I need to prove that the modification of MTF, Move to front on every even request of an element, list update problem has a competitive ratio of 2.

How does one go about proving such results? (I'm aware of the amortized analysis but not sure how to apply in this case)

  • $\begingroup$ "need to prove" ? $\endgroup$ Commented Apr 26, 2012 at 6:02
  • $\begingroup$ want to prove.. $\endgroup$
    – Swair
    Commented Apr 26, 2012 at 6:08
  • 3
    $\begingroup$ This smells like homework. $\endgroup$
    – Jeffε
    Commented Apr 26, 2012 at 6:21
  • $\begingroup$ Reading first chapter of the book Online Computation and Competitive analysis. Exercise 1.5 $\endgroup$
    – Swair
    Commented Apr 26, 2012 at 6:22
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    – Kaveh
    Commented Apr 26, 2012 at 6:33

1 Answer 1


This question is given as an exercise in the textbook by Borodin and El-Yaniv. Unfortunately, it is impossible to solve. Indeed, it was later discovered that MTF-every-other-access is not 2-competitive. See arxiv.org/abs/1311.7357 for a proof that the competitive ratio of the algorithm is in fact 2.5, and for a history of the false belief that the algorithm was 2-competitive.


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