Problem Detail: I am trying to learn(self-study, not homework) how to perform transitive reduction according to what what Prof. Leskovec explains in section 10.8.6 in Mining Massive Datasets. The book is free to access online. The section is actually talking about Read More …
Category: Uncategorized
[Solved]: Is the maximum coverage variant of Vertex Cover also NP-hard?
Problem Detail: In Chapter 3 of “Approximation Algorithms for NP Hard Problems” edited by Prof. Dorit S. Hochbaum, there is such a sentence that “Maximum Coverage Problem is clearly NP-hard, as Set Cover is reducible to it” in p.135. Given a Read More …
[Solved]: Reference request: Category theory as it applies to type systems
Problem Detail: I keep hearing about how one must learn category theory to truly understand programming language theory. So far, I’ve learned a good deal of PL without ever stepping foot into the realm of categories. However, I figured it was Read More …
[Solved]: Smallest(k) in red-black tree. How is it O(logn)?
Problem Detail: Is it the same as find minimum for a binary search tree? I know recoloring runs in O(logn) and rotations are O(1). Even if we are wanting it to find the ‘k-th’ smallest key in the red-black tree. Could Read More …
[Solved]: NP-complete decision problems – how close can we come to a solution?
Problem Detail: After we prove that a certain optimization problem is NP-hard, the natural next step is to look for a polynomial algorithm that comes close to the optimal solution – preferrably with a constant approximation factor. After we prove that Read More …
[Solved]: Every graph with $delta(G) ge 2$ has a cycle of length at least $delta(G)+1$?
Problem Detail: I’m reading up on graph theory using Diestel’s book. Right on the outset I got confused though over proposition 1.3.1 on page 8 which reads: Proposition 1.3.1. Every graph G contains a path of length $delta(G)$ and a cycle Read More …
[Solved]: Problems that are NP but polynomial on graphs of bounded treewidth
Problem Detail: I heard here that the Hamiltonian cycle problem is polynomial on graphs of bounded treewidth. I am interested in examples/references to different problems which is essentially hard but having polynomial complexity on graphs of bounded treewidth. Asked By : seteropere Read More …
[Solved]: Finding MST after adding a new vertex
Problem Detail: Let $G=(V,E)$ which is undirected and simple. We also have $T$, an MST of $G$. We add a vertex $v$ to the graph and connect it with weighted edges to some of the vertices. Find a new MST Read More …
[Solved]: CoNP and NPhard intersection
Problem Detail: Can a problem be both NP-Hard and CoNP? Can a problem be both NP and CoNP-Hard? Asked By : Turbo Answered By : Peter Shor There is a problem which is both NP-hard and in coNP if and only if NP Read More …
[Solved]: $log^*(n)$ runtime analysis
Problem Detail: So I know that $log^*$ means iterated logarithm, so $log^*(3)$ = $(loglogloglog…)$ until $n leq 1$. I’m trying to solve the following: is $log^*(2^{2^n})$ little $o$, little $omega$, or $Theta$ of ${log^*(n)}^2$ In terms of the interior functions, $log^*(2^{2^n})$ Read More …
