Problem Detail: In 1962, you could win a prize of $ 10 000 (about $ 80 000 in today’s money) if you found the solution to an Euclidean travelling salesman problem defined on 33 cities. http://www.math.uwaterloo.ca/tsp/history/pictorial/car54.html Looking at the picture, the Read More …
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Why is the dynamic programming algorithm of the knapsack problem not polynomial?
Problem Detail: The dynamic programming algorithm for the knapsack problem has a time complexity of $O(nW)$ where $n$ is the number of items and $W$ is the capacity of the knapsack. Why is this not a polynomial-time algorithm? I have read Read More …
why are deterministic PDAs not closed under concatenation?
Problem Detail: I can understand that they are not closed under concatenation because without non determinism, PDA cannot decide whether to loop in the first PDA or jump to the next one. But can someone prove this with an example. Also Read More …
Deterministic vs. Non-Deterministic PDA?
Problem Detail: The following is an example of language $a^nb^n$ where $n geq 1$ From what I have heard that in finite state machines if you see epsilon moves, then it is NFA otherwise it is DFA. But in this case, Read More …
Modifying Dijkstra’s algorithm to favor the path with least amount of edges
Problem Detail: I need to modify the Dijkstra’s algorithm to get the shortest path in a directed graph and get the one with the least amount of edges if there are equal paths. I am thinking to add another data field Read More …
Which algorithms can not be parallelized?
Problem Detail: Is there any algorithm which is very difficult to parallelize or the research is still active? I wanted to know about any algorithm or any research field in parallel computing. Anything, I searched for, has a ‘parallel’ implementation done. Read More …
Minimum s-t cut in weighted directed acyclic graphs with possibly negative weights
Problem Detail: I ran into the following problem: Given a directed acyclic graph with real-valued edge weights, and two vertices s and t, compute the minimum s-t cut. For general graphs this is NP-hard, since one can trivially reduce max-cut to Read More …
How do I find my wife in a supermarket?
Problem Detail: If two people are lost in a maze, is there an algorithm that they can both use to find each other without having previously agreed what algorithm they will be using? I think there are some characteristics that this Read More …
Explanation of Tag, Index, and Offset in Direct Mapping Cache
Problem Detail: I’m going through an exercise trying to store address references into a direct mapped cache with 128 blocks and a block size of 32 bytes. The address are 20000, 20004, 20008, and 20016 in base 10. When I start Read More …
Using Funk SVD with SGD?
Problem Detail: I work on a recommender system framework which is implemented with a variant on Funk SVD (See his explanation of his algorithm here). However the framework that we are trying to integrate doesn’t support Funk SVD, only SGD (Stochastic Read More …
