Rendezvous

1
Rendezvous

• Xiaohui Zhang
• Computer science department
• The University of Liverpool

2
Introduction

• About the problem
• Previous work
• Key point
• The algorithm
• Other related problem

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What is the Rendezvous

• n. pl. rendezvous (-v z )
• A meeting at a prearranged time and place. See
  Synonyms at engament.
• A prearranged meeting place, especially an
  assembly point for troops or ships.
• A popular gathering place The café is a favorite
  rendezvous for artists.
• Aerospace The process of bringing two spacecraft
  together.

• French, from the phrase rendez vous, present
  yourselves, from Old French rendez, second
  person pl. imperative of rendre, to present see
  render vous, yourselves, you (from Latin v s,
  you see w s in Indo-European roots).

4
The model
ASSUMPTIONS
N nodes ring K agents and tokens Limited
memory (log k) Detectable Same strategy Same
starting time
GOAL
Can they rendezvous?
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Special cases
Symmetric
Periodic
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Previous work

• Need large memory log(n)
• Very complicated algorithm randomised
  algorithms or different deterministic algorithms
• Very hard to prove

7
Key idea

• Different speed

• Changeable speed

• Extra counter
• Three status (runner, marker and loser)
• Three stages (0,1 and 2)

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Stage 0

• Set status to runner
• Leave token -- Ti
• Start traverse in anti-clockwise direction
• Full speed on first segment, half on the others

CATCH EVENT!!!
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Catch event (in stage 0)

• Ai catches Ai1 as its first catch
• Change Ai1s status to marker
• Take Ai1 back to Ti
• Go to stage 1

For the agent being caught

• Lose self-control

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Stage 1

• Continue traverse in anti-clockwise direction
• Full speed on first segment, half on the others
• Do N full rounds traverse

Catches someone
Be caught

• Switch it off
• Set its status to loser
• Continue traverse

• Lose self-control

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About marker

• Every time, when a runner meet its marker, push
  it one node ahead.

Marker
Counter

How to identify marker ?
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After N full rounds

• All the runners must use same speed to traverse
• Its time to change the speed
• Traverse another 2N full rounds
• Change speed again
• And so on and so on
• Until Ai try all kind of speeds to traverse
• Go to stage 2

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Why 2N full rounds
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Stage 2

• Calculate how many agents had been caught

K-1
Less than K-1
Traverse one more round, pick up all the markers
and losers.
This is the periodic case, stop running.
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What if

• Agent are running in different directions

• Group them
• Rendezvous separately
• Get others from another group

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Question time

• Cloud (Xiaohui Zhang)
• http//www.csc.liv.ac.uk/cloud/
• cloud_at_csc.liv.ac.uk
• Algorithm group
• Computer science department
• The University of Liverpool

17
The flow