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Rendezvous

Rendezvous. Xiaohui Zhang Computer science department The University of Liverpool. Introduction. About the problem Previous work Key point The algorithm Other related problem. What is the Rendezvous. n. pl. ren·dez·vous (-v z )

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Rendezvous

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  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 Cloud (Xiaohui Zhang)

  3. What is the Rendezvous n.pl. ren·dez·vous (-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).] Cloud (Xiaohui Zhang)

  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? Cloud (Xiaohui Zhang)

  5. Special cases Symmetric Periodic Cloud (Xiaohui Zhang)

  6. Previous work • Need large memory – log(n) • Very complicated algorithm – randomised algorithms or different deterministic algorithms • Very hard to prove Cloud (Xiaohui Zhang)

  7. Key idea • Different speed • Changeable speed • Extra counter • Three status (runner, marker and loser) • Three stages (0,1 and 2) Cloud (Xiaohui Zhang)

  8. 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!!! Cloud (Xiaohui Zhang)

  9. Catch event (in stage 0) • Ai catches Ai+1 as its first catch • Change Ai+1’s status to “marker” • Take Ai+1 back to Ti • Go to stage 1 For the agent being caught • Lose self-control Cloud (Xiaohui Zhang)

  10. 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 Cloud (Xiaohui Zhang)

  11. About marker • Every time, when a runner meet its marker, push it one node ahead. Marker = Counter How to identify marker ? Cloud (Xiaohui Zhang)

  12. After “N” full rounds • All the runners must use same speed to traverse • It’s 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 Cloud (Xiaohui Zhang)

  13. Why “2N” full rounds Cloud (Xiaohui Zhang)

  14. 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. Cloud (Xiaohui Zhang)

  15. What if… Agent are running in different directions • Group them • Rendezvous separately • Get others from another group Cloud (Xiaohui Zhang)

  16. Question time Cloud (Xiaohui Zhang) http://www.csc.liv.ac.uk/~cloud/ cloud@csc.liv.ac.uk Algorithm group Computer science department The University of Liverpool Cloud (Xiaohui Zhang)

  17. The flow Cloud (Xiaohui Zhang)

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