Deterministic algorithm

1
Deterministic algorithm

• Algorithm Move-To-Min (MTM) Awerbuch, Bartal,
  Fiat 93
• (in some sense, it is derandomization of
  Coin-Flipping)
• Theorem MTM is 7-competitive
• Remark The currently best deterministic
  algorithm achieves
• competitive ratio of 4.086

After each steps, choose to be the node
which minimizes , and move to
. ( is the best place to place page in the
last steps)
2
Proof of competitiveness of MTM

• We fix any phase, and introduce the following
  notation
• node holding the page of MTM in the
  phase
• position of OPTs page at the beginning of
  the phase
• position of OPTs page at the end of -th
  step

Potential function At the beginning of
phase At the end of phase
3
MTM proof lower bound on OPT
Fix any
4
MTM proof Upper bound on MTM
Potential at the beginning Potential at the
end Bound on OPT
It remains to prove that for any
5
MTM proof Crucial Lemma

• Lemma For any it holds that
• Proof