H H H

4, the two met agents(Senior Explorer) will explore the ring in opposite direction. The explored nodes called safe region. BH

5, When two Senior explorers meet, they both become checkers and count the distance of the safe region. BH

6, When two Senior explorer meet, they both become checkers and counter the size of the safe region. If the distance is n-2, the algorithm terminates. 14-2=12=n-2

What happens if the juniors can not meet? H H H H When a SE meet a JE, it will become a checker

What happens if the juniors choose the same direction? H H H H When they meet, both of them will become SE, then explore the ring in opposite direction

What happens if a junior meet a senior? H H H H The JE will become SE to the left This is like everybody getting into a higher level

What is Shadow Check?

Result: we show not only that a black hole can be located in a ring using tokens with scattered agents, but also that the problem is solvable even if the ring is un-oriented. More precisely, first we prove that the black hole search problem can be solved using only three scattered agents. with k (k > 4) scattered agents, the black hole can be located in O(kn + n log n) moves. when k (k > 4) is a constant number, the move cost can be reduced to O(n log n),