# Questions tagged [np-hardness]

Questions related to NP-hardness and NP-completeness.

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### Hardness of maximizing difference of functions [closed]

Suppose that the problem of maximizing a real function $f$ over a certain domain $D$ is NP-HARD but maximizing $f-g$, with $g$ being another function over $D$, is easy (in PTIME). What can be said ...
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### 3-SAT mixed with 2-SAT formulas

Context: Refering to the question: Complexity of the $(3,2)_s$ SAT problem? and since the paper by Porshen and Speckenmayer : Satisfiability of mixed Horn formulas, we know that even when $F_3$ is ...
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### Is finding the optimal ordering of predicates NP?

Assume we want to find the elements from a set of elements $\mathscr{E}$ for which all predicates from a set of $n$ predicates $\mathscr{P}$ evaluate to true. In programming terms, we want to compute <...
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### Why is the reduction from 3-SAT to 3-dimensional Matching Parsimonious?

In this talk at the Simons Institute, Holger Dell notes that there is a parsimonious reduction from 3-SAT to the 3-dimensional Matching (3-DM) problem. In other words, there is a reduction between ...
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### Is the knapsack variant with small profit and unlimited repetition of items NP-hard?

Consider the unbounded Knapsack problem where we are given $n$ items of integral weights $w_i$, integral profits $p_i$, and a max weight $W$. The goal is to maximize the total profit $\sum_i x_ip_i$ ...
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### Problems Between P and NPC

Factoring and graph isomorphism are problems in NP that are not known to be in P nor to be NP-Complete. What are some other (sufficiently different) natural problems that share this property? ...
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### Complexity of acyclicity of a “nondeterministic” graph

By "nondeterministic" I mean the graph is a collection of sets of "candidate" edges sharing a single destination: $E \subseteq 2^V \times V$. The problem is whether it is possible ...
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### What would be the consequences of factoring being NP-complete?

Are there any references covering this?
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### Recent progress on the next-to-shortest-path problem for directed graphs?

In the paper "Computing strictly-second shortest paths" (1997), Lalgudi and Papaefthymiou consider the following problem: Let $G$ be a directed graph with edge-weighting $w$. Let $u,v$ be vertices in ...
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### Minimizing the gaps with incremental capacity

There are a single job, a machine and a set of $n$ slots. The machine has a capacity that increments by $\zeta(t)$ every slot $t=1,2,\ldots,n$. Initially (before the first slot), the machine has 0 ...
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### On the paper “Quantum Computing Hamiltonian cycles”

The paper Quantum Computing Hamiltonian cycles claims: An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve ...
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### What are good approximation algorithms for the subset sum problem so far?

By "good", I mean either the algorithm provides a relatively tight bound or it has a relatively fast running time. Any reference is welcome.
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### Complexity of a scheduling problem with a fixed left bound of jobs

Consider the following scheduling problem. We have a finite set of jobs $\mathcal{J}= \{j_1, j_2, ..., j_n\}$ to do. Every job $j_i$ has its own value $c_i$ (the amount of money we are paid for ...
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### Complexity of constructing minimum depth decision trees

I am interested in the computational complexity of Problem 1: Given a finite, non-empty set $J$, given $A, B \subseteq \{0,1\}^J$ such that $A \cap B = \emptyset$, and given $n \in \mathbb{N}$, does ...