Figure 7 The performance and the worst-case efficiency of IBRC.
First, for the public excludable good problem, the Shapley value mechanism minimizes the worst-case efficiency loss over all truthful, deterministic, and budget-balanced mechanisms that satisfy equal treatment.
Second, even with randomization and approximate budget-balance allowed and dropping equal treatment, the worst-case efficiency loss of the Shapley value mechanism is within a constant factor of the minimum possible.
Experiments show a worst case parallel efficiency of 50% for parallel refinement with 24 threads.
We establish a good worst case bound on efficiency when the bundles of interest are known, which also applies in some cases when the bundles are not known.
By changing the mesh generation scheme one may create a worst case scenario for the efficiency of asynchronous integrators.
A comparison based on the worst case scenario is presented to prove the efficiency of the present algorithm.
HoWever, showe Pthatand theveneedy algorithe have a polynomial time complexity and require centralized control, their implementations in practice are restricted within a limited class of wireless networks.
A violation of these requirements can lead to poor PCR efficiency and, in the worst case, can result in false-positive amplicons.
However, the worst case scenario (PPM-W) profoundly affected the operational efficiency, as depicted in both Figs. 9 and 10.
Our measure of efficiency is defined as the worst case ratio of the total utility of a utility proportional fair rate vector and the maximum possible total utility.
