# Questions tagged [np-complete]

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### What would be the consequences if all _infinite_ NP-complete languages are p-isomorphic?

The famous Isomorphism Conjecture of Berman and Hartmanis says that all $NP$-complete languages are polynomial time isomorphic ($p$-isomorphic) to each other. It has been an early attempt (published ...
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### Dance Partner Problem NP-completeness [closed]

I really can't think of a concise way to phrase this problem, which makes it hard to search for, so forgive me if this is a duplicate question. I've come across a problem and I would like to know if ...
141 views

### Could you explain to me the reduction? [closed]

I am looking at the following solved exercise: I haven't really understood at the reduction the part that we construct for each number $a_i$ a package of measurement $(\frac{4}{A}a_i, 5,3)$. Why do ...
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### Is sparse embedding of a NP-complete problem in a polynomial problem NP-complete?

Consider the following problem P: Input is a finite graph G. If the number of vertices in G is 2^2^i for some integer i, then output a minimum vertex cover of G; otherwise output empty set. Can I say ...
260 views

### NP-hardness on Cayley graphs

What is known about complexity of NP-hard problems on Cayley graphs? Suppose that the graph is given explicitly as the multiplication table of the group and the list of generators. So the input ...
307 views

### Problem of graph bi-partition (related to graph isomorphism)

I am considering the following problem: Input: 3 graphs $G=(V,E)$, $H_1$, $H_2$ Question: Is there some $V_1\subseteq V$ such that $G[V_1]$ (the subgraph induced by $V_1$) is isomorphic to $H_1$, ...
93 views

### About representability of optimization versions of NP-complete questions as polynomial optimization over the hypercube

Naively, in my very limited awareness, it feels that the Max-CUT is a very "special" NP-Hard problem because for a graph with edge-set $E$, it can be written as the question of trying to maximize a $n$...
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### 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 $f(w)\in B$?
391 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 ...
243 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 ...
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 ...