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2
votes
0answers
74 views

Variant of set cover problem with symmetric difference instead of union? [duplicate]

I am wondering if this problem has been studied, and in particular if there is an algorithm for it. Consider a universe $\mathcal U$ and a set $A \subseteq U$, and a family of sets $\mathcal F ...
6
votes
1answer
110 views

A bounded-independence variant of the Berry-Esseen theorem

I came across a presentation by Ryan O'Donnell regarding invariance principles. After proving the Berry-Esseen theorem, there is a slide that discusses extensions of the theorem and one that is ...
4
votes
0answers
66 views

Random Sampling Threshold to Get a Connected Induced Subgraph

Working on network design this summer I have come across certain applications that have inspired me to ask the following question: Given an undirected connected graph $G=(V,E)$ what is the minimum ...
1
vote
0answers
67 views

“conservative approximate Set Cover”?

We are given a lattice graph $L$, embedded on the plane, and a certain "shape" (a connected, acyclic subgraph $S$ of $L$). The task is to approximately cover $L$ with translated, rotated and flipped ...
8
votes
2answers
151 views

Computed circuit complexity of decision problems

Has anyone explored what is the circuit complexity of classic decision problems such as Primes or Graph-Isomorphism for small input size $N$? While most people are interested in the how the scaling ...
12
votes
1answer
237 views

Gentle introduction to the algorithmic aspects of tree-depth

Treewidth and pathwidth are popular parameters, measuring the closeness of a graph to a tree or a path, respectively. Indeed, it seems treewidth is so popular it is featured in many papers, books, and ...
2
votes
3answers
111 views

Heuristic with worst-case exponential complexity

I have been working with some colleagues on a metaheuristic for an NP-Hard optimization problem. It is a genetic algorithm using a steady-state population replacement strategy (at each iteration a ...
4
votes
0answers
132 views

What is the application of combinatorial game theory

I find Combinatorial Game Theory very interesting as my primary interest is mathematics. My question is why do Computer Scientists (who tend to have a more practical approach) study it as well? Are ...
4
votes
1answer
147 views

Assignment problem with multiple workers for each job

I am wondering if there are any results on the following version of the assignment problem. We are given a set of jobs $J$ and a set of workers $W$, and for each job $j$ and worker $w$ we are given ...
-2
votes
0answers
28 views

References for family network studies [closed]

Is there any recent review/list of research articles/book on studies of family networks from the network science/theory point of view? I am studying network properties of family trees of a few ...
6
votes
1answer
89 views

Lexicographic perturbation for euclidean shortest path instances?

Assume we have an undirected graph $G=(V,E)$ and vertex locations $\pi: V \rightarrow \mathbb{R}^2$. I am looking for a procedure to perturb the vertex positions to obtain new positions $\pi'$ such ...
20
votes
1answer
466 views

Number of distinct differences of $\omega(\sqrt{n})$ integers chosen from $[n]$

I encountered the following result during my research. $$\lim\limits_{n\to \infty} \mathbb{E}\left[ \frac{\#\{|a_i-a_j|,1\le i,j\le m \}}{n} \right] = 1$$ where $m=\omega(\sqrt n)$ and ...
17
votes
1answer
312 views

“Embedding” a language in itself

Main/General Question Let $L$ be a language. Define the languages $L_i$ with $L_0 = L$ and $$L_i = \{xwy : xy \in L_{i-1}, w \in L\}$$ for $i \geq 1$. Consider $\hat{L} = \bigcup L_i$. So, we ...
7
votes
1answer
171 views

Embedding a graph in the euclidean space

Given a graph $G=(V,E)$, find a mapping $f\colon V \rightarrow \mathbb R^d$ such that for every edge $(u,v) \in E$ we have that $||f(u)-f(v)|| \leq r$; and for every $(u,v) \not \in E$, we have the ...
9
votes
4answers
443 views

Is there algorithmic mathematical analysis?

There are algorithmic graph theory/number theory/combinatorics/information theory/game theory. Is there algorithmic mathematical analysis? According to wiki, mathematical analysis includes the ...
5
votes
1answer
250 views

Sparser Bipartite graphs?

Maximal Planar Bipartite graphs are sparser than maximal planar graphs. For which other classes of graphs are maximal Bipartite members sparser than arbitrary maximal members. Let $\mathcal{C}$ be a ...
3
votes
2answers
166 views

Runtime of Tucker's algorithm for generating a Eulerian circuit

What is the time complexity of Tucker's algorithm for generating a Eulerian circuit? The Tucker's algorithm takes as input a connected graph whose vertices are all of even degree, constructs an ...
1
vote
0answers
94 views

Has there been work on formal Semantics for linear algebra?

Could I get some references on formal semantics for a calculus on linear algebra that helps you study matrix or tensor based programming languages? I am looking for anything that encompasses linear or ...
11
votes
0answers
90 views

Which monotone Boolean functions are representable as thresholds on sums?

I will introduce my problem with an example. Say you are designing an exam, which consists of a certain set of $n$ independent questions (that the candidates can get either right or wrong). You want ...
22
votes
2answers
1k views

Complexity zoo for unary languages

Of course, some complexity results may collapse for unary languages but I wonder if there is somewhere a survey summarizing the known results in this case: a kind of complexity zoo for unary ...
7
votes
1answer
118 views

Formalized priority argument

A priority argument, an important proof technique in recursion theory, was introduced by Friedberg and Muchnik, to solve Post's Problem, i.e., the existence of two r.e. sets that do not Turing reduce ...
1
vote
1answer
82 views

Reference for CTL* logic

I need a reference for CTL* logic (preferably easy to understand). I have gathered some disperse information regarding temporal and CTL logic but I need a more orderly coverage. A chapter of the ...
2
votes
1answer
59 views

List of papers on Runtime and Statistical Tradeoffs on Machine Learning

I was interested in the connection between (statistical) learning guarantees (or any statistical properties) and their relation to run time. For example, I was wondering, in what cases does having ...
10
votes
2answers
211 views

Name the graph class: Disjoint union of a clique and an independent set

Let $G$ be a graph which is the disjoint union of a clique and an independent set, i.e. $$G = K_{n_1} + \overline{K_{n_2}} = K_{n_1} + I_{n_2} .$$ The graph class of all such graphs is characterized ...
9
votes
6answers
600 views

Are there any topics in theoretical CS that are more about pure math?

I am a graduate student in theoretical computer science, and in particular, approximation algorithms. I find now that I am more interested in pure math (I can say this because I seem to have enjoyed ...
3
votes
1answer
217 views

Analogies between VNP and NP

Valiant introduced the class VNP with respect to "arithmetic circuits" over 35 years ago in a "rough" analogy to NP. Recently, there have been major advances in the area of arithmetic circuits eg as ...
7
votes
1answer
191 views

Information theory and convex optimization

I'm taking a graduate level course in information theory and I'm constantly struck by how much convex optimization there is in this subject. However, the proofs seem to shy away from using the full ...
3
votes
2answers
128 views

Question about an old result of Erdős and Simonovits

My question concerns the following result of Erdős and Simonovits. A graph $G$ is $d$-almost-regular if $d\delta(G)\geq \Delta(G)$. Theorem 1 of the above paper states that a large $n$-vertex ...
2
votes
1answer
60 views

Complexity for single-linkage clustering with max norm

Let $S\in\mathbb Z^d$ be a set of points, with some notion of distance $d(x,y)$ between two points $x,y\in S$. I am specifically interested in the max distance, that is $d(x,y)=\max_{1\le i\le d} ...
2
votes
1answer
201 views

Knapsack combining sum and product

I cannot find references concerning the complexity of the variant of the knapsack problem (decision version) where one of the two conditions must be a product instead of a sum (0 not allowed). A ...
1
vote
0answers
45 views

complexity of factoring multivariate polynomials over Fn

recently multivariate polynomial factoring has been related to Polynomial Identity Testing / PIT (by Kopparty, Saraf, Shpilka). where is the complexity of factoring multivariate polynomials over ...
4
votes
0answers
181 views

research papers for undergraduate students

The papers presented at conferences like SODA, FOCS are hard to understand for undergraduates. Also a lot of background knowledge is assumed for understanding such papers. Are there any ...
2
votes
0answers
70 views

Dynamical systems analysis of deep learning

I am interested in finding out references that apply dynamical systems analysis to develop the "theory" of deep learning, specifically (say) feedforward deep neural nets. The only paper I seem to have ...
1
vote
1answer
48 views

Far point queries in high dimensions

Given a set of points $X\subset R^d$ and a number $r\in R$, create a data structure for queries of the form: "given a point $q\in R^d$ return a point $x\in X$ with $\text{dist}(q,x)\ge r$". This is ...
11
votes
0answers
102 views

s-t connectivity on infinite planar graphs with finite description

I would like to know if the following problem is known and has been studied: Consider an infinite directed graph that can be built on the infinite lattice "tiling" a finite set of subgraphs, more ...
4
votes
1answer
219 views

Sample complexity of distinguishing two Gaussian distributions?

Below is a description of the problem: Suppose I have two $p$-dimensional Gaussian distributions with the same covariance matrix $\Sigma$ and means $\mu_1$, $\mu_0$. And I can get $n$ samples ...
2
votes
1answer
65 views

How to simulate sequential registers from causal ones?

Background: In distributed shared memory (DSM) model, the problem of register simulations/constructions is to simulate registers with certain characteristic out of registers with weaker features. For ...
0
votes
0answers
60 views

Recently Practical Problems for a Distributed system model

I've read the article of Grosu and Chronopoulos in 2005. For the load balancing problem and the model of distributed system in this article, I am seeking for recently practical problems and real ...
13
votes
2answers
730 views

Time complexity of counting triangles in planar graphs

Counting triangles in general graphs can be done trivially in $O(n^3)$ time and I think that doing much faster is hard (references welcome). What about planar graphs? The following straightforward ...
9
votes
2answers
179 views

Category theory and parsers — references wanted

Since I'm interested in parsers (mainly in parser expression grammars), I'm wondering if there's some work that gives a categorical treatment of parsing. Any reference on applications of category ...
3
votes
1answer
71 views

Results about computability power or limitations of shared read/write registers

I want to know more results about the computability power or limitations of shared $\texttt{read/write}$ registers/objects in distributed/concurrent computing theory. Two typical examples are: [1]. ...
3
votes
1answer
80 views

How well can an arbitrary (unknown) quantum state be imperfectly cloned?

How well can an arbitrary unknown (quantum) state $\rvert \psi \rangle = \alpha\rvert 0 \rangle + \beta \rvert 1 \rangle$, be imperfectly/approximately cloned? Given an unknown state ${\rvert \psi ...
12
votes
5answers
541 views

Additive combinatorics applications in algorithm design

I'm reading surveys by Trevisan and Lovett on applications of additive combinatoric in TCS. The majority of these applications fall under computational complexity, e.g., lower bounds. I wonder if ...
22
votes
2answers
560 views

Is the Cheeger constant $\mathsf{NP}$-hard?

I have read in uncountably many articles that determining the Cheeger constant of a graph is $\mathsf{NP}$-hard. It seems to be a folk theorem, but I have never found either a quote or a proof for ...
8
votes
2answers
276 views

The hardness of generating an instance of a problem that is harder than the complexity of the resulting problem

In the movie Inception Cobb asks a asks Ariadne to design a maze that takes twice as much time to design. This lends itself to a generalized problem where we have an situation where we are resource ...
2
votes
0answers
75 views

Techniques introduced to log-rank conjecture

What have been some of techniques (like discrepancy, arithmetic combinatorics) that have been introduced to shed light on Log-rank conjecture which roughly states that deterministic communication ...
2
votes
1answer
73 views

Finite state transducer with infinitary outputs or without emphasis on acceptance?

1) Is there a notion of (deterministic) finite state transducer (FST) that allows the possibility of producing an infinite stream of output symbols? In other words, one where the transduction ...
1
vote
0answers
78 views

Complexity of Approximating Vandermonde Determinant

Given an $n\times n$ Vandermonde integer matrix with structured integers (such as arithmetic or geometric progression). Is complexity of approximately computing Vandermonde determinant upto ...
5
votes
1answer
176 views

possible bridge between group growth theory and complexity theory?

RJ Lipton conjectures a link between group growth theory and complexity theory. Group growth theory has undergone rapid advance in the last decade and has many surface similarities/ parallels with ...
4
votes
1answer
161 views

Introductions to steganography from an information-theoretic standpoint

Can I get some introductory references for steganography from an information-theoretic standpoint? I recently listened to a talk on it, and the speaker said that he knew of no good introductions to ...