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Questions tagged [np-hard]

NP-hard problems (Non-deterministic Polynomial-time hard problems) are those problems which are not easier than any problem in NP; in other words, an algorithm for an NP-hard problem can be used to solve any problem in NP by transforming the input in polynomial time. Problems which are in both NP-Hard and NP are known as NP-Complete.

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How to find what numbers in a set add up to another given number?

Here's a problem that I seem to be running into working with an accounting system. I have a set of transactions, but their sum does not equal the amount that the accounting department thinks that it should. They are not questioning the math, just…
Even Mien
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List of problems that are in general NP-hard but have polynomial-time solution in planar graphs?

I encountered many problems that can be formulated as graph problem. It is in general NP-hard but sometimes the graph can be proved to be planar. Hence, I am interested in learning these problems and the algorithms. So far as I know: Max cut in…
Ivan Xiao
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How to do Binary Encoding in Genetic Algorithm for better results in Timetable Scheduling Problem?

I have a problem of University Timetable Scheduling which I am trying to solve with Genetic Algorithm. I want to know the best encoding type for this problem that can also help me in satisfying few of the constraints. For this problem, the timetable…
Awais Shahid
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Why is TSP NP-hard while the Hamiltonian path NP-complete?

Why aren't these 2 problems, namely TSP and Hamiltonian path problem, both NP-complete? They seem identical.
User
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NP-Complete vs. NP-hard

If a problem A known to be NP-Complete can be reduced to another problem B in polynomial time then B is (A) NP-Complete (B) NP-hard Nothing is given about problem B whether it is in NP or not. I'm confused because in Hopcraft and Ullman book there…
Prashant Bhardwaj
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Selecting k sub-posets

I ran into the following algorithmic problem while experimenting with classification algorithms. Elements are classified into a polyhierarchy, what I understand to be a poset with a single root. I have to solve the following problem, which looks a…
dareios
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Is this a linear programming problem?

I have been pulling my hair out on one problem... The overall problem is complicated... but let me try my best to explain the part that really matters... I have a graph where each edge represents the correlation between the connected two nodes. Each…
h0cked
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What is the minimum number of swaps needed so that the difference of sums of arrays a and b is minimum?

Given 2 arrays of integers a[] and b[] with the same size of n (1 <= n <= 100) numbered from 1 to n. (0 <= a[i], b[i] <= 6) You can swap any a[i] with b[i]. What is the minimum number of swaps needed so that the difference of the sums of array a[]…
unglinh279
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Fast approximation of simple cases of relaxed bipartite dimension of graph problem

Given boolean matrix M, I need to find a set of submatrices A = {A1, ..., An} such that matrices in A contain all True values in matrix M and only them. Submatrices don't have to be continuous, i.e. each submatrix is defined by the two sets of…
Dimitrius
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fair partitioning of set S into k partitions

There is a set S containing N integers each with value 1<=X<=10^6. The problem is to partition the set S into k partitions. The value of a partition is the sum of the elements present in it. Partition is to be done in such a way the total value of…
Akhil
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How hard is this in terms of computational complexity?

So I have a problem that is basically like this: I have a bunch of strings, and I want to construct a DAG such that every path corresponds to a string and vice versa. However, I have the freedom to permute my strings arbitrarily. The order of…
danharaj
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Multiple Knapsack using Dynamic Programming

I'm wondering if there is a reasonable way of solving Multiple Knapsack using DP. I get the point in 0-1 Knapsack Problem. The recurrence is quite straightforward, add item/ not add item. dp[item][capacity] = max{ value[item] + dp[item -…
André Gomes
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What do you call the property of a list that describes the degree to which it contains duplicates?

I have a function that selects Cartesian products of lists such that the number of duplicate elements is highest: import Data.List (nub) f :: Eq a => [[a]] -> [[a]] f xss = filter ((==) minLength . length . nub) cartProd where minLength =…
marc_r
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Fast Exact Solvers for Chromatic Number

Finding the chromatic number of a graph is an NP-Hard problem, so there isn't a fast solver 'in theory'. Is there any publicly available software that can compute the exact chromatic number of a graph quickly? I'm writing a Python script that…
Chris Harshaw
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Single candidate and multiple interviewers?

There is 1 candidate who is to be interviewed by the n interviewers, so a total of n consecutive slots are needed for the same, for example The table below illustrates the availability of four interviewers (I1, I2, I3, I4) at four time slots (S1,…
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