Author: ignougroup

Problem Detail: Given an $n times n$ matrix $mathbf{A}$. Let the inverse matrix of $mathbf{A}$ be $mathbf{A}^{-1}$ (that is, $mathbf{A}mathbf{A}^{-1} = mathbf{I}$). Assume that one element in $mathbf{A}$ is changed (let’s say $a _{ij}$ to $a’ _{ij}$). The objective is to Read More …

Problem Detail: I have few CS textbooks with me which discuss languages, well actually 2 plus old course notes supplied a few years ago. I have been searching the web too any only seem to come up with vague responses just Read More …

Problem Detail: I am learning about information theory and mutual information. However, I am quite confused with MI(Mutual information) vs. PMI(Pointwise mutual information) especially signs of MI and PMI values. Here are my questions. Is MI values a non-negative value or Read More …

Problem Detail: I was wondering about a variation on the Stable Marriage Problem. Initially, we have two sets of entities, usually males and females, and they have preference lists ranking the other group, and through a series of proposals, we end Read More …

Problem Detail: I’ve tried to solve a exercise 4.1-5 in algorithm book “Introduction to algorithms”. it is about Maximum sub-array problem, which is an algorithm that determines the greatest sum of sub-array A[i], A[i+1] , … , A[j] in given array Read More …

Problem Detail: I just read some pages in Sipser’s book Introduction to Theory of Computation about Post Correspondence Problem, and I’m thinking that PCP is actually in NP. The certifier is: for an input configuration of pile $$(t_1/b_1, t_2/b_2,…t_n/b_n)$$ concatenating $t_1, Read More …

Problem Detail: In some (historical) papers, chess has been referred to as the drosophila of artificial intelligence. While I suppose that in current research, the mere application of a search algorithm is at best advanced computer science, I believe that there Read More …

Problem Detail: I have been reading Karp’s famous paper on the NP-Completeness of different problems, Reducibility among combinatorial problems, and I have a question on the reduction from SAT to 0/1 Integer Programming defined there. The problem 0/1 Integer Programming is Read More …

Problem Detail: I am curious what is the difference between diameter of a graph vs longest path of a graph. I just read diameter of a graph can be solved using Floyd warshall in O(V^3) while longest path can be calculated Read More …

Problem Detail: I was thinking the other day, and it occurred to me that computer programs all seem to be representable as a graph (an abstract syntax tree for example), or, once common expressions are combined, an abstract syntax graph. It Read More …