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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
Q: How does the bitlength of the divisor affect the running-time complexity of division algorithms?

genWikipedia 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
Q: What is graph clustering?

nbroThere 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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