# Questions tagged [subset-sum]

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### Solution to Subset Sum Problem (in some sense) using Gaussian elimination modulo 2

Consider a set of natural numbers $S \in \mathbb{N}^n$ for some $n \in \mathbb{N}$. Assume that each number $s_i = S^T\cdot e_i$ meets $s_i \leq 2^m$ i.e. is written on at most $m$ number of digits, ...
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### strong NP-completeness of multi-dimensional Equal-Subset-Sum

I want to show that the multi-dimensional Equal-Subset-Sum is NP-complete in the strong sense: Given a set of $d$-dimensional vectors of non-negative integers, does there exist two distinct nonempty ...
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### Unbounded Knapsack: Does Increasing capacity increase optimal value?

Our decision problem is as follows: given weights $\mathbf{w}$, values $\mathbf{v}$, and capacities $C_1$ and $C_2$, where $C_1 < C_2$, does the optimal value of unbounded knapsack with the above ...
256 views

### How many numbers are needed such that the possible subset sums cover $\{1, \frac{1}{2}, \frac{1}{3},\dots, \frac{1}{2^m}\}$?

For a multiset $N$ of positive numbers, the set of possible subset sums is $f(N)=\{s\in \mathbb{R}: \exists S\in 2^N, s=\sum_{a\in S} a\}$. We say $N$ generates $T$ if $T\subseteq f(N)$. For example, ...
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### Feature selection problem under promise

Are there well used examples of feature selection problem where the problem is defined under certain promise? Let's say the task is to select the minimum number of features such that the mutual ...
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1 vote
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### Understanding David Pisinger's balanced algorithm for the subset-sum problem with bounded weights

I'm trying to understand David Pisinger's balanced algorithm for the subset-sum problem with bounded weights, which can be found on page 5 of his paper Linear Time Algorithms for Knapsack Problems ...
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### Bin Covering problem with variable bin sizes

I have a decision problem that I cannot seem to map to a standard studied problem, although it seems similar to a few. I am wondering if anyone has come across this problem before, or if someone can ...
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### Partition of a set of integers into subsets where the max. of the subset-sums is minimum

Let $S$ be a set of $n$ positive integers, and $p$ be a partition of $S$ into $m$ mutually disjoint subsets, such that no subset contains more than $k$ elements. Let $\mathcal{P}$ denote the set of ...
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### Is the following equitable factoring problem $NP$-hard or in $P$?

Consider the following factoring problem: Given an integer $r$ and another integer $N$ along with all of its $n$ number of prime factors and their corresponding multiplicities $\{p_i,e_i\}_{i=1}^n$, ...
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### Can this relaxed subset-sum problem be solved with a smaller dynamic program? [closed]

Cross-post from CS.SE In the subset sum problem, the input is a list of positive integers $x_1,\ldots,x_n$ and an integer $T$, and the goal is to decide whether there is a subset of sum exactly $T$. ...
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1 vote
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### Is this a variant of the set cover problem?

$\textbf{Decision Problem:}$ Given a finite set of elements $E$ and a collection $C$ of non empty sets, $C=\{E_1,...,E_n\}$, such that each $E_i$ covers at least one element of $E$. The goal is to ...
1 vote
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### Two valued variant of subset sum problem

I'm interested in the complexity of the following problem: Given a multiset $S$ containing only two positive integers $a$ and $b$, find a $k$-partition of $S$ that maximizes the sum of part with ...
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### Strongly NP-complete variants of subset sum or partition problem

Some problems have variants that appear to be harder. For instance, Graph Automorphism (GA) problem has quasi-polynomial time algorithm ( by Babai's GI result). However, the fixed-point free GA ...
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### Interesting real life problem similar to subsetsum /bin packing problem

I have a real life scenario, where I need to solve a construction related problem somewhat similar to bin packing problem.The situation is as follows : I have large number of cable reels/drums (let's ...
1 vote
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### At what parameters is following $NP$-hard?

Problem Instances at given $\alpha>0$. $(1)$ Given $a_1,\dots,a_{n^\alpha}\in\Bbb Z$ with $|a_i|\in(2^{n-1},2^n-1)$ is there a subset of that sums to $0$? $(2)$ Given $a_1,\dots,a_{n}\in\Bbb Z$ ...
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### NP completeness of linear $0-1$ assignment problem

Supposing we have a linear equation in $n^2$ variables with integer (negatives allowed) coefficients of at most $m$ bits each. Partition $\Pi_1$ the variables into $n$ disjoint sets of $n$ variables ...
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### "Any" Subset Sum. Is it hard?

Here is a variant of the classic partition problem: Given a list of integers can it be partitioned into $S_1$, $S_2$, and $S_3$, with $S_1$ and $S_2$ nonempty, so the sum of elements in $S_1$ equals ...
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### Does this problem related to subset sum have a name?

I'm looking for research into this problem -- computational complexity, solution algorithms, approximation algorithms, etc. If it has a canonical name, that would help me look into prior research. ...
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### Another variant of PARTITION

I've got a reduction of the following partition problem to a certain scheduling problem: Input: A list $a_1\leqslant\cdots\leqslant a_n$ of positive integers in non-decreasing order. Question: Does ...
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### Faster pseudo-polynomial time algorithm for subset-sum?

Let $S(X) = \{\sum_{i\in Y} i | Y\subset X \}$, the set of subset sums of $X$. $S_n(X) = S(X)\cap \{1,\ldots,n\}$. Consider the following variant of subset sum. ALL-SUBSET-SUMS INPUT: positive ...
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### Is DAG subset sum approximable?

We are given a directed acyclic graph $G=(V,E)$ with a number associated with each vertex ($g:V\to \mathbb{N}$), and a target number $T\in \mathbb{N}$. The DAG subset sum problem (might exist under a ...
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### Subset Sum bounds

Are there any bounds for the subset problem with respect to the number of the terms involved in the sum and the range of the possible values?For example looking for some 2 terms whose sum equals 3 you ...
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### Combining subset sum and subset product problems

The subset sum problem and subset product problem are NP-complete. Is the following problem polynomial-time solvable: given a set of positive integers, find a subset whose sum is $S$ and whose product ...
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### Interesting SUBSET-SUM problems

I know the following variants of SUBSETSUM problems: $\mathtt{UNARY\mbox{-}SUBSETSUM} \in \mathsf{L}$ (Elberfeld at. al., 2010), NP-complete $\mathtt{SUBSETSUM}$, and NEXP-complete \$ \mathtt{...
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