We generalize his notions of average-case complexity classes, Random-NP and Average-P. Ben-David et al. use the notation of [C, F] to denote the set of randomized decision problems (L, mu) such that L is a set in C and mu is a probability density function in F. This paper ...
such a gap translates to an increasingly larger runtime gap on concrete instances and thus a larger concrete security margin in realistic situations. we can also consider starting from even stronger forms of average-case hardness. a very natural...
Case 2: Assume L is nonempty and does not contain the entry n−ℓ−1. Let m be the largest entry in L. Let L˜ be the permutation obtained from L by replacing m with n−ℓ−1. Let R˜ be the permutation obtained from R by decreasing each of the entries m+1,…,n...
We are hence interested in average-case error estimates. In this paper we establish such bounds for the strong Lucas primality test, as there exist only worst-case, but no average-case error bounds. This allows us to use this test with more confidence. Let us examine an algorithm that ...
\thetarepresents the offloading ratio, denoting the proportion of tasks offloaded. In this particular case, we presume the initial task computation queue of the Sat*-MEC server to be empty. The notation()^+implies that if the value within the parentheses falls below 0, it should be ...
Notation τ: interval of scheduled downs (yrs). Ai: age limit on the age of component i∈IABM (decision variable). Ci: control limit on the degradation level of component i∈ICBM (decision variable). Hi: CM threshold on the degradation of component i∈ICBM. μi: expected life time of ...
All transportation delays have to be done by a single robot, which can perform at most one transportation at a time. And release dates rj may be given for the jobs. New complexity results are derived for special case. For a new heuristic algorithm, the worst-case performance is 3/2, ...
ATETs over time Example 4: Dynamic treatment effects We could also ask what the evolution of the treatment effect is after treatment. For instance, we might want to know what happens one period after the onset of treatment, two periods after treatment, and so forth. It might be the case ...
It is based on information theory, which is a highly interesting, deep topic that unfortunately we can't go into too much detail about. It attempts to balance the complexity of the model, which in this case means the number of parameters, with how well it fits the data. Let's p...
Let us recall that, as per notational rules of box-plots, a box-plot shows 25%–75% quartile of data in a ‘box’ notation and that quartile is quite tiny in the case of the right box-plot in Fig. 4, since half of the citation values are simply zero and other are quite small,...