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Results tagged with np-complete
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user 83257
Questions about the hardest problems in NP, i.e. of those that can be solved in polynomial time by nondeterministic Turing machines.
5
votes
NP-hard problems but only for n≥3
There are many problems like this listed in Computers and Intractability: A Guide to the Theory of NP-Completeness by Michael Garey and David S. Johnson. For instance,
[ND14] Graph Partitioning: NP- …
- 1,046
1
vote
1
answer
287
views
Find a truth assignment of 2SAT that has the most number of true variables?
Given a 2SAT instance in CNF where each clause has at most two literals. Let $m$ be the number of clauses and $n$ be the number of variables et let $k$ be a positive number.
Question: Is there a trut …
- 1,046
1
vote
1
answer
47
views
Minimize the sum of gaps
I have a set of $n$ objects $\{1,2,\ldots,n\}$ where object $i$ has weight $w(i)$ and we have a capacity $W$. I would like to pick a subset $S=\{a_1,\ldots,a_m\}\subseteq \{1,2,\ldots,n\}$ of the obje …
- 1,046
0
votes
1
answer
108
views
Multiple Knapsack Problem with Set of Admissible Balls
We have $m$ bins and $n$ balls.
Each bin $i=1,2,\ldots,m$ can contain at most two balls (not any two balls but two balls from some specific set), see 3.
Each ball $j=1,2,\ldots,n$ can be put into b …
- 1,046
2
votes
1
answer
130
views
How to partition a set in order to minimize the number of the elements and their interactions?
Given two sets $S_1$ and $S_2$ of $n$ elements each. Each set $S_1$ (resp. $S_2$) has a revenue $R_1$ (resp. $R_2$). Each element $i$ of $S_1$ (resp. $S_2$) has a gain $g_{i1}$ (resp. $g_{i2}$). From …
- 1,046
1
vote
1
answer
2k
views
A Special Case of Multiple Choice Knapsack Problem: Is it NP-hard?
The multiple choice knapsack problem (MCKP) can be defined as follows:
MCKP is known to be NP-hard in general. I have a special case of MCKP for which
$N_i=\{1,2,\cdots,|N_i|\}$, for all $1\leqs …
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