Problem Detail: I am trying to search for an algorithm that can tell me which node has the highest download (or upload) capacity given a weighted directed graph, where weights correspond to individual link bandwidths. I have looked at the maximal Read More …
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Perfect shuffle in parallel processing
Problem Detail: How is Perfect shuffle a better interconnect scheme for parallel processing? For example if we consider a problem of sum reduction, I want to understand how this scheme is useful when implementing sum reduction in parallel , for example Read More …
Construct two functions $f$ and $g$ satisfying $f ne O(g), g ne O(f)$
Problem Detail: Construct two functions $ f,g: R^+ → R^+ $ satisfying: $f, g$ are continuous; $f, g$ are monotonically increasing; $f ne O(g)$ and $g ne O(f)$. Asked By : Jessie Answered By : Shaull There are many examples for such functions. Read More …
Why is $3^n = 2^{O(n)}$ true?
Problem Detail: $3^n = 2^{O(n)}$ is apparently true. I thought that it was false though because $3^n$ grows faster than any exponential function with a base of 2. How is $3^n = 2^{O(n)}$ true? Asked By : David Faux Answered By : SamM Read More …
Proving ALLTM complement not recognizable
Problem Detail: A few definitions.. $$ begin{align*} mathrm{ALL}_{mathrm{TM}} &= Bigl{langle M rangle ,Big|, text{$M$ a Turing Machine over ${0,1}^{*}$},;; L(M) = {0,1}^{*} Bigr} [2ex] overline{mathrm{ALL}}_{mathrm{TM}} &= Bigl{langle M rangle ,Big|, text{$M$ a Turing Machine over ${0,1}^{*}$},;; L(M) ne {0,1}^{*} Bigr} [2ex] Read More …
Is word size, the size of a memory location? the size of the data bus? or the cpu register size?
Problem Detail: Is word size, the size of a memory location? the size of the data bus? or the cpu register size? Suppose you have a computer, memory address #0 has byte AB memory address #1 has byte F3 memory address Read More …
Multitape Turing machines against single tape Turing machines
Problem Detail: Introduction: I recently learned that a multi-tape Turing Machine $text{TM}_k$ is no more “powerful” than a single tape Turing machine $text{TM}$. The proof that $text{TM}_k equiv text{TM}$ is based on the idea that a $text{TM}$ can simulate a $text{TM}_k$ Read More …
Why are NP-complete problems so different in terms of their approximation?
Problem Detail: I’d like to begin the question by saying I’m a programmer, and I don’t have a lot of background in complexity theory. One thing that I’ve noticed is that while many problems are NP-complete, when extended to optimization problems, Read More …
Correctness proof of greedy algorithm for 0-1 knapsack problem
Problem Detail: We have a 0-1 knapsack in which the increasing order of items by weight is the same as the decreasing order of items by value. Design a greedy algorithm and prove that the greedy choice guarantees an optimal solution. Read More …
Is computation expression the same as monad?
Problem Detail: I’m still learning functional programming (with f#) and I recently started reading about computation expressions. I still don’t fully understand the concept and one thing that keeps me unsure when reading all the articles regarding monads (most of them Read More …
