Problem Detail: Given N numbers and M range queries (starting and ending points), I need to compute majority (most frequent element, if it exists) in these ranges. I’m looking for an algorithm that would answer queries in logarithmic or even constant Read More …
Author: ignougroup
[Solved]: Find subset with minimal sum under constraints
Problem Detail: Let $M$ be a finite set of even cardinality. Define $C={{a,b}:a,b in M, a neq b}$ the set of all pairs over $M$. Let $w:C rightarrow mathbb{R}^+_0$ be a function. Now find $C’ subset C$ with the following constraints: Read More …
[Solved]: Proving that if $mathrm{NTime}(n^{100}) subseteq mathrm{DTime}(n^{1000})$ then $mathrm{P}=mathrm{NP}$
Problem Detail: I’d really like your help with proving the following. If $mathrm{NTime}(n^{100}) subseteq mathrm{DTime}(n^{1000})$ then $mathrm{P}=mathrm{NP}$. Here, $mathrm{NTime}(n^{100})$ is the class of all languages which can be decided by nondeterministic Turing machine in polynomial time of $O(n^{100})$ and $mathrm{DTime}(n^{1000})$ is Read More …
[Solved]: Where is the mistake in this apparently-O(n lg n) multiplication algorithm?
Problem Detail: A recent puzzle blog post about finding three evenly spaced ones lead me to a stackoverflow question with a top answer that claims to do it in O(n lg n) time. The interesting part is that the solution involves Read More …
[Solved]: Prove REGULAR_TM is undecidable
Problem Detail: I am studying the proof of the following theorem: Given the language $mathit{REGULAR}_mathit{TM} = {langle M rangle | M $ is a turing machine and $mathit{Accept}(M)$ is regular$}$ $mathit{REGULAR}_mathit{TM}$ is undecidable. The proof given in Sipser shows that if Read More …
[Solved]: If one-way functions exist are we definitely using them?
Problem Detail: I know that if one-way functions exist then there are certain universal one-way functions that exist, but to my knowledge they are too impractical to implement (which is the main reason why they are not being used in modern Read More …
[Solved]: minimum subset of dominating 2D points
Problem Detail: From an initial set $S$ of 2D points, how to efficiently compute a minimum(-size) dominating subset $M$ ? $M$ is a dominating subset of $S$ if for any $(x,y)$ in $S$ there is at least one point (a,b) in Read More …
[Solved]: Transform unstructured flow charts into structured ones
Problem Detail: Has anyone studied the problem of converting a generic flowchart to a semantically equivalent “structured flowchart” (i.e. one that only uses the ‘if’ and ‘while’ block structure)? I can see this may be relevant to code generation and optimization Read More …
[Solved]: Algorithm to extract the subgraph of all nodes with degree at least four
Problem Detail: I have an undirected graph represented by a list of nodes and a list of edges. What I need to produce from this is a list of nodes and edges representing a new graph containing only the nodes which Read More …
[Solved]: How to compare the time-complexity of an optimized algorithm with that of the original?
Problem Detail: I had an algorithm with time-complexity of $O(htimes w)$, knowing $h$ is the height and $w$ is the width of an image being processed (or a simple matrix of size $htimes w$). I managed to reduce the range that Read More …
