Questions tagged [reference-request]

Reference-request is used when the author needs to know about work related to the question.

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Weak simulation of Clifford circuits

Quantum circuits composed by Clifford gates can be simulated by classical computation in polynomial time. More precisely, this simulation should be a weak simulation, i.e. it is possible to sample the ...
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Name for words without squared symbols

Is there a common name in combinatorics for words that do not have square of size 1 ? That is words such that no symbols appears twice in a row or, more formally, words not in $\bigcup_{s\in\Sigma} \...
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Is there a term for 'no-turn-back walk' in graph theory?

Let $G$ be a finite undirected graph. A walk in $G$ is a finite sequence $<v_1,e_1,v_2,e_2,\dots,v_{k-1},e_{k-1},v_k>$ where $v_j$'s are vertices in $G$, $e_j$'s are edges in $G$, and $e_j=v_jv_{...
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Comparative communication complexity?

I was reading the book "Communication Complexity" by Kuschilevitz and Nisan and in Exercise 1.18 they introduce a variant of the normal vanilla 2-person deterministic communication ...
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1answer
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Reference for automatically deriving dynamic programming algorithms from recursive algorithms?

This is what I'm looking for. Take a recursive algorithm: def fib(n): if n == 0 or n == 1: return n else: return fib(n-1) + fib(n-2) and turn it into ...
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Summing over weighted paths optimally

Given an edge-weighted directed graph, how do you sum over all weighted paths between A and B while using the smallest number of multiplications? Is there a name for this problem? This comes up in ...
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Split a string of positive numbers into substrings with decreasing totals

Suppose we're given a string of $n$ positive numbers and asked to split it into the maximum number of substrings whose totals are decreasing. I have an $O(n)$ time DP algorithm, but is it already ...
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Using error-correcting codes in multi-player games

There is a connection between any two from error-correcting codes, interactive schemes, and PCP. For quantum works, I found papers such as JV15 & Ji15. And there are classical examples about 20 ...
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Cycle double covers of cubic graphs using only a few cycles

This is a reference request question. Let $G$ be an arbitrary cubic graph. Is the problem of finding a cycle double cover $D$ of $G$ with minimum number of cycles in $D$ studied in the literature? I ...
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Cycle decompositions of locally linear 4-regular graphs

(Preface) We consider only finite, simple, undirected graphs here. An orientation of a graph $G$ is obtained by assigning some direction to each edge of $G$. (Question starts) A graph is locally ...
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Bin packing with non-additive load functions

I am looking for information on the bin packing problem, where the load of each bin is not the sum of items in the bin, but some other monotone set function. For example, suppose each item $i$ has ...
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1answer
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What is known about (upper bounds on) the LP gap of the (symmetric) Travelling salesman in special instances?

What is known about the LP gap of (the natural Held-Karp relaxation of) the (symmetric) Travelling salesman in special instances? I'm only aware of one special case where the extreme points are all ...
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Is arrangement-type graph on cyclic $k$-permutations of $n$ already studied?

The arrangement graph $A_{n,k}$ is the graph whose vertices are $k$-permutations of an $n$-vertex set $X$ (say, $X=\mathbb{Z}_n$) and two $k$-permutations are adjacent if they differ in exactly one ...
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NP-hardness of Euclidean k-Median for k = 2

In the Euclidean $k$-median problem, we are given a set $C$ of clients in $\mathbb{R}^d$. The task is to open a set $F \subset \mathbb{R}^d$ of $k$ facilities such that the cost function $\Phi(F) = \...
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Are there any references for this theorem of Lercher?

Let $\Delta = \lambda x.(x)x$ and consider $\Omega = (\Delta)\Delta$. Then $\Omega$ is exactly the only $\lambda$-term of the form $(\lambda x.t)v$ such that $(\lambda x.t)v=t\{v\ /\ x\}$. Does ...
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Complexity of detecting general position in the plane?

What is the complexity of detecting whether a given set of points in the plane is in general position? This surely must have been studied, but a quick search turns up nothing. For concreteness, let'...
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Type theory and fixed points of datatypes

For the purposes of this question, say that a datatype is a type constructor with one type parameter (this is sometimes called a type operator). In Haskell, we can define a fixed point ...
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A counter example for the set mean objective

Let $\mathcal{P} = \{P_1, \cdots,P_n\}$ be a family of finite point sets in $\mathbb{R}^d$, each having at most $m$ points. Consider the following objective function \begin{align} cost(\mathcal{P},c) =...
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Complexity of optimal elimination for a planar tensor network

Edit Dec 15 it's not obvious this problem is tractable when further restricting to trees, see cs.SE question Suppose we need to sum out variables in a tensor network (a factor graph where each ...
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Construction of arbitrary functions with exponential-size $MODp \circ MODq$ circuits

It is mentioned in multiple papers [1], [2] that $MODp \circ MODq$ circuits for two distinct primes $p, q$ can compute arbitrary functions in exponential size. However, [1] provides no citation for ...
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Full names of C. K. Chow and C. N. Liu

Where can I find the full names of C. K. Chow and C. N. Liu, of the Chow-Liu tree fame? https://en.wikipedia.org/wiki/Chow%E2%80%93Liu_tree https://ieeexplore.ieee.org/document/1054142
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Reference request for linear algebra over GF(2)

I have been looking for materials on the linear algebra over $GF(2)$ but so far I haven't found any substantial textbooks or notes on this subject. In fact in one of the notes I found the introduction ...
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Expressiveness of pushdown automata whose stack height sequence is unambiguous

I consider pushdown automata on an alphabet $\Sigma$, which are intuitively finite automata with a stack. Formally, a pushdown automaton $A = (Q, q_0, F, \Gamma, \Delta)$ is a finite set $Q$ of states,...
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Are the non-lazy / non-weak semantics of the $\lambda$-calculus related to weak evaluation?

Vague question The most common semantics of the call-by-name $\lambda$-calculus (Hyland/Wadsworth’s observational equivalence $\approx_\text{HNF}$ and Morris’s observational equivalence $\approx_\text{...
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Is there a primal-dual algorithm for the Tree Augmentation Problem or the Cactus Augmentation Problem?

The TAP problem and the CacAP problem can be seen as covering problems for the minimum cuts of a graph. It seems like these problems would fall under the framework of network design problems (...
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1answer
202 views

Lower bound for the OR problem

Let us have booleans $x_1, \cdots, x_n$. Any algorithm that determines $\bigvee_1^n x_i$ with probability at least $2/3$ requires $\Omega(n)$ time. It is not too difficult to prove this, but the proof ...
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1answer
120 views

Regular Expressions that converts into unambiguous automata

Brüggemann-Klein and Wood (1992) proved that a certain kind of regular expressions, that they call “Deterministic Regular expressions”, when converted into automata using the Glushkov's Construction, ...
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Canonical tester for dense graphs: from tester to removal lemma?

A theorem of Goldreich and Trevisan [1] on property testing in the dense graph model states the following (docusing on the one-sided part): Suppose there exists a one-sided testing graph algorithm ...
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2answers
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Algebraic characterisation of star-free safety languages

It is known that star-free languages are definable by aperiodic syntactic monoids. But is there any algebraic characterisation of star-free safety $\omega$-languages? Edit: A language $L$ is safety if ...
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75 views

Large CLIQUE approximation

I am interested in algorithms to identify large cliques in graphs where the largest clique is a large fraction (definitely greater than half, perhaps as great as 4/5) of the total number of vertices. ...
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Exact FPT Algorithm for Continuous Euclidean $k$-Means

The continuous Euclidean $k$-means problem is defined as follows: Given a set $X$ of $n$ points in $d$ dimensional Euclidean space $\mathbb{R}^{d}$. Given a parameter $k>0$, find a partitioning $P$ ...
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2answers
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Status of certain problems in knot theory

I found it somewhat difficult to understand the status of certain problems from knot theory. Is it correct to say that it's been neither proved nor disproved that any of the following problems are NP-...
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1answer
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Diophantine equations with bounds on variables

Solving Diophantine equations is famously known to be undecidable. What about Diophantine equations to be solved over a finite domain? In particular, if I put an upper bound $k$ over the value of the ...
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EXPSPACE-complete problems involving numbers

This is a subset of this question. I'm looking for EXPSPACE-complete problems, for using in a reduction, which involve numbers in some ways, since my target problem involves numbers and linear ...
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75 views

Low-Treewidth Sorting Networks

It was previously asked if there exist Boolean circuits of treewidth $O(\log n)$ that compute the majority function $\text{MAJ}_n$ on $n$ inputs. While a construction using online algorithms and the ...
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1answer
93 views

Property testable in sublinear time in bounded degree graphs but not in general graphs

Is there some natural property that is testable in strongly sublinear time (i.e. $O(n^{1-\epsilon})$ for some $\epsilon > 0$) in bounded-degree graphs but not in general graphs? If not such ...
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1answer
210 views

Is this a novel technique for determining whether or not two rotated rectangles collide?

I was trying to determine whether or not two rectangles rotated around their centers were colliding and randomly thought to try the following algorithm: Rotate both rectangles by the negative rotation ...
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Input length and calculation time to simulate a quantum measurement

Let us consider $n$ quits $b_i$. Let us start from the state $|0,0,...,0>$ and apply a circuit $C$ composed by $m$ quantum gates, with $m$ polynomial in $n$. The final state is $C|0,0,...,0>$. ...
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1answer
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What is tightest known (VC-style) sample complexity bound for uniform convergence of empirical means?

The following result is adapted from Anthony and Bartlett, 1999 (Theorem 4.9). Theorem There exist positive constants $m_0 \le 400$, $c_1 \le 8$, $c_2 \le 41$, $c_3 \ge 1/576$ such that, if $(\Omega,\...
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1answer
109 views

Can I research in web technologies with an academic approach?

I'm an undergraduate computer engineering student. I know that I like to become a researcher in my major in the future. I also work as a junior web developer at a small start-up, and I think I really ...
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1answer
198 views

Does this notion of entropy have a name?

Recently I stumbled upon the following notion of entropy which seems quite natural to me. I am looking for its "real" name and/or any references where it might come up. I tried searching ...
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1answer
110 views

Communication complexity of reconstructing a random bit-string of length $n$

This seems like a folklore claim but I cannot find any reference to it. If Alice has a bit-string of length $n$ where each entry is independently set to 0 or 1 equiprobably, and Bob's goal is to ...
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68 views

Complexity of (Graph) Ramsey Theorem in Sum-of-Squares Proof System

(One formulation of) Ramsey's theorem states that any colouring of edges of the complete graph with $4^n$ vertices with two colours will contain a monochromatic clique of size $n$. I am new to proof ...
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226 views

Succinctness of regular expressions with empty word

Consider regular expressions on some alphabet $\Sigma$, without the empty word: $$e,f:=a\in\Sigma\mid e\cdot f \mid e+f\mid e^+$$ These $\varepsilon$⁻free expressions can define all regular languages ...
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Low Rank Approximation of a hidden subset

Let $P$ be a set of $n$ points in $\mathbb{R}^d$ and $Q\subseteq P$ with $\vert Q\vert \geq \alpha n$ for some constant $\alpha\in(0,1]$. Given a $j$-dimensional affine subspace(flat) $F$ consider the ...
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1answer
212 views

The "electricity packing" problem

The question is inspired by this paper. In a distant village, there are $n$ electricity consumers. Consumer $i$ has a power demand of $d_i$ watts. The total electricity supply is $s$ watts. If $s\geq \...
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39 views

A variant of k-median clustering

Suppose $\mathcal{P} =\{P_1,\cdots,P_n\}$ is a family of $n$ finite sets in $\mathbb{R}^d$. Given set $C=\{c_1,\cdots,c_k\}$ of $k$ points, consider the follwoing objective funtion $cost(\mathcal{P},C)...
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68 views

Reference request: characterisation of simultaneous substitution

For simply typed λ-calculus, a simultaneous substitution from $\Gamma$ to $\Delta$ is concretely a type-preserving map from variables in $\Delta$ to terms in $\Gamma$. See, for example, Programming ...
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140 views

How can I find the PhD thesis of A. V. Kostochka?

I've searched for the doctoral thesis of Alexandr V Kostochka in internet but couldn't find it. Can somebody help me? I have searched in his publications list (which contains only one article ...
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Complexity of inclusion of transfinite expressions

Transfinite expressions on an alphabet $\Sigma$ are generated by the grammar : $$e,f:= a\in\Sigma\mid e\cdot f\mid e+f\mid e^*\mid e^\omega.$$ They describe languages of transfinite words, i.e. words ...

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