Problem Detail: It occurred to many that in all the $textbf{NP}$-completeness proofs I’ve read (that I can remember), it’s always trivial to show that a problem is in $textbf{NP}$, and showing that it is $textbf{NP}$-hard is the… hard part. What $textbf{NP}$-complete Read More …
Category: Uncategorized
[Solved]: Is a stack machine with a forward read iterator Turing complete?
Problem Detail: It is well known that a machine with a single stack as only unlimited storage is not Turing complete, if it can only read from the top of the stack. I want a machine which is (slightly) more powerful Read More …
[Solved]: What is the difference between radix trees and Patricia tries?
Problem Detail: I am learning about radix trees (aka compressed tries) and Patricia tries, but I am finding conflicting information on whether or not they are actually the same. A radix tree can be obtained from a normal (uncompressed) trie by Read More …
[Solved]: Show that if d(n) is O( f (n)) and e(n) is O(g(n)), then d(n)−e(n) is not necessarily O( f (n)−g(n))
Problem Detail: I have this question as an assignment in my Java Algorithms class, and i’m aware that d(n)+e(n) is the same as O(f(n)+g(n)). I dont know why the same doesnt apply to subtracting. Can someone help me? I’m lost.. Asked Read More …
[Solved]: What is “polynomial delay?”
Problem Detail: I am reading a paper and it uses the expression “polynomial delay” which I don’t understand. It is used in conjonction with the big O notation, which I’m familiar with. Here is a example sentence showing how it is Read More …
[Solved]: What is a good algorithm for generating random DFAs?
Problem Detail: I am generating random DFAs to test a DFA reduction algorithm on them. The algorithm that I’m using right now is as follows: for each state $q$, for each symbol in the alphabet $c$, add $delta (q, c)$ to Read More …
[Solved]: Is an inverse homomorphism always a homomorphism?
Problem Detail: Given a homomorphism $h: Sigma rightarrow Delta^*$ such that e.g. $forall a in Sigma: h(a) = delta$, where $delta in Delta$ (i.e. all symbols from the alphabet $Sigma$ have the same image $delta$), is the inverse homomorphism $h^{-1}$ a Read More …
[Solved]: Create a random graph based on the Degree Distribution and Clustering Coefficient Distribution
Problem Detail: I am currently working with a very large Social Network and I want to recreate this graph with a smaller dimension, using the original Degree Distribution and Clustering Coefficient Distribution. The degree distribution is the relative frequency of vertexes Read More …
[Solved]: About metric TSP instances
Problem Detail: Christofides’ 1.5-approximation considers complete graphs as inputs, and as I understand this is essential. If the input graph is not complete, how can I add new edges with suitable weights such that the resulting complete graph still satisfies the Read More …
[Solved]: Proving correctness of the algorithm for convex polygon minimum cost triangulation
Problem Detail: I have read many solutions for the minimum cost of triangulation problem and intuitively get the idea , however I am struggling to figure out how to prove it formally. I kind of feel that it has to be Read More …
