Problem Detail: Recently, I am reading papers about dichotomy. I do not understant what condition can be called as a dichotomy? What is the meaning of “a question is either in P or in NP–complete“? (assume P $neq$ NP) For example, Read More …
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[Solved]: Is $log(n!)$ in $Theta(n log(n))$?
Problem Detail: I had two questions on my automated test which I don’t understand the answer for. $log(n!) = log(ncdot (n-1)cdot cdots cdot 2cdot 1) = log(n)+log(n-1)+….+log(1)$. So it is in $O(nlog(n))$. But is it also in $Omega(n log(n))$? I don’t Read More …
[Solved]: Universal/existential quantification?
Problem Detail: I’m struggling to understand the purpose of universal and existential quantification of types. I’m playing around with writing a toy language based on the calculus of constructions. I’ve been reading about Morte and Henk to help me get a Read More …
[Solved]: Understanding Closest Pair Algorithm (CLRS)
Problem Detail: I’m reading CLRS Section 33.4 Finding the closest pair of points. At exercise 33.4-2 they say 33.4-2 Show that it actually suffices to check only the points in the 5 array positions following each point in the array Y’ Read More …
[Solved]: High Dimensional Data Structures
Problem Detail: I have a 20-dimensional dataset, with a large amount of data points. I would like to have each dimension discretized into bins. Per bin, I would like to be able to access two neighbours per dimension (i.e. +1 and Read More …
[Solved]: What mechanisms prevent a process from taking over the processor forever?
Problem Detail: Suppose a process keeps running code (e.g. an infinite loop). How can other programs take over? What prevents the process from remaining active forever? Asked By : Dionysus Answered By : Gilles Various peripherals are connected to the main processor. When Read More …
[Solved]: Do recursive algorithms generally perform better than their for-loop counterpart?
Problem Detail: I’m sure this is not a challenge for you but it remains an open question for me: Is it wise to prefer a recursive algorithm over its for-loop counterpart? E.g. take the evaluation of the natural logarithm of a Read More …
[Solved]: Why is And-Or-Graph-Search called a search algorithm?
Problem Detail: An algorithm in Artificial Intelligence: A Modern Approach for planning in stochastic, fully observable environments is called And-Or-Graph-Search, implying that it’s a search algorithm. However, I don’t see how it is one. Wikipedia defines search algorithms as, “an algorithm Read More …
[Solved]: Recovering a point embedding from a graph with edges weighted by point distance
Problem Detail: Suppose I give you an undirected graph with weighted edges, and tell you that each node corresponds to a point in 3d space. Whenever there’s an edge between two nodes, the weight of the edge is the distance between Read More …
[Solved]: Complete Problems for $DSPACE(log(n)^k)$
Problem Detail: We know that the $polyL$-hierarchy doesn’t have complete problems, as it would conflict with the space hierarchy theorem. But: Are there complete problems for each level of this hierarchy? To be precise: Does the class $DSPACE(log(n)^k)$ have complete problems Read More …
