This page describes how guarantees for resources can be implemented.
comment2,
Providing a guarantee through limiting
The idea of getting a guarantee is simple:
if any group Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g_i}
requires a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle G_i}
units of resource from Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R}
units available then limiting all the rest groups with Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R - G_i}
units provides a desired guarantee
For Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N}
groups in the system this implies solving a linear equation set to get limits Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle L_i}
like this:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{cases} L_2 + L_3 + \ldots + L_N = R - G_1 \\ L_1 + L_3 + \ldots + L_N = R - G_2 \\ \ldots \\ L_1 + L_2 + \ldots + L_{N-1} = R - G_N \\ \end{cases} }
In a matrix form this looks like
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A L = G\; }
where
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A = \begin{bmatrix} 0 & 1 & 1 & \cdots & 1 & 1 \\ 1 & 0 & 1 & \cdots & 1 & 1 \\ & & \cdots \\ 1 & 1 & 1 & \cdots & 1 & 0 \\ \end{bmatrix} , L = \begin{bmatrix} L_1 \\ L_2 \\ \vdots \\ L_N \end{bmatrix} , G = \begin{bmatrix} R - G_1 \\ R - G_2 \\ \vdots \\ R - G_N \end{bmatrix} }
and thus the solution is
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle L = A^{-1}G\; }
Skipping boring calculations, the reverse matrix Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A^{-1}\;}
is
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A^{-1} = \frac {1} {N - 1} \left( A - (N - 2) E \right) }
This solutions looks huge, but the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle L}
vector is calculated in Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle O(N)}
time:
void calculate_limits(int N, int *g, int *l)
{
int sum;
int i;
if (N == 1) {
l[0] = R;
return;
}
sum = 0;
for (i = 0; i < N; i++)
sum += R - g[i];
for (i = 0; i < N; i++)
l[i] = (sum - (R - g[i]) - (N - 2) * (R - g[i]))/(N - 1);
}
Disadvantages of this approach
This approach has only one disadvantage: O(n) time needed to start a new container.
