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Problem Detail: Suppose we have a balanced binary tree, which represents a recursive partitioning of a set of $N$ points into nested subsets. Each node of the tree represents a subset, with the following properties: subsets represented by two children nodes Read More …

Problem Detail: This is about basic machine learning which I do not understand clearly. I have 2 Gaussian models $G_1$ and $G_2$ and given a list of data as below. (1, 3, 4, 5, 7, 8, 9, 13, 14, 15, 16, Read More …

Problem Detail: Suppose I am given a finite set of points $p_1,p_2,..p_n$ in the plane, and asked to draw a twice-differentiable curve $C(P)$ through the $p_i$’s, such that its perimeter is as small as possible. Assuming $p_i=(x_i,y_i)$ and $x_i<x_{i+1}$, I can Read More …

Problem Detail: Let $N(G)$ be the null graph. What’s the number of vertex cover for this graph? I wanted to modify the reduction from SAT to vertex cover by adding vertices that are not connect to any vertices. Asked By : Fayez Read More …

Problem Detail: I’m asked to prove that, if P=NP, that 0*1* is NP-complete, but I’m having trouble going about doing it. I know it’s fairly easy to prove it’s NP by creating a TM to verify an input (which can be Read More …

Problem Detail: I have a weighted directed graph (it’s sparse, 35,000 nodes and 19 million edges) and would like to calculate similarity scores for pairs of nodes. SimRank would be ideal for this purpose, except that it applies to unweighted graphs. Read More …

Problem Detail: Say that there are $n$ days and there is $x_1, x_2, …,x_n$ amount of data to process on each day. Your computer can process $s_1$ amount of work on the first day since rebooting your computer, $s_2$ work on Read More …

Problem Detail: Alexia Massalin’s Dissertation on Synthesis was a Phd thesis on Operating Systems that contained a concept called ‘Quajects’ (see Chapter 4). This is some additional commentary on the Phd Thesis. Best I can work out – a Quaject is Read More …

Problem Detail: I am trying to wrap my head around recursion and divide and conquer algorithms. Can someone provide a proof and explanation of how many times a list of n elements can be divided in 1/2 on both sides.. In Read More …

Problem Detail: I’m just learning about Turing Machines, and I’m a bit confused by the difference in formal description between Wikipedia and my textbook. My textbook says the following: $$M=langle Q,Sigma,Gamma,delta,q_{0},q_{accept}, q_{reject} rangle$$ where: $Q$ is the set of states, $Sigma$ Read More …