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
E
E
E
W
W
W
Shadow Check
1, Upon waking up, an agent becomes a Junior Explorer(JE)
2, agents start to explore the ring using Cautious Walk.
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H
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3, When 2 agents meet, they both become Senior Explorer(SE)
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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?
When a SE meet a JE,
it will become a checker
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What happens if the juniors choose the same direction?
When they meet, both of them will become SE,
then explore the ring in opposite direction
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What happens if a junior meet a senior?
The JE will become SE to the left
This is like everybody getting into a higher level
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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),