Questions tagged [np-complete]

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Is orthogonal polygon with crossings count NP-complete?

The are several NP-complete problems related to the construction of orthogonal polygons. Rapport showed that it is NP-complete to to decide the existence of orthogonal simple polygon that passes ...
-1 votes
1 answer
126 views

Cook's theorem and universal machine

From Papadimitriou and Yannakakis, "A Note on Succinct Representations of Graphs" second parragraph of the proof of the main result. Cook (1971) presented in his classical paper a ...
6 votes
0 answers
133 views

Computing Sequences with Addition Chains In pseudopolynomial time?

Computing Sequence $a_1, \ldots, a_n$ with addition chains (CSAC) is the problem of finding the shortest sequence $b_1, \ldots, b_m$ with the following properties: $b_1=1$. Every $b_i$ with $i>1$ ...
6 votes
1 answer
223 views

Finding a minimal addition chain for a given number

An addition chain for computing a positive integer $n$ is a sequence of natural numbers starting with $1$ and ending with $n$, such that each number in the sequence is the sum of two previous numbers. ...
1 vote
1 answer
81 views

Exact Cover by 3-Sets variation: Partition Into Exact Covers by 3-Sets

In the Exact Cover by 3-Sets problem, we are given a set $X = \{x_1, x_2,\ldots, x_{3n}\}$ and a family of subsets $F = \{\{x_{i_1}, x_{i_2}, x_{i_3}\}\}$ of 3-element subsets of $X$. The question is ...
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1 vote
0 answers
127 views

Can NP-complete language be in $mP/poly$?

Can NP-complete language be in monotone $P/poly$?
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1 answer
84 views

Is "choosability of subsets" NP-hard?

Let $n\in\mathbb{N}$ be a positive integer, and let ${\cal A}$ be a collection of subsets of $n=\{0,\ldots,n-1\}$. We say ${\cal A}$ has the choosability property if there is $R\subseteq n$ such that $...
8 votes
0 answers
119 views

Does NP Completeness always fall on one side or the other of an intermediate computation?

Let $L$ be an NP complete language. My loose intuition for completeness suggests that, at any point in a computation tableau for $L$, either the computation has "already done an NP complete ...
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64 views

Short UNSAT Certificates for X3SAT

Exactly 1 in 3 SAT ($X3SAT$) is a variation of the Boolean Satisfiability problem. Given an instance of clauses where each clause has three literals, is there a set of literals such that each clause ...
0 votes
0 answers
48 views

Relativized Version of NP^A-complete

I was reading this post about whether Cook-Levin relativizes and at the bottom of the answer, they include a quote from Computational Complexity by C. Papadimitriou (this is a longer version of the ...
3 votes
0 answers
235 views

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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2 votes
1 answer
147 views

Is the weighted sum of subset prefix product problem NP-hard?

I have this strange problem where we have a set of positive numbers $M$, a fixed number $n$, and a function $f: M \rightarrow R^+$ mapping each number in M to another positive number. We want to know ...
5 votes
1 answer
277 views

Hardness assumption: an NP-complete problem whose ratio of hard instances do not tend to zero?

I am wondering about the following property $\text{(P)}$ of an $NP$-complete language $L$ $\begin{align}\exists M\text{ a polytime machine}\lim_{n\to\infty}P(\text{M solves a random instance of size $...
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1 vote
0 answers
55 views

Partition of multisets of polynomials

Problem: Given a multiset S of irreducible polynomials in Z[x], say YES if S can be partitioned into two nonempty multisets A and B such that both the product of all the elements of A and the product ...
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1 vote
1 answer
185 views

How to show that Color Tiles is NP-Complete

Color Tiles is a puzzle game where color tiles are laid out in a rectangular grid. A tile is visible to an empty grid cells if there is a clear line-of-sight in one of the 4 cardinal directions (You ...
0 votes
0 answers
37 views

Bounded-Frequency Minimum Set Cover Problem

Consider the special case of the minimum set cover problem where each element of the universe occurs in at most 3 sets. Can this problem be solved in polynomial time? Is there a nontrivial upper ...
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7 votes
1 answer
299 views

Cook inspiration for NP completeness

An academic descendant of Cook just lectured on NP completeness. He said that the idea came from a well-known theorem in first-order logic that talks about completeness of satisfiability for ...
0 votes
1 answer
191 views

Lexicographic Boolean satisfiability

Maximal Satisfying Assignment (Lexicographic Boolean satisfiability / LexMaxSAT), the problem of finding the lexicographically maximum x_1, . . . , x_n ∈ {0, 1}^n that satisfies Boolean formula φ, or ...
14 votes
0 answers
300 views

Is this problem on unambiguous finite automata NP-complete?

An unambiguous finite automaton (UFA) is a nondeterministic finite automaton (NFA) such that each word has at most one accepting path. In this post, for $n\in \mathbb{N}$, what I call an $n$-UFA (resp....
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5 votes
1 answer
498 views

Unary language examples between L and NP

I am looking for some examples of unary languages lay between $L$ and $NP$, i.e., $ L \subseteq NL \subseteq P = AL \subseteq NP $. What I found after some search(e.g., Complexity zoo for unary ...
9 votes
0 answers
142 views

Is 4-Coloring restricted to graphs with crossing number 1 NP-complete?

Planar graphs are 4-colorable. Determining if a planar graph is 3-colorable is NP-Complete. A graph with a crossing number 1 (graph such that it can be drawn with $\le 1$ crossing) is 5-colorable. ...
1 vote
1 answer
89 views

Choosing one number from each set so that the sum of squares of each distinct number counts is minimized

Problem is as follows: We are given $K$ subsets of $\{1,2,...,n\}$. We need to pick one number from each of these subsets such that $\sum_{i=1}^n p_i^2$ is minimized where $p_i$ is the number of times ...
1 vote
2 answers
75 views

Disjoint subsets problem complexity

Is the decision problem below NP-complete? Given sets $S_1, ... , S_n$, as well as bounds $b_1, ... , b_n$, is it possible to pick pairwise disjoint subsets $U_1, ... , U_n$ such that $U_i \subset ...
-4 votes
1 answer
31 views

Polynomial-time reducibility of Primality and 3-SAT

Is 3-SAT $\leq_{p}$ Primality? And/or is Primality $\leq_{p}$ 3-SAT? I think the answer is no and yes, respectively, but I'm not sure. Any help would be appreciated. Thank you.
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1 vote
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40 views

Efficient algorithm for finding segregators in a directed acyclic graph

Given a directed acyclic graph $G=(V,E)$, we define a $(\alpha,\beta)$-segregator of $G$ to be a subset $S$ of $V$ of size $\alpha$ such that no vertex in $G\setminus S$ has more than $\beta$ ...
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2 votes
1 answer
120 views

NP-completeness: sum of "some" paths in a spanning tree

I suspect this problem is NP-complete but I couldn't prove it, if anyone can help I'll be very grateful: Instance: undirected, unweighted, connected graph $G=(V,E)$, positive integer $K \in \mathbb{Z}...
3 votes
2 answers
521 views

Is the maximum independent set in cubic planar graphs NP-complete?

In their famous book, Garey and Johnson, write a comment that the maximum independent set problem, in cubic planar graphs is NP-complete(page 194 of the book). They say this is by a transformation ...
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8 votes
7 answers
1k views

NP-complete decision problems on deterministic automata

Do you know any NP-complete decision problems on deterministic automata? Most NP-complete problems that come to my mind are either (see, or here) graph theoretical, or involve some string rewriting or ...
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1 vote
0 answers
47 views

Minimum rank graph cut

Consider the following problem: Input: A graph $G=(V,E)$ and a matroid $M$ on $E$, given by an independence oracle. Task: Find a cut $C\subseteq E$ in the graph, such that the rank of $C$ in the ...
0 votes
0 answers
163 views

Complexity of multi-objective optimization problems

How can we define and prove the worst-case complexity of multi-objective optimization problems (MOOP)? It is easy to see that, if one of the objectives is an NP-Hard optimization problem, then the ...
2 votes
1 answer
67 views

Maximum subgraph problem with unknown complexity

Let $Q$ be a polynomial time decidable graph property. In a graph let us call a subgraph $S$ a $Q$-subgraph, if $S$ has the property $Q$. Consider the following optimization problem: Maximum $Q$-...
5 votes
0 answers
106 views

Reconstructing a colored grid with vertical and horizontal shifts

Consider the following simple problem (puzzle): given a $N \times N$ $c$-colored grid $G$ a $N \times N$ $c$-colored target grid $G_T$ a number $m$ represented in unary Can we transform $G$ into $...
6 votes
1 answer
377 views

Complexity of finding the largest induced subgraph with all even degrees

What is the complexity of the following problem? Instance: Simple, undirected graph $G$, and a positive integer $k$. Question: Does $G$ have an induced subgraph on at least $k$ vertices, such that ...
10 votes
1 answer
751 views

Relationship between two graph optimization problems

Let $Q$ be a polynomial time computable graph property of simple, undirected graphs. Consider the following two optimization problems on any input graph: P1. Find a largest induced subgraph of the ...
-4 votes
1 answer
125 views

Example of decidable NP-hard problem that is not NP-complete [closed]

I am looking for an example of a decision problem which fulfills the following conditions: 1. It is decidable 2. It is NP-hard 3. It is not NP-complete All my search attempts yielded examples that ...
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1 vote
1 answer
1k views

What languages can be reduced to a NP-complete problem in polynomial time

NP-complete: Language is NP-complete, when it is in NP and every problem in NP is reducible to it in polynomial time. But what languages are reducible to a NP-complete problem (for example SAT) in ...
4 votes
0 answers
75 views

Short $\exists$SO sentences over strings that define an NP-complete problem

[Q1] I'm wondering if there are some "official" SHORT existential second order sentences with ONE binary relation, over strings (over a small alphabet) that define an NP-complete set. (Something ...
10 votes
2 answers
357 views

"Relatives" of the shortest path problem

Consider a connected undirected graph with non-negative edge weights, and two distinguished vertices $s,t$. Below are some path problems that are all of the following form: find an $s-t$ path, such ...
5 votes
0 answers
63 views

Hardness result or reference for optimal Gaussian elimination process

I'm wondering if the following problem is NP-Complete or has any hardness result. References on related problem are also welcome. Input: integers $n\geq1,k\geq0$ and an invertible matrix $M\in\mathbb ...
2 votes
0 answers
72 views

Hardness result or reference for a set partition problem

I'm wondering if the following problem is (or has been proven to be) NP-Complete. Input: integer $n\ge0$, set $S_1,S_2,\ldots,S_{2n}$, set $T_1,T_2,\ldots,T_n$. Accept iff: there exists $\{a_i,...
5 votes
1 answer
113 views

$NP$ completeness of Hamiltonicity of cubic polyhedral plane graphs with bounded face degree?

Let $\mathscr{C}_d$ be the class of cubic 3-connected simple plane graphs, with face degree bounded by $d$. Is there any $d$ such that Hamiltonian cycle is $NP$ complete on $\mathscr{C}_d$? If so, ...
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11 votes
1 answer
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Natural candidates for NP-E and E-NP

It has been known since the early 70's that ${\bf NP}$ and ${\bf E}=DTIME(2^{O(n)})$ are not equal (because ${\bf E}$ is not closed under polynomial-time many-one reductions, in contrast to ${\bf NP}$...
0 votes
2 answers
243 views

NP-hard problems on the class of caterpillars

My question is whether there exist an NP-hard problem that has only a caterpillar as input. By saying only caterpillar as input, I wanted to emphasize that no function (eg: weights on vertices or ...
3 votes
0 answers
255 views

new subset sum approach results

I have been working on a new approach for a subset sum exact solver, and the current state provides an algorithm operating on $O{n/2 \choose n/4}$, demonstrating as well the hardest target value is ...
1 vote
1 answer
264 views

Does BQP contain any NP-Complete problem?

From the Wikipedia documentation, "the suspected relationship of BQP to other problem spaces" diagram suggests no intersection between NP-complete problems and BQP. Has this been demonstrated or not?
0 votes
1 answer
178 views

Subset Sum Problem and hard looking instances that are not really hard

I have been working in a subset sum solver (some new approach) and while working on the time complexity analysis I found what I describe below. Maybe this could explain why some "hard looking" ...
2 votes
1 answer
170 views

Is balanced Hamiltonian cycle NP complete on maximal plane graphs?

I know that the Hamiltonian cycle is NP complete on the class of maximal plane graphs. If we instead ask about balanced Hamiltonian cycles (i.e. same number of faces on both sides) on maximal plane ...
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0 votes
1 answer
283 views

A dominate vector subset sum problem

Let $k$ be some constants (e.g. one can take $k=2$ for simplexity), for any $u,v\in \mathbb{R}$, we say $u$ dominate $v$ if $\forall 1\le i\le k,~ u[i]\ge v[i]$, write it as $u\succ v$. Consider the ...
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4 votes
1 answer
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Complexity of finding Exact Size Cut-Sets in Bipartite Graphs

I am interested in the problem of deciding if a cut-set of a given size $k$ (i.e. the number of edges crossing the partitions is $k$) exists in a given bipartite graph (both the graph and $k$ are part ...
9 votes
2 answers
494 views

NP-Complete Static Square Puzzles

In order to empirically test some CSP algorithms, I would like to compile a list of NP-Complete static board games. By static, I mean that a solution of the puzzle is simply an assignment of values to ...