Problem Detail: I’m trying to find a polynomial time algorithm for finding the minimum vertex cover for a graph. I’ve written the algorithm below; I know this problem is $mathsf{NP}$-hard, which means there are probably some graphs for which this algorithm Read More …
Month: January 2017
[Solved]: Proving Equivalence of 1-dimensional Cellular Automaton and Turing Machines
Problem Detail: I’m considering an automaton $A$ over a alphabet $Sigma$, with a set of states $Q$, such that $Sigma subset Q$, which includes special “accept” and “blank” states not in $Sigma$. It also has an infinite list of cells, which Read More …
[Solved]: SAT not reducible to 2SAT
Problem Detail: Why is the reduction $textbf{SAT} leq_P textbf{3SAT}$ possible, but $textbf{SAT} leq_P textbf{2SAT}$ not possible, given, that $textbf{SAT}$ is $textbf{NP}$-complete, $textbf{2SAT} in textbf{NP}$ and $textbf{3SAT} in textbf{NP}$? Asked By : Anderson Answered By : mdxn I believe the asker is wanting to Read More …
[Solved]: Is the shadow ray in a Whitted ray tracer occluded by transparent objects?
Problem Detail: In a Whitted ray tracer, each ray-object intersection spawns a transmitted ray (if the object was translucent), a reflected ray and a shadow ray. The shadow ray contributes the direct lighting component. But what happens if the shadow ray Read More …
[Solved]: Please explain a greedy algorithm in a naive manner
Problem Detail: I am a beginner in the topic of algorithms. I have a query about Greedy Algorithms. From what I understand, if there is a function and we are supposed to find its maxima/minima, if we find the local maxima/minima, Read More …
[Solved]: Understanding Multilevel Caches
Problem Detail: I’m reading multi-level cache and came across a question through which i got confused. I’ve read that Between processor and Cache Word/ Byte is transfered Between Cache and Main memory Block(Block of words) is transfered. If there is a Read More …
[Solved]: Adding a node between two others, minimizing its maximum distance to any other node
Problem Detail: We are given an undirected graph weighted with positive arc lengths and a distinguished edge $(a,b)$ in the graph. The problem is to replace this edge by two edges $(a,c)$ and $(c,b)$ where $c$ is a new node, such Read More …
[Solved]: How to show that the complement of a language in $mathsf P$ is also in $mathsf P$?
Problem Detail: If $L$ is a binary language (that is, $L subseteq Sigma = {0,1}^∗$) and $overline{L}$ is the complement of $L$: How can I show that if $L in mathsf P$, then $overline{L} in mathsf P$ as well? Asked By Read More …
[Solved]: Is the relation between the input and output of an arbitrary algorithm describable by a mathematical function?
Problem Detail: I hope that this question is clear, and not off-topic: I have been reading about neural networks (in the AI sense), and the textbook said that an artificial neural network can always be described by a single mathematical function Read More …
[Solved]: If A is poly-time reducible to B, is B poly-time reducible to A?
Problem Detail: Basically, is the following statement true? $A leq_p B$ $rightarrow$ $B leq_p A$ Asked By : robowolverine Answered By : Sasho Nikolov Short answer: No. For one example, take $A$ to be the language $A = {0, 1}^*$, i.e. the language Read More …