Questions tagged [reference-request]
Reference-request is used when the author needs to know about work related to the question.
1,534
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Citation for isometric embeddability of $\ell_2$ into $\ell_p^\binom{n}{2}$ for $p \geq 1$?
I need to use the following well-known result in my paper:
Let $X$ be a set of $n$ points in $\mathbb{R}^d$. Then $(X,\ell_2^d)$ embeds isometrically in $\ell_p^\binom{n}{2}$ for all $p \geq 1$.
...
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0
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70
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Hardness of vertex colouring on hypergraphs with $O(\log n)$ edges
I'm interested to know whether there has been any work done on the problem in the title. For the problem to be meaningful, we would naturally need that the hyperedges must have large ($\omega(1)$) ...
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1
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How can I find dependent rounding procedures with the desirable properties?
I'm seeking for materials on dependent rounding. However, what I've found are two papers:
Gandhi, R., Khuller, S., Parthasarathy, S., Srinivasan, A., 2006. Dependent rounding and its applications to ...
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113
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Network design with reachability pattern
We are given two sets of terminals $A$ and $B$. For each $a\in A$, we are also given $R_a\subseteq B$. Let $|A|+|B|=n$.
We want to find a directed acyclic graph $G$ where $A$ and $B$ are subsets of ...
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How do conference proceedings add to academic prestige?
I come from mathematics and, for whatever reason, am trying to publish in theoretical computer science. I'm still trying to understand the role of conference proceedings, and I have two specific ...
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1
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Is $\{0,1\}$-Vector bin packing NP-Hard when vectors have constant dimension?
The paper https://cs.brown.edu/people/seny/pubs/vbponline.pdf discusses $\{0,1\}$-Vector Bin packing in the online setting and give lower bounds. However, they do not mention anything about the ...
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votes
1
answer
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Complexity class of efficient streaming algorithms
Consider the class of problems $\mathsf{StreamL}$ which can be solved in logarithmic space reading the input in a single pass from left to right. In other words:
$L \in \mathsf{StreamL}$ if there ...
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3
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Reference Request: Computational Learning Theory
Pretty soon I will be finishing up Understanding Machine Learning by Shai Ben-David and Shai Shalev-Shwartz. I absolutely love the subject and want to learn more, the only issue is I'm having trouble ...
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1
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What is FO(REGULAR)? (The descriptive complexity equivalent of NC1)
According to Immerman's Descriptive Complexity diagram, there is a logic called $\mathsf{FO(REGULAR)}$ which captures $\mathsf{NC}^1$. However, I can't find the reference where this logic is defined. ...
- 842
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179
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Automatic theorem prover for first-order logic versus model checker
What's the formal difference between a model checker, and an automated theorem prover for first-order logic, i.e. something like Meson/Metis/Sledgehammer/Vampire/E? Link to a clear discussion of the ...
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Finding the size $k$ subset in a metric space that maximizes the min distance between elements
I have a metric space $(X,d)$ and I'd like to find a subset of size k of far away elements.
We can cast this as the following optimization problem $\max_{S \subseteq X, |S| = k} ( \min_{i \not = j, ...
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Improving boolean circuits w.r.t. a probability distribution
This is a reference request. Consider the following problem on boolean circuits [ 1 ]:
Given: Boolean circuit $B$ and probability distribution $\mathbb{P}$ on inputs to $B$.
Task: Find one or more ...
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160
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Subgraph isomorphism on graph sequences
I'm looking for a subgraph isomorphism algorithm that takes advantage of properties of graph sequences.
Say $\{G_i\}_{i=1}^k$ is a sequence of graphs on vertex set $\{1 ... n\}$, and two consecutive ...
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0
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Proof systems induced by NP-complete problems
Satisfiability is the fundamental NP-complete problem. Cook-Reckhow theorem states that the existence of a propositional proof system that admits polynomial size proofs for all tautologies implies ...
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Programmatic higher inductive/inductive-inductive types with equalities between equalities
I can think of practical HITs in verified software that capture some form of alpha equivalence, context equivalence or the example which defines well-typed syntax of type theory from Signatures and ...
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0
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105
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Complexity of a scheduling problem with a fixed left bound of jobs
Consider the following scheduling problem. We have a finite set of jobs $\mathcal{J}= \{j_1, j_2, ..., j_n\}$ to do. Every job $j_i$ has its own value $c_i$ (the amount of money we are paid for ...
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2
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On the coloring number of small graphs with small cliques
Given a parameter $k$, and a graph $G$ with $O(k^2)$ vertices that has a maximum clique with $\le k$ vertices, I want to investigate the maximum number of colors $C(k)$ needed to properly color $G$, i....
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1
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Is this greedy algorithm for vertex cover studied before?
For the vertex cover problem (Given a graph $G$, find a minimum set $S$ of vertices such that $G - S$ is edgeless), there are two famous greedy algorithms. The edge greedy (finding an edge and taking ...
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How can I understand the Coppersmith–Winograd algorithm?
I want to do research on matrix multiplication algorithms. I glanced at the Coppersmith-Winograd algorithm paper, but I didn't understand anything. How can I complete the background to read this paper?...
3
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1
answer
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Embarrassingly Parallel: Formal Definition & Citation
I've been unable to find a good answer for this question: Formally, what makes a problem embarrassingly parallel? Intuitively, it would seem to me that an embarrassingly parallel problem is one where:
...
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3
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Best parameterized algorithm for maximum clique
I have seen the basic algorithm for the maximum clique problem parameterized by the maximum degree at an algorithms course. However, I struggle to find anything better. Searching for things like "...
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Equational Theories for Type Systems
I was reading through Gunter's Semantics of Programming Languages: Structure and Techniques and in the second chapter on simply typed $\lambda$ calculus he introduces an equational theory with $\beta\...
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514
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Fast Computation of First k Eigenvectors of Graph Laplacian
I'm looking for references for the following; Given the unnormalized Laplacian matrix of a graph $L = D - A, ~ L \in \mathbb{R}^{n\times n}$
Algorithm(s) to efficiently estimate the first $k$ (...
1
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0
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218
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Fast algorithms for evaluating functions with high Kolmogorov complexity
Motivation:
I am motivated by a concrete example that occurs in neuroscience, dendritic computation, which may be approximated by functions computable on binary trees [1]. To be more precise, I ...
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203
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Kolmogorov Complexity of the composition of two computable functions
Let's suppose we encode two computable functions $f$ and $g$ as binary strings so $f,g \in \{0,1\}^*$. What I am curious about is whether we can find good upper and lower bounds for:
\begin{equation}...
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3
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0
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112
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Isomorphic subforest problem
I recently read that the following problem is NP-Complete:
Given a tree $T$, and a forest $F$, is there a subgraph of $T$ isomorphic to $F$?
The reference provide was to the textbook “Computers and ...
- 507
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2
answers
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NP-hard problems with very fast exponential-time algorithms
NP-hard problems with very fast exact exponential-time algorithms, say with $O(1.01^n)$ time, are very rare.
Is any fact like
"For any constant $\epsilon>0$ there is an NP-hard 'natural' ...
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102
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Weighted circular balls into bins
I would like to ask you for a help about modified balls into bins problem.
Consider $n$ weighted balls such that each ball has a weight $w_i$ that is at most $W$. Furthermore, each of $m$ bins has a ...
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votes
1
answer
446
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If NP in BPP then NP equals RP
I am looking for a reference to the fact that if NP is included in BPP then NP is equal to RP. See for instance these links:
https://cs.stackexchange.com/q/80509
http://www.inf.ed.ac.uk/teaching/...
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Complexity of graph isomorphism with properly colored edges (ref. request)
An edge-colored graph $G$ is a graph whose edges are labeled with a color (generally represented by an integer). Such a coloring is proper if all adjacent edges in $G$ have different colors. I ...
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Is this a known problem, and is it #P-complete?
Let $G=(V,E)$ be an undirected graph. What I call a selection function of $G$ is a partial function $f:V \to E$ such that for every node $v$, if $f(v)$ is defined then it is one of the adjacent edges ...
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When was the dynamic array first used as an example for amortized analysis?
I'm writing a report on amortized analysis, and I'm using the example of a dynamic array to explain each method. I think it would be nice to add a reference to when this example was first used, as it ...
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$NP$-Completeness of $\epsilon$-balanced graph partitioning for fixed $\epsilon$
Consider this graph partitioning problem: Let $G = (V, E)$ be a simple undirected graph and $0 \leq \epsilon \leq 1, M \geq 0$ be constants. Are there disjoint subsets $V_1, V_2$ with $V = V_1 \cup ...
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A Simple Auction Game
You are playing the following game.
You have a budget of $B$ dollars. There are $n$ days. Every day $d$, you have to make a bid $b_d\geq0$ that does not exceed your budget. After making the bid, a ...
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Reconstructing a colored grid with vertical and horizontal shifts
Consider the following simple problem (puzzle): given
a $N \times N$ $c$-colored grid $G$
a $N \times N$ $c$-colored target grid $G_T$
a number $m$ represented in unary
Can we transform $G$ into $...
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communication complexity lower bound for computing median
In the textbook by Kushilevitz/Nisan, they give an $O(\log n)$-bit protocol for computing the median in the standard 2-party model of communication complexity, where Alice is given a set $X \subseteq [...
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PHOAS with extrinsic typing?
Parameterized Higher Order Abstract Syntax (PHOAS) is a representation of syntax trees that allows the host language's binding to be used to represent binding in the language being modelled, while ...
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115
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Metrics for modelling convergence in the lambda-calculus
I wonder if there have been efforts to reconcile the measure approach to termination and Scott's domain theory or other topological models of computation. In other words, can we translate this measure ...
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Short $\exists$SO sentences over strings that define an NP-complete problem
[Q1] I'm wondering if there are some "official" SHORT existential second order sentences with ONE binary relation, over strings (over a small alphabet) that define an NP-complete set.
(Something ...
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Incompleteness and term extraction
Is there a formalization, which from a proof that a system includes enough arithmetic extracts an arithmetic sentence in the language of PA, which is not provable in the given system? Imagine the ...
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The source of the modular decomposition graph
When introducing graph modular decomposition, most authors use the 11-vertex graph, which I copy from wikipedia.
The question is who is (are) the original designer of it. (I'm not asking who drew ...
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1
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525
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Why is the Greedy Conjecture so difficult?
I recently learned about the Greedy conjecture for the Shortest Superstring Problem.
In this problem, we are given a set of strings $s_1,\dots, s_n$ and we want to find the shortest superstring $s$ ...
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votes
1
answer
141
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Eliminating tautological axioms in tree-like $k$-DNF resolution
The propositional proof system $k$-DNF-resolution, a.k.a. $Res(k)$, is a generalization of propositional resolution, where the lines in a proof are $k$-DNF formulas, i.e., disjunctions of $k$-terms of ...
- 4,501
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A canonical complete problem for EXP and NEXP in terms of formulae
3SAT is a complete problem for NP. TQBF is a complete problem for PSPACE.
Is there direct way to define canonical complete problems for EXP and NEXP in terms of boolean formulae? I have only seen ...
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1
answer
405
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On theoretical aproaches for solving $\mathsf{SAT}$ in special cases
In what cases $\mathsf{SAT}$ can be solved in polynomial time?
I know two cases: $2$-$\mathsf{SAT}$ and Horn-$\mathsf{SAT}$.
Question 1: Is there a reference with algorithms for solving $\mathsf{...
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What are some good resources for strengthening my theoretical foundation for machine learning?
I'm a computer science major and I'm taking a lot of machine learning courses. I'm finding that my theoretical foundation on subjects like calculus and linear algebra are not as strong as I'd like ...
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3
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Can Non-termination be considered an algebraic effect?
Non-termination is sometimes considered an effect. I have been reading about algebraic effect systems (What is algebraic about algebraic effects and handlers?), and I suspect non-termination (like ...
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4
votes
1
answer
381
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Satisfiability problems with restricted (not bounded) number of occurrences per variable
Intro
It is known that SAT is hard even when restricted to, e.g., formulas with exactly 3 literals per clause and at most 4 occurrences per variable. On the other hand it is easy if there are exactly ...
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votes
1
answer
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Counting avoiding improper 3-colorings
Given a graph $G=(V,E)$, what I call an improper $3$-coloring of $G$ is simply a function $c:V \to \{1,2,3\}$. I say that $c$ is $1$-$2$-avoiding when
there do not exist two adjacent nodes $u,v$ with $...
- 1,095
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0
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Characterizing the ANF of Single-Cycle Boolean Permutations
Given a function $F: \{0, 1\}^n \to \{0, 1\}^n$, we say that $F$ is a boolean permutation (also sometimes called a vectorial boolean function or an s-box in the literature) if $F$ is a bijection. We ...
