# Questions tagged [approximation-algorithms]

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### Approximating a monotone submodular function using a concrete coverage function

Is it possible to approximate a monotone submodular function using a concrete coverage function, i.e. Given a ground set $U$ and a monotone submodular function, $f:2^U\to \mathbb{R}$, the goal is to ...
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### Monotone supermodular function minimization under partition matroid constraints

Is there a known approximation algorithm for the problem of minimizing a monotone (non increasing) supermodular function under partition matroid constraints ?
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### Learning hidden variable distribution

Consider a set of $k$ continuous variables. Each variable $x_k$ is associated with a hidden distribution from which its value is sampled independently of other variables. I am given a set of ...
124 views

### Stacks serving interval storage requests

An interval storage request is represented by a tuple $(s,t,v)$ satisfying $s<t$, meaning that the value $v$ needs to be stored from time $s$ to time $t$. A stack serves the request $(s,t,v)$ in ...
96 views

### Unbalanced connected partition

Let $G = (V, E)$ be a connected graph with (possibly negative) vertex weights $w(v)\in\mathbb{Z}$. We want to partition the vertices into two parts such that the induced graphs $G'$ and $G''$ are ...
594 views

### Proof assistant usage in complexity theory research?

Considering the topics covered at a conference like STOC, are any algorithm or complexity researchers actively using COQ or Isabelle? If so, how are they using it in their research? I assume most ...
201 views

### Geometric max cover

Consider $n$ points and a distance function $d$ that satisfies the triangle inequality. We are also given a number $r$. Each point $p$ defines a set $B_p$ (or a ball) that covers all other points ...
624 views

### Common terminology used for lower/upper bounds

Suppose you have developed an upper bound on the number of vertices of a particular graph. This bound is the best possible bound that can be found for any given instance. What do you call such a bound?...
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### Truthful posted-price mechanism with optimal efficiency (social welfare)

I am interested in mechanism design. In the paper On Profit-Maximizing Envy-free Pricing, SODA, 2005, the authors provided a truthful competitive posted-price mechanism with $4\log h$ guarantee of ...
143 views

### Maximize number of edges covered by an independent set of vertices

Smallest vertex cover which is also an independent set asks about finding an independent set that covers all edges. This problem is known as the independent vertex cover problem and is equivalent to ...
159 views

### Algorithms to approximate a Riemann integrable function by a piecewise constant function

We know that any general function that is Riemann integrable can be approximated to arbitrary precision by piecewise constant functions. So in this regard, I was looking for references on algorithms (...
267 views

### Finding smallest context free grammar that generates a set of sets

Are there any results known about the size of smallest context free grammar that generates a set of sets? That is, I am given an alphabet $\Sigma$ as well as a set $S \subseteq \mathbb{P}(\Sigma)$ ...
Given two matrices $X \in \mathbb{R}^{m \times k}$, $Y \in \mathbb{R}^{n \times k}$, maximum inner product search (MIPS) asks for the largest $l$ entries of $X Y^T$. Typically $k \ll m, n$ (many ...