Problem Detail: I was making a program for solving 2 SAT problems, using Krom’s algorithm. I did not found a lot of information searching in Google, so I used Wikipedia’s description of Krom’s algorithm to implement it but I’m stuck in Read More …
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[Solved]: Dijkstra’s algorithm runtime for dense graphs
Problem Detail: The runtime for Dijkstra’s algorithm implemented with a priority queue on a sparse graph is $O((E+V)log V)$. For a dense graph such as a complete graph, there can be $V(V-1)/2$ edges. Since $E sim V^2$, is the runtime $O((V+V^2)log Read More …
[Solved]: If we sort a table column-wise and then row-wise why the table is still sorted column-wise?
Problem Detail: Say we have a $n times n$ table which elements are sorted column-wise, for example: $$ left( begin{array}{ccc} 2 & 4 & 1 3 & 5 & 6 7 & 9 & 8 end{array} right) $$ I would like Read More …
[Solved]: Term rewriting; Compute critical pairs
Problem Detail: I have tried to solve the following exercise but I got stuck while trying to find all the critical pairs. I have the following questions: How do I know which critical pair produced a new rule? How do I Read More …
[Solved]: What do we gain by having “dependent types”?
Problem Detail: I thought I understood dependent typing (DT) properly, but the answer to this question: Why was there a need for Martin-Löf to create intuitionistic type theory? has had me thinking otherwise. After reading up on DT and trying to Read More …
[Solved]: Detecting coplanarity by given pairwise distances
Problem Detail: Consider an undirected weighted graph $G = (V,E)$, where $V subset mathbb{R}^3$ so the points are 3D, and the weight of an edge equals the (Euclidean) distance between its endpoints. Note that we’re not given the coordinates of the Read More …
[Solved]: Transforming an arbitrary cover into a vertex cover
Problem Detail: Given is a planar graph $G=(V,E)$ and let $mathcal{G}$ denote its embedding in the plane s.t. each edge has length $1$. I have furthermore a set $C$ of points where each point $c in C$ is contained in $mathcal{G}$. Read More …
[Solved]: How do I apply patch sized features to larger images?
Problem Detail: I’ve been trying to teach myself some machine learning, and I wanted to ask what seems a simple question, but I’ve not been able to find any resources that explain the next step. Let’s say I am doing semi-supervised Read More …
[Solved]: Searching the space of permutations
Problem Detail: I’m given n objects, and a set of n permutations of these n objects (out of n! total permutations). There is a true underlying permutation, which I know is one among the set of n permutations, but I don’t Read More …
[Solved]: How do you prove Sigma Star is regular
Problem Detail: I noticed in another answer on this forum Note that the languages ∅, {ϵ} and Σ* are regular. How do you prove Sigma Star is regular. Asked By : gatech-kid Answered By : David Richerby It’s easy to design a DFA Read More …
