# Tag Info

Accepted

### Sample a set of N numbers without replacement, each element taken from N different weighted sets

There is a mapping from each possible list $P$ to an interval $[\ell,r)$ contained in $[0,1)$, such that the resulting intervals (if you consider all possible lists) form a partition of $[0,1)$. In ...
1 vote
Accepted

### A lower bound for the makespan of heterogenous fog nodes

Under the assumption that $EXT(N_i) = \mathit{MinMakespan}$, $$\sum_{k \in N_i \mathit{Tasks}} \mathit{length}(T_k) = \mathit{MinMakespan} \times \mathit{CPUrate}(N_i).$$ Therefore  \sum_k \mathit{...
Accepted

### Boolean Logic for Floats

I recommend that you look up 'Fuzzy Logic'.

### N Queens Problem - Number of Possible Placements

About the "computationally expensive": They calculated the number of ways to put eight queens onto 8 fields of an 8x8 chessboard, ignoring the identity of the queens. But anybody in their ...
1 vote

### Alternate proof of the Caro-Wei theorem for lower bounding the independence number

Induction on the order of G . True for |G| = 1. Assume for |G| = n let prove it for |G| = n +1. Choose a vertex v of minimum degree . Consider H = G - N[v]. Clearly a(G)> = 1 + a(H) > = 1 + sum {...
1 vote

### Alternate proof of the Caro-Wei theorem for lower bounding the independence number

There are several non-probabilisitc proofs : 1/ using greedy algorithm deleting minimum degree : See : https://www.sciencedirect.com/science/article/pii/S0166218X13001339 https://onlinelibrary.wiley....
Accepted

### N Queens Problem - Number of Possible Placements

4,426,165,368 is the number of ways to place 8 identical queens into 64 places, i.e the number of combinations. "Identical" means positions are considered equivalent if one queen is swapped ...
This is called Enumerative Coding and was introduced by Tom Cover. Consider a word $W$ that is $n$ bits long, where the one bits are in locations $x_k, \ldots, x_1$ with \$x_k>x_{k-1}>\cdots>...