Questions tagged [complexity-theory]

Questions related to the (computational) complexity of solving problems

811 questions with no upvoted or accepted answers
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Is it NP-hard to fill up bins with minimum moves?

There are $n$ bins and $m$ type of balls. The $i$th bin has labels $a_{i,j}$ for $1\leq j\leq m$, it is the expected number of balls of type $j$. You start with $b_j$ balls of type $j$. Each ball of ...
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Approximate minimum-weighted tree decomposition on complete graphs

Say I have a weighted undirected complete graph $G = (V, E)$. Each edge $e = (u, v, w)$ is assigned with a positive weight $w$. I want to calculate the minimum-weighted $(d, h)$-tree-decomposition. By ...
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NP-hardness of a special traveling salesman problem

Consider we have $n$ vertices, $v_1,\ldots,v_n$. We have two positive values $(a_i,b_i)$ associated with each $v_i$. The edge weight $w(v_iv_j)=a_ia_j+b_ib_j$. Is it NP-hard to solve the traveling ...
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Problems with Θ(n³) complexity on TMs with lower bounds by communication complexity arguments

One of the most used simple examples of application of Communication Complexity is the $\Omega(n^2)$ lower bound for recognizing palindromes of length $2n$ on a single tape Turing machine. Is there a ...
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On the Turing Completeness of First Order Logic

It is well known that in Descriptive Complexity Theory FO is equivalent to AC0. However, this accepts a couple of a theory and a string <T,s> iff the ...
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Complexity of Set Optimization with Sum of Rational Functions Objective

I encountered the following optimization problem. Let $S = \lbrace 1, 2, \ldots, n \rbrace$ be a set of items. Each item $i \in S$ has a non-negative benefit $b_i \in \mathbb R^+$, non-negative ...
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Decomposition of graphs that uses centers

Do you know of any kind of decomposition of graphs that involves centers, especially in the context of parametrized complexity? If so, please provide some reference. If not, do you see any reason (...
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Complexity of still life extentions in Game of Life

The game of life is one of the most famous cellular automata in 2D. It has a variety of objects, some of them are moving like gliders, some have an oscillating behavior and others do not change at all,...
Find a permutation that maximize the minimum of $\frac{a_n}{a_{n-1}} + \frac{a_n}{a_{n+1}}$
Consider a sequence of $n$ positive real numbers $a_0,\ldots,a_{n-1}$. Let $S_n$ be the set of permutations on $\{0,\ldots,n-1\}$. We are interested to find  \max_{\pi\in S_n}\left( \min_{i=0}^{n-...