BIB-VERSION:: CS-TR-v2.0
ID:: ncstrl.dartmouthcs//TR96-302
ENTRY:: December 03, 1996
ORGANIZATION:: Dartmouth College, Computer Science
TITLE:: Cross-input Amortization Captures the Diffuse Adversary
TYPE:: Technical Report (paper)
REVISION:: 1
AUTHOR:: Young, Neal E.
DATE:: December 1996
RETRIEVAL:: For a paper copy, email <reports@cs.dartmouth.edu>
RETRIEVAL:: For a paper copy, write to
       Technical Report Librarian
       Department of Computer Science
       Dartmouth College
       6211 Sudikoff Laboratory
       Hanover, NH 03755-3510
       USA
RETRIEVAL:: Compressed Postscript at http://www.cs.dartmouth.edu/reports/TR96-302.ps.Z
RETRIEVAL:: PDF at http://www.cs.dartmouth.edu/reports/TR96-302.pdf
ABSTRACT:: 
  Koutsoupias and Papadimitriou recently raised the question of how well
deterministic on-line paging algorithms can do against a certain class of
adversarially biased random inputs.  Such an input is given in an on-line
fashion; the adversary determines the next request probabilistically, subject
to the constraint that no page may be requested with probability more than a
fixed $\epsilon>0$.
  In this paper, we answer their question by estimating, within a factor of
two, the optimal competitive ratio of any deterministic on-line strategy
against this adversary.  We further analyze randomized on-line strategies,
obtaining upper and lower bounds within a factor of two.  These estimates
reveal the qualitative changes as $\epsilon$ ranges continuously from 1 (the
standard model) towards 0 (a severely handicapped adversary).
  The key to our upper bounds is a novel charging scheme that is appropriate
for adversarially biased random inputs.  The scheme adjusts the costs of each
input so that the expected cost of a random input is unchanged, but working
with adjusted costs, we can obtain worst-case bounds on a per-input basis.
This lets us use worst-case analysis techniques while still thinking of some of
the costs as expected costs.
END:: ncstrl.dartmouthcs//TR96-302