Questions tagged [partition-problem]
17 questions
6
votes
1 answer
Dividing a weighted planar graph into $k$ subgraphs with balanced weight
I've been looking for an algorithm which divides an undirected, weighted, planar and simple graph into $k$ disjoint subgraphs. Here, the graph is sparse, $k$ is fixed, and there are no negative edge weights. After cutting, each subgraph must be…
davidbsp
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5
votes
1 answer
Reduction from PARTITION to MAX-CUT
I am trying to prove the NP-Hardness of the MAX-CUT problem. Other sources seem to reduce from the NAE-3SAT problem, however I have been trying to reduce from PARTITION because PARTITION and MAX-CUT are both in Karp's list of 21 NP-Complete problems…
Dave White
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4
votes
1 answer
Variant of (WEAK) PARTITION with 2 distinct solutions
I am interested in the complexity of the following problem:
Input: A list $a_1\leq ⋯ \leq a_n$ of positive integers.
Question: Are there two vectors $x, x'\in\{−1,0,1\}^n$, with at least one $x_i$ and one $x'_i$ non-zero (the subsets must be…
user2370336
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4
votes
1 answer
3 dimensionnal matching to partition transformation
We want to transform $3DM$ to $PARTITION$, I am reading Garey and Johnson book and I really don't understand how they do the transformation, I know how they create elements $a_i$ from triples of set $M = W \times X \times Y$, but I don't know why…
HFA
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3
votes
1 answer
Partitioning planar graphs without minimizing edge cuts
I am looking for an algorithm that, given an undirected, planar graph $G = (V,E)$ with node weights, meets the following conditions:
Creates balanced (within some margin) $k$ partitions of $V$ according to node weight.
All partitions have to be…
soandos
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2
votes
1 answer
Compact, reversible mapping from set partitions of length k to integers
Given a set $S$ of length $n$, I'm looking to map all the $k$-length partitions of $S$ onto the set of integers such that these integers are as close to 0 as possible. Ideally the range would be $\left[0, {n \brace k}\right)$.
Ideally this mapping…
Jordy Dickinson
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2
votes
1 answer
3-partition problem: why $b/4 < x_i < b/2$?
Why does the definition of the 3-partition problem contain the condition
$$\frac{B}{4}
Franz
- 23
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2
votes
1 answer
How to find partition set of a Partition Problem using its decision problem
I understand Partition Problem is NP-complete.
Given we have a magic black box that can answer Yes or No for the partition problem. I was wondering how to come up with a polynomial time algorithm to find the actual set using this black box.
Thank…
formatjam
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1
vote
0 answers
Non-standard partition problem
I've been writing codes to solve a standard partition problem. I've investigated brute force, greedy, Karmarkar-Karp and complete Karmarkar-Karp algorithms.
Standard partition problem: divding a set into two subsets such that the difference between…
innisfree
- 145
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1
vote
0 answers
DISTINCT 3-PARTITION with all integers between $B/4$ and $B/2$
In the definition of 3-PARTITION of Garey&Johnson, the instance is a set of $3m$ integers such that the sum of all these integers is $mB$ and such that each integer is strictly between $B/4$ and $B/2$. This problem is strongly NP-hard.
The special…
user2370336
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1
vote
0 answers
Graph Partition Across Cluster - Minimize Largest Matrix Size
I am writing some code for modeling semi-biologically realistic neural networks, which is to be run/distributed across nodes in a computer cluster. I begin with a very large adjacency matrix (representing the neural connectivity), and I want to…
joebuild
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1
vote
1 answer
Partition partition with constraint of equal size
I see the problem here which is the well know partition problem but with constraint that the size of both sets must be equal.
I look at the answer and I don't understand that why Colin said add max(S)⋅length(S), and run the algorithm as normal would…
user196736
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0
votes
0 answers
Reduction from 3-Partition to a cutting problem
My problem is the following:
Input: a set of $m$ non-negative integers $\{b_1,...,b_m\}$ and a parameter $n$ with $n
user2370336
- 53
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0
votes
1 answer
A partition algorithm
I have encountered the following problem that I found very interesting to solve:
Given an array of positive integers $\{a_1, a_2, ..., a_n\}$ you are required
to partition the array into $3$ blocks/partitions such that the maximum
of sums of…
user21069
0
votes
1 answer
Multiprocessor Scheduling is NP-Complete
Consider this version of MS where we have set $A$ of tasks, $l(a)$, length of each task in $A$ and $m$ number of processors and also a deadline $D$. The question is where we can partition A into m disjoint subsets, $A = A_1 \cup A_2 \cup \ldots…
HFA
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