However, if edges arrive in a random order, and the input graph has a degree that is at least logarithmic, then smaller competitive ratios can be achieved.
12.
The geometric view of binary search trees provides a different way of understanding the problem that has led to the development of alternative algorithms that could also ( conjecturally ) have a constant competitive ratio.
13.
The competitive ratio of our algorithm on this input is 20, 500 / 6000 or approximately 3.4, and by adjusting the parameters of this example the competitive ratio of this algorithm can be made arbitrarily large.
14.
The competitive ratio of our algorithm on this input is 20, 500 / 6000 or approximately 3.4, and by adjusting the parameters of this example the competitive ratio of this algorithm can be made arbitrarily large.
15.
Indeed, for sparse graphs, the standard greedy coloring strategy of choosing the first available color achieves this competitive ratio, and it is possible to prove a matching lower bound on the competitive ratio of any online coloring algorithm.
16.
Indeed, for sparse graphs, the standard greedy coloring strategy of choosing the first available color achieves this competitive ratio, and it is possible to prove a matching lower bound on the competitive ratio of any online coloring algorithm.
17.
For randomized online algorithms, the competitive ratio is lower bounded by \ Omega ( \ log n / \ log \ log n ) and upper bounded by O ( \ log ^ 2 n \ log \ log n ).
18.
The term Price of Anarchy was first used by Koutsoupias and Papadimitriou, The concept in its current form was designed to be the analogue of the'approximation ratio'in an approximation algorithm or the'competitive ratio'in an online algorithm.
19.
This conjecture states that there is an algorithm for solving the " k "-server problem in an arbitrary metric space and for any number " k " of servers that has competitive ratio at least " k ".
20.
However, it has the advantage that it may be used in the online algorithm setting in which the input graph is not known in advance; in this setting, its competitive ratio is two, and this is optimal : no other online algorithm can achieve a better performance.
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