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2
votes
0answers
61 views

An NP-complete variant of factoring and relation to factoring [closed]

After reading this post An NP-complete variant of factoring. I come up with a question. To summerize the post, we have the factoring problem (F) which ask for a number $p$ that is prime and divides ...
6
votes
1answer
235 views

Is every coNP-complete language P-isomorphic to an P-immune coNP-complete language? OR Is there a P-immune coNP-complete language?

A set is $\mathsf{P}$-immune iff it has no non-trivial $\mathsf{P}$ subset. Is every $\mathsf{coNP}$-complete language $\mathsf{P}$-isomorphic to an $\mathsf{P}$-immune $\mathsf{coNP}$-complete ...
4
votes
2answers
199 views

Partition graph into 2 or more claw-free subgraphs

Is it NP-hard to partition the vertex set of graph G into k subsets so that they induce k claw-free subgraphs of G?
1
vote
2answers
279 views

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 ...
14
votes
2answers
207 views

Poly time superset of NP complete language with infinitely many strings excluded from it

For any arbitrary NP complete language is there always a polytime superset the complement of which is also infinite? A trivial version which does not stipulate the superset to have infinite ...
7
votes
1answer
295 views

Conjecture: All FPT NP-complete languages are fixed-parameter-isomorphic

Berman–Hartmanis conjecture: all NP-complete languages look alike, in the sense that they can be related to each other by polynomial time isomorphisms[1]. I am interested in a more fine-grained ...
17
votes
1answer
476 views

“Almost easy” NP-complete problems

Let us say that a language $L$ is P-density-close if there is a polynomial time algorithm that correctly decides $L$ on almost all inputs. In other words, there is an $A\in$ P, such that $L\Delta ...
6
votes
1answer
345 views

Problems can be solved in quasi-polynomial time, but not in polynomial time

Recently, there is a breakthrough in TCS: László Babai claimed an astounding theorem, that the Graph Isomorphism problem can be solved in quasipolynomial time. He first showed this result in a talk ...
1
vote
0answers
71 views

Distributing bags of apples equally

Assume you have $N$ bags of apples that you want to equally distribute to $K$ people. Each bag contains $n_i$ apples and you are not allowed to open and divide the bags; you must distribute the bags ...
11
votes
1answer
198 views

Slowest many-one reduction?

When we want to prove that an $L\in \bf NP$ is $\bf NP$-complete, then the standard approach is to exhibit a polynomial time computable many-one reduction of a known $\bf NP$-complete problem to $L$. ...
21
votes
3answers
451 views

How much would a SAT oracle help speeding up polynomial time algorithms?

Access to a $SAT$ oracle would provide a major, super-polynomial speed-up for everything in ${\bf NP}-{\bf P}$ (assuming the set is not empty). It is less clear, however, how much would $\bf P$ ...
4
votes
1answer
82 views

NP-Complete Convergent Reductions?

A professor I knew in grad school told me about asking his students to reduce an NP-Complete problem to another, then back to the original, then back again and then watching with amusement as the ...
3
votes
0answers
43 views

Is this permutation-sum problem NP-complete? [duplicate]

A new, tighter tardiness bound has been found for global Earliest-Deadline-First scheduling of jobs on symmetric multiprocessors. But this bound seems to be particularly hard to compute. In ...
-3
votes
1answer
210 views

Consequences of polynomial time algorithm to variant of integer factorization

Given $N,U,V\in\Bbb N$ is there $n\in[U,V]\cap\Bbb N$ such that $n|N$ is $\mathsf{NP}$-complete modulo Cramer's conjecture on prime gaps is shown in An NP-complete variant of factoring. So supposing ...
12
votes
1answer
353 views

Which complexity class does this number theory problem belong to?

'Given $a,b,c\in\Bbb N$, is there $x,y\in\Bbb N$, $ax^2+by=c$' is $\mathsf{NP}$-complete. Which complexity class does 'Given $a,b,c\in\Bbb N$, is there $x,y\in\Bbb N$, $ax^2+by^2=c$' belong to?
5
votes
0answers
75 views

Question about a unary language construction

For any language $L$, let us define another language $Tally(L)$, as follows: $$Tally(L)=\{1^n\;|\;\exists x \;\mbox{with}\; x\in L \;\mbox{and}\; |x|=n\}$$ That is, $Tally(L)$ encodes whether there is ...
2
votes
0answers
80 views

Space time lower bound with $\mathsf{PSPACE}$ oracle

Does a single tape Turing machine with access to $\mathsf{PSPACE}$ oracle needs more than $\mathsf O(1)$ working tape memory and $\mathsf O(1)$ working time to solve $\mathsf{NP}$-complete problem? ...
-1
votes
1answer
104 views

Will a non-linear lower bound on some NP complete problem prove non-linear lower bound on 3SAT?

A problem $\Pi$ is $\mathsf{NP}$ complete if there is a polynomial time reduction from an $\mathsf{NP}$ complete problem $\Pi^\circ$ to $\Pi$ with polynomial blow up on number of variables and ...
0
votes
0answers
44 views

Complexity of variant polynomial factorization

Few years back a question on whether a variant of integer factorization was $\mathsf{NP}$ complete was asked, which according to state of mathematics today does not have a conclusive answer. Is ...
-3
votes
1answer
62 views

How to reduce LCS from Vertex-Cover [closed]

I am trying to understand the demostration of intractability of the LCS problem, as stated as a reduction from Vertex-Cover problem, and so far, i'm stuck with the demostration of the problem in this ...
7
votes
1answer
181 views

What do we know about checking real-stability of multivariate complex polynomials?

Given a polynomial $p : \mathbb{C}^n \rightarrow \mathbb{C}$ it is to be called "real-stable" if (1) all its coefficients are real and (2) if it has no roots such that all the coordinates of the root ...
1
vote
0answers
160 views

Finding an equivalent NP-complete instance for this game-theory problem

I apologize if this question is not a good fit for CSTheory. I'm a PhD student who has just started out and I'm working on a game-theory problem in one of my classes. Although my professor hasn't ...
0
votes
0answers
108 views

Is there a reduction from a 0-1 knapsack problem to the unbounded problem?

As we know, an unbounded knapsack problem could be described as: $\max \sum_{i=1}^nc_1x_i$ s.t. $\sum_{i=1}^na_ix_i\le b$ $x_i\ge0,x_i\in\mathbb Z,i=1,\cdots,n$ And for an 0-1 knapsack problem, we ...
-7
votes
1answer
217 views

Travelling sales man with Quantum Computers [closed]

I know that it takes billions of years to solve the travelling sales man when n = 25 (Number of cities). I am wondering how fast can a quantum computer solve the travelling sales man problem (for ...
2
votes
0answers
139 views

Looking for reference on NP-Completeness of proofs of length n

Given a deductive system $\Lambda$, and some well-formed-formula S, one can ask the question "Is there a proof S in $\Lambda$ of length n?" If n is presented in base-1 and if all the axioms of ...
0
votes
0answers
76 views

Bijection between NP-complete problems

If $A$ and $B$ are NP-complete problems, is there a bijective function $f$ (computable in polynomial time) such that $w\in A$ iff $f(w)\in B$?
2
votes
0answers
221 views

Subset sum solver. Worth continue working on this method? [closed]

I have been working in a subset sum problem solver for some time. The implementation is an exact/exhaustive search solver. The variable determining the asymptomatic growth rate is just $N$ (the ...
2
votes
2answers
196 views

Balls & Bins: A punishment and reward game

Consider a game where one has a set of bins $(b_1, b_2, ...)$, and each bin has an associated initial count of balls $(c_1, c_2, ...)$. The rules of the game are as follows: (1) Once a bin has a ...
4
votes
1answer
214 views

Is the problem NP-C or polynomially solvable?

I am considering a problem of the following: Given a set $X$ of integers and another integer B, are there two subsets of $X$, say $X_1$ and $X_2$, such that $X_1-X_2=B$ ? (Here, $X_i$ also denotes the ...
1
vote
0answers
90 views

Properties of “second-order” NP (complete) languages

Reading the question Natural NP-Complete Problems with Large Witnesses, I was interested in this language: $L = \{ \varphi ~~:~~ \varphi \text{ is SAT formula with more than } |\varphi|^2 \text{ ...
2
votes
0answers
83 views

Which complexity information of Ising model is more important?

In 1982, Barahona proved that finding the ground state of an Ising model is NP-hard. Later, in 2000, Istrail proved that it is NP-complete. When I look up the citations of these two papers using ...
5
votes
1answer
289 views

Does the Cook-Levin theorem relativize?

My only motivation for asking this question is long-standing curiosity, but I am interested in seeing a proof (or disproof) that the Cook-Levin theorem relativizes. If you have a proof that the ...
0
votes
1answer
71 views

Flow networks: Push flow on either edges but not both!

I have a flow network with random capacities on edges, is there some way to add a constraint of the type (push flow on either one of these two edges but not on both)? I'm not sure if this is correct ...
6
votes
1answer
2k views

Magic constant to solve NP-complete problem in polynomial time

Let's suppose that $P\ne NP$. Is that possible to solve all the instances of size $n$ of an NP-complete problem in polynomial time using some "universal magic constant" $C_n$ that has a polynomial ...
2
votes
1answer
220 views

Easier and Harder instances of NP-complete problems?

Following previous questions here and here around $NP$-complete problems (and P vs NP). Are there "easier" or "harder" (sets of) instances of an $NP$-complete problem? If yes (which i assume), how a ...
0
votes
1answer
123 views

Any result connecting an NP-complete problem with slight super-polynomial time?

Helo everybody, is there any result or research that connects some $NP$-complete problem with only slightly super-polynomial (strongly sub-exponential) time? This would not necessarily ...
9
votes
0answers
137 views

Complexity question from mathematical music theory

Fix an positive integer $N$. A row means any linear ordering $R=(n_i)_{0\leq i <N}$ of the additive group ${\Bbb Z}/N{\Bbb Z}$. Call $R$ a (generalized) all-interval row if the elements of the ...
6
votes
2answers
378 views

Proof for ACYCLIC PARTITION being NP-complete

I'm new to this site, so please pardon me for any mistakes and please feel free to edit the question to help get better answers. I'm interested in reading any proof of ACYCLIC PARTITION (Garey and ...
17
votes
1answer
333 views

Natural candidate against the Isomorphism Conjecture?

The famous Isomorphism Conjecture of Berman and Hartmanis says that all $NP$-complete languages are polynomial time isomorphic (p-isomorphic) to each other. The key significance of the conjecture is ...
8
votes
1answer
264 views

Can a natural graph problem be universally hard?

Is there a natural $\mathsf{NP}$-complete graph problem, which remains $\mathsf{NP}$-complete even when it is restricted to any polynomial-time recognizable graph class? To avoid degenerated cases, ...
2
votes
1answer
401 views

Multiple subset sum where subsets have complementary cardinality

$\underline{\mathsf{EQUAL\mbox{ }k-COMPLEMENTARY\mbox{ }SUBSET\mbox{ }SUM(EkCSS)} }$Problem: Input: $a_1,\dots,a_n,b\in \mathbb Z$, with distinct $a_i$ and $k\in\Bbb Z^+$. Output: $k$ $\mbox{ ...
3
votes
0answers
97 views

Symmetry of optimal solutions to discrete optimization problems

Given a graph, say one wants to find the clique number, independence number, chromatic number, vertex cover number etc., one knows that a solution exists. However if the solution space has more than ...
4
votes
1answer
186 views

Are there any implementations for zero-knowledge proofs of NP-complete problems?

It's been known for a long time that any claim in NP has a zero-knowledge proof for it. Has anybody actually implemented a zero-knowledge proof system for a NP-complete language? Using a search ...
1
vote
0answers
325 views

Are there upper bounds on the worst case complexity of NP-complete problems?

I have proven some problem to be (weakly) NP-complete and try to find out some algorithm to solve it exactly. Except for some pseudo-polynomial stuff, I would be happy with an algorithm running in ...
6
votes
0answers
136 views

Generalization of SAT, where we replace OR with another symmetric function

Let $\sigma(y_1,\dots,y_k)$ denote some boolean symmetric function on $k$ boolean inputs, $\sigma:\{0,1\}^k\to\{0,1\}$. In $k$-SAT, an instance is a conjunction of clauses, where each clause is the ...
2
votes
1answer
230 views

Complexity of a linear algebra problem

Let matrix $M \in \{0,1\}^{r \times s}$ ($s>r$), let function $f:\Bbb Z^{} \rightarrow \pm1$ and let $\alpha \in \Bbb Z \cap (0,s)$ be given. Is it NP-complete to decide if $\exists u \in ...
-2
votes
2answers
517 views

Where are NP-complete problems if P=NP [closed]

Where are exactly NP-complete problems if P=NP? They will be definitely in P, but will they be P-complete?
2
votes
2answers
234 views

Finding the identity with permutation chains

I have the following problem: I'm given a list of size $K$ of random integer permutations of $[1..n]$, named $P_1$ to $P_K$, and an additional random permutation $Q$. How hard is to find a sequence ...
6
votes
1answer
135 views

What's complexity of this set problem which looks like “Linear Programming”?

I came up with a problem below, which looks like a linear programming problem: Given $n$ sets $S_{1}, S_{2},..., S_{n}$, with constraints of : $$ \forall i=1, 2, 3,...,n\space\space \left | ...
2
votes
3answers
721 views

How can you prove that a problem is not solvable in a certain time complexity?

One of the most interesting questions in computer science is of course whether $P = NP$ or $P \neq NP$. If one wants to prove that $P \neq NP$ one can try to prove that an NPC problem is not solvable ...