 4:00 AM
@smac89 (about cs.stackexchange.com/questions/105808/…) Exactly, I don't think OP is asking for an ordering of the element of 𝑎. Please read my answer carefully, especially the formal formulation. 4:11 AM
I don't follow your formulation. You say "To determine the function I such that m(a(k))=b(I(k)) for all k, it will take Θ(nlogn) queries against O in the worst case"
However, you use I in the definition of the function I. Is I a recursive function? Also what is m in your definition of I? I see, my typo. It should have been, "To determine the function 𝐼 such that 𝑎(𝑘)=𝑏(𝐼(𝑘)) for all \$k\$," 0<= k<=n-1. In fact, it should have been, to output I(0), I(1), ....
since the function is determined by that equality already. Ok I see your edit, so what is the output of I(0) for example? I(0) is the index t such that a(0)=b(t). I(k) is the index t such that a(k)=b(t). @Apass.Jack Ok so how do you query the oracle? i.e. what are the inputs e and f? Are you assuming that E is ordered? Is that what you mean by "strict linear ordering"? 4:28 AM
\$e\$ and \$f\$ are the input. (Hm, so I should have written "when input are \$e\$ and \$f\$") For example, given 1 and 3 to the oracle, the oracle can reply 1. Yes, a strict linear ordering on E means E is ordered.
The input to the oracle must be an ordered pair of elements each of which is in \$E\$. Given element \$e\$ and \$f\$, the oracle replies -1 if \$e<f\$. Given element \$e\$ and \$f\$, the oracle replies 0 if \$e\$ and \$f\$ are the same element. Given element \$e\$ and \$f\$, the oracle replies 1 if \$e>f\$.

8 hours later… 12:58 PM
2  Wikipedia lists \$O(M(n))\$ as the best complexity (out of the algorithms listed) for division on two n-digit numbers, where \$M(n)\$ is the complexity of the multiplication algorithm of choice. This is the complexity of the Newton-Raphson division. My question is this: what are some of the best kn...

1 hour later… 2:04 PM
@user3371603 (cs.stackexchange.com/questions/105758/…) "One way for computing 𝑑𝑝2[𝑚][𝑛] is to find the maximum value of 𝑑𝑝[𝑚−1][𝑥]+𝑓(𝑥) for 𝑥≤𝑛, where 𝑓(𝑥) means optimum value for finding largest (just one) rectangle between x-th and n-th bar. It seems that it has the complexity of 𝑂(𝑀𝑁^2). Is it a good way?" Yes, it is a good way. 2:57 PM
Could somebody take a look at cs.stackexchange.com/a/105833/68251 ? I think this is a good idea, but I'm still not sure of a good way to approach finding this \$g(k)\$ function I am talking about. I have always done it by trial and error in the past, but a rigorous method would be super helpful.
Any thoughts/feedback would be greatly appreciated

2 hours later… 5:20 PM
1  There are several (family of) algorithms that can be used to cluster a set of \$d\$-dimensional points: for example, k-means, k-medoids, hierarchical clustering (agglomerative or divisive). What is graph-based clustering? Are we clustering the nodes or edges of a graph instead of a set of \$d\$-dim...

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