Problem Detail: BACKGROUND: Recently I tried to solve a certain difficult problem that gets as input an array of $n$ numbers. For $n=3$, the only solution I could find was to have a different treatment for each of the $n!=6$ orderings Read More …
Category: Uncategorized
[Solved]: Reduction to Maximum Independent Set
Problem Detail: Suppose you had a set $P$ of people. Every person $p_j in P$ is familiar with atleast one other person $p_i$ (familiarity is symmetric). Is there a subset $S$ of people such that for $|S| ge k$, no two Read More …
[Solved]: Constructing all context-free languages from a set of base languages and closure properties?
Problem Detail: One way of looking at regular expressions is as a constructive proof of the following fact: it’s possible to construct the regular languages by starting with a small set of languages and combining them via a small, fixed set Read More …
[Solved]: Complexity of deciding if a formula has exactly 1 satisfying assignment
Problem Detail: The decision problem Given a Boolean formula $phi$, does $phi$ have exactly one satisfying assignment? can be seen to be in $Delta_2$, $mathsf{UP}$-hard and $mathsf{coNP}$-hard. Is anything more known about its complexity? Asked By : sdcvvc Answered By : Juho Your Read More …
[Solved]: Randomized Rounding of Solutions to Linear Programs
Problem Detail: Integer linear programming (ILP) is an incredibly powerful tool in combinatorial optimization. If we can formulate some problem as an instance of an ILP then solvers are guaranteed to find the global optimum. However, enforcing integral solutions has runtime Read More …
[Solved]: Solve Integer Factoring in randomized polynomial time with an oracle for square root modulo $n$
Problem Detail: I’m trying to solve exercise 6.5 on page 309 from Richard Crandall’s “Prime numbers – A computational perspective”. It basically asks for an algorithm to factor integers in randomized polynomial time given an oracle for taking square roots modulo Read More …
[Solved]: Is this an instance of a well-known problem?
Problem Detail: Context I am developing an application and came across a problem that seemed difficult to solve. Before attempting to reinvent the wheel (and trying to solve an NP complete problem on my own), I would like to get Read More …
[Solved]: How to perform alphabetically ordered DFS?
Problem Detail: I’ve been working on this graph and just completely botching it. I mean to say that my solution may be the worst possible other than if a monkey had thrown darts at the graph to decide the next path. Read More …
[Solved]: Voronoi diagram algorithm with non-euclidean metric
Problem Detail: Do you know any easy to implement algorithm for constructing a Voronoi diagram from a given set of points on a surface, using some different metric (taxicab, for instance)? It can be some modification of Fortune’s algorithm. Asked By Read More …
[Solved]: What’s a uniform shuffle?
Problem Detail: What does it mean exactly a “uniform shuffle” algorithm ? Is this method considered a uniform shuffle ? public void shuffle(Comparable[] a) { int n = a.length; int k, j; for (int i = 0; i < n; i++) Read More …
