The average case analysis of algorithms usually assumes independent, identical distributions for the inputs. In [?], Kenyon introduced the random-order ratio, a new average case performance metric for bin packing heuristics, and gave upper and lower bounds for it for he Best Fit heuristics. We introduce an alternative definition of the random-order ratio and show that the two definitions give the same result for Next Fit. We also show that the random-order ratio of Next Fit equals to its asymptotic worst case, i.e., it is 2.
Coffman et al. REF showed that the random-order ratio of the next-fit algorithm is 2.
Random-order bin packing
SIAM J. COMPUT
Computer Science Mathematics