# Questions tagged [time-complexity]

Time complexity of decision problems or relations among time-bounded complexity classes. (Use the [analysis-of-algorithms] tag for the time taken by particular algorithms.)

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### Is the following special case of multiway number partitioning NP-hard?

The following problem is a decision problem of multiway number partitioning (wikipedia) (Note that $k$ is also a part of an input in the following problem, while $k$ is a fixed number in wikipedia ...
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### Graph classes where giving a q-clique edge cover makes testing for q-colouring easy

A $q$-clique of a graph is a complete subgraph on $q$ vertices. A $q$-clique edge cover of $G$ is a set of subgraphs of $G$ such that each subgraph is a $q$-clique and each edge of G is contained in ...
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1 vote
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### Additive error approximations of GapP functions

Consider a GapP function $g(x)$ for $x \in \{0, 1\}^{*}$. Consider an approximation $\tilde g(x)$ such that $$\left|g(x) - \tilde g(x)\right| \leq \epsilon.$$ Consider a ...
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### Fastest approximate triangle counting algorithms in dense graphs

One may compute the number of triangles in a graph by matrix multiplication in time $O(n^\omega)$. There is also a very simple algorithm that runs in time $O(n^3/(\epsilon^2 T))$ (where $T$ is the ...
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1 vote
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### Amortized time and worst case (non-amortized) separation

Assume a reasonable computation model (thinking about pointer machine or RAM model), is there a problem where there is a clear separation between amortized and worst case complexity? Say, if ...
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### Is the exponent in the rectangular matrix multiplication convex?

My question is regarding the paper "Improved Rectangular Matrix Multiplication using Powers of the Coppersmith-Winograd Tensor". In the paper, the authors show an algorithm for multiplying a ...
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### Looking for information about a problem of a least subset of vectors modulo 2 summing to another vector [duplicate]

I'm quite interested in the following algorithmic problem, on which I can't find any information. Phrased as a decision problem: Given a set of vectors $V$ in $\text{GF}(2)^n$, a vector $\mathbf u$ ...
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### Is the Triangle Finding decision problem in $coNTIME(\tilde{O}(n^2))$?

The Triangle Finding decision problem asks whether there exists a triangle in a graph $G$ containing $n$ vertices. A triangle is a triple of vertices $(a, b, c)$ such that $a$ is adjacent to $b$, $b$ ...
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1 vote
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### Complexity of solving systems of linear equations with hash preimages

Introduction: I'm researching a decision problem that I thought was in NP because there are certificates for its instances that have a polynomial number of elements. However, I realized that there are ...
1 vote
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### Sorting using comparisons that are not simple mappings of simple comparisons

The Python language has a sort(x) function that sorts a list based on the intrinsic comparison operator associated with the type of the elements of its input list x. One can also provide a cmp ...
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### Are there problems in $DTIME(n^k) - DTIME(n^{k-1})$ that are not hard for $DTIME(n^{k-1})$ under nearly linear time reductions?
Background It can be challenging to find computational problems that are solvable in $DTIME(n^k) - DTIME(n^{k-1})$ where $k \geq 2$. Although some natural problems are known to exist, many of them ...