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

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4
votes
1answer
92 views

Kth best problem that is NP-hard for K polynomial

A Kth best problem is, given some constraint, to find a solution that has the Kth best value compared to all solutions that meet the constraint. One way to write this as a decision problem is to ...
4
votes
2answers
115 views

Characterisation of P in terms of register machines

It is a well-known result that Turing machines and random access machines (RAMs) can simulate each other with a polynomial slowdown. It is relatively straightforward to prove that indirect addressing ...
-1
votes
0answers
19 views

Reference Request : Computing directed domination number of Oriented graphs

An oriented graph ($\overrightarrow{G}$) is a directed graph having no symmetric pair of directed edges (arcs). A directed dominating set in a directed graph $D$ is a subset $S$ of vertex set $V$ ...
3
votes
1answer
115 views

Median finding with “green forests”?

I have a vague memory of a series of papers working to reduce the constant factor in the number of comparisons for deterministic linear time median finding, using increasingly elaborate (but ...
0
votes
0answers
48 views

How much variance is captured by the RFF maps? [migrated]

The RFF maps here are possibly the most used feature maps. I was wondering if there are cases where anyone has theoretically estimated the total variance captured by these maps? Is any simplification ...
6
votes
1answer
101 views

Complexity of testing if a hypergraph has generalized hypertreewidth $2$

A hypergraph $H = (V, E)$ consists of a set of vertices $V$ and a set $E$ of hyperedges, i.e., subsets of $V$. The generalized hypertreewidth (GHW) parameter is a measure of the cyclicity of a ...
5
votes
0answers
83 views

Minimizing a submodular function given noisy oracle access

Let $f\colon 2^{[n]} \to \mathbb{R}$ be a submodular function (one can assume $f$ is bounded, if this helps). We are given noisy oracle access to $f$: on any $S$ and for any $\tau > 0$, one can ...
0
votes
0answers
45 views

Individualization of two Subgraphs

Notation: $H$ is the adjacency matrix of graph $H'$ respectively. $H_k$ is the block or sub-matrix of matrix $H$. The adjacency matrix of graph $H_k \cup H_e$ (subgraphs of $H'$) is $M_{(k,e)}$ ...
3
votes
0answers
36 views

Complexity of propositional LTL with past operators and freeze quantifier?

In "A Really Temporal Logic", by R.Alur and A.Henziger, they introduce an extension of Linear Temporal Logic with a freeze quantifier $x.\phi$, which allows to "give a name" to the current time point ...
6
votes
0answers
57 views

Complexity of #SAT for monotone DNF formulae whose hypergraph is a hypertree

A monotone DNF on variables $x_1, \ldots, x_n$ is a disjunction of clauses, each clause being a conjunction of some of the $x_1, \ldots, x_n$. The #SAT problem asks, given a monotone DNF $\Phi$, how ...
9
votes
0answers
162 views

reference request: deciding validity of higher-order quantified boolean formulas is not Kalmar-elementary

$\newcommand\iddots{⋰}$In "A simple proof of a theorem of Statman" (TCS 1992), Harry Mairson gives a simple proof of Statman's result that deciding $\beta\eta$-equality of terms in simply typed lambda ...
7
votes
1answer
135 views

On bandwidth of graphs

I am trying to find references on algorithms for graphs of bounded bandwidth, in the same way as it is done with treewidth for instance. I could only find research related to computing the bandwidth, ...
4
votes
0answers
62 views

Graph Isomorphism of Strongly Regular Graph with fixed parameter

$G, H$ are strongly regular graphs with parameter $(n, r, \lambda, \mu)$ where $\lambda$ is constant. Here, $n$ is the number of total vertices. Each graph is $r$ regular. Every two adjacent ...
6
votes
0answers
87 views

Petrank's proof for the APX-hardness of MAX k-VERTEX COVER on subcubic graphs

My question is about the following maximization problem, which is the "fixed cardinality" version of MIN VERTEX COVER. I am interested in the restriction to subcubic graphs (i.e. of maximum degree 3). ...
4
votes
1answer
184 views

Where is the quote “Informal proofs are algorithms, formal proofs are code” from?

Does anyone know the origin of the quote, Informal proofs are algorithms; formal proofs are code. Its made in Benjamin C. Pierce et al.'s Software Foundations.
0
votes
0answers
56 views

Trade-off between number of spheres and wasted space in covering a 3d object by spheres

Consider the following optimization problem: Input: a 3-dimensional "object" $O$. Output: a covering of $O$ by a list of $k$ spheres $S_1, \ldots, S_k$ (given by their centers and radii) minimizing ...
8
votes
1answer
146 views

3-color a cubic graph such that a MIS receives only two colors

According to Brooks'_theorem, a cubic graph (3-regular graph) containing no $K_4$ can be properly colored by three colors. (Such a color can actually be found in linear time, which is not our primary ...
4
votes
2answers
113 views

Constant-time bounds on offline 2-choice hashing?

I'm reading up on cuckoo hashing and came across Michael Mitzenmacher's blog posts on the subject. In his motivation of why cuckoo hashing seems like a reasonable strategy, he mentions a connection to ...
5
votes
0answers
100 views

Vertex Disjoint Path Covers of Hypercube-Like Graphs

This is a followup question relating to an older question I posted, namely: Decomposing the n-cube into vertex-disjoint paths. Given a graph $G = (V, E)$ and sets of distinct vertices $S = \{s_1, \...
7
votes
1answer
110 views

Lower bound on prefix code lengths

For a prefix code $C:\{0,1\}^*\to\{0,1\}^*$, define $f(n)$ as the length of the longest encoding of a number with up to $n$ bits: $$ f(n)=\max_{|k|\le n}\left|C(k)\right|. $$ (Note that by taking ...
3
votes
0answers
105 views

Fast Approximation Algorithms for Covering Design

The covering design problem is as follows: We are given a universe $\mathcal{U}$ of size $n$. By $C(n,k,l)$ we denote the smallest cardinality of any set system $\mathcal{A} \subset 2^\mathcal{U}$ ...
10
votes
1answer
236 views

Introduction to probabilistic automata

Where can I find an introduction to probabilistic automata and what they recognize (certain functions from words to $[0,1]$)? Is there a standard term for such functions which are recognized by ...
6
votes
2answers
239 views

Implementing “Internal” Languages

One of the most practical consequences of the "Curry-Howard-Lambek" correspondence is that the syntax of many lambda-calucli/logics can be used to perform constructions in a sufficiently structured ...
11
votes
1answer
162 views

Is there a survey of the field of quantum automata?

I'm looking for a survey paper of the important concepts in the field of Quantum Automata. I've found Quantum Automata Theory -- A Review by Hirvensalo, but it sounds too succinct to grasp the topic. ...
13
votes
1answer
678 views

Rabin's “degree of difficulty of computing a function, and a partial ordering of recursive sets”

I am looking for: Michael O. Rabin, "Degree of difficulty of computing a function, and a partial ordering of recursive sets", Hebrew University, Jerusalem, 1960 Summary: “We attempt to measure ...
14
votes
1answer
330 views

Novel proof of pumping lemma for regular languages

Let $\mathcal{L}$ be the family of all languages over $\Sigma$ satisfying the pumping property of regular languages. Namely: for each $L\in\mathcal{L}$, there is an $N\in\mathbb{N}$ s.t. every word $w\...
7
votes
0answers
112 views

Kleinberg Rubinfeld Short Paths in Expander Graphs for Hypergraphs

In the 1996 paper "Short Paths in Expander Graphs" by Kleinberg and Rubinfeld, the authors show a randomized polynomial-time algorithm for finding an embedding of a graph $H$ into a graph $G$, if $G$ ...
8
votes
3answers
252 views

Convergence theorem for Genetic Programming?

Genetic Programming (GP) is stochastic algorithm, there has been early attempts to explain its convergence with the Schmea Theorem (Holland 1975) for Genetic Algorithm adapted for GP such as (Koza ...
13
votes
1answer
324 views

Expected minimum influence of a random Boolean function $f\colon\{-1,1\}^n \to \{-1,1\}$

For a Boolean function $f\colon\{-1,1\}^n \to \{-1,1\}$, the influence of the $i$th variable is defined as $$ \operatorname{Inf}_i[f] \stackrel{\rm def}{=} \Pr_{x\sim\{-1,1\}^n}[ f(x) \neq f(x^{\oplus ...
5
votes
0answers
140 views

Machine learning algorithms on hypergrap models

Graphical models are a very useful tool with many applications, whereby a joint distribution of a set of random variables is modeled using only pairwise dependencies between the variables, and two ...
8
votes
1answer
124 views

Tree-decomposition with clique interfaces

Let $G=(V,E)$ be a finite undirected graph. A tree decomposition $(T,\lambda)$ of $G$ is a tree $T$ with labeling function $\lambda : T \to 2^{V}$ such that: For every edge $\{v_1,v_2\} \in E$, ...
8
votes
0answers
109 views

Recognition of a primitive root

Adleman and McCurley published a paper in 1994 called "Open problems in number theoretic complexity, II" (http://ww.cstheory.com/papers/open.ps.gz) Problem 18 of this list of open problems is about ...
8
votes
1answer
146 views

Complexity of the edge-disjoint cycle covers

I am interested in decompositions of a directed graph $G=(V,E)$ into non-intersecting Eulerian subgraphs $G_i=(V_i, E_i)$. I want to find the decomposition that covers the largest number of edges. I ...
4
votes
1answer
117 views

Problems still “hard” in the SMP/Referee model with shared randomness?

In the referee (SMP: Simultaneous Message Passing) model introduced by Yao (see e.g. [1]), Alice and Bob have respectively inputs $x\in X$ and $y\in Y$, and wish to communicate with a third-party, the ...
9
votes
0answers
104 views

“k-Swap SAT” problem

I would like to know if the following NP-complete problem has a name and has been studied: Input: Given a CNF formula $\varphi$ on $n$ variables, a truth assignment $\sigma:[n] \to \{T,F\}$ and an ...
2
votes
0answers
23 views

Stochastic optimization with erroneous oracles

I am interested in a class of optimization problems of which we know that the input variable is first subjected to noise $\xi$ before entering the data-producing process $f$. I write the objective in ...
3
votes
0answers
100 views

Hashtable vs cache-oblivious [closed]

I'd like to know more about real performances of data structures, in particular two families attract my interests: hash tables cache oblivious My researches didn't find any "comprehensive" (let me ...
8
votes
3answers
398 views

How to design concurrent data structures?

I previously asked this question on Programmers.SE, without success. I'm looking for written learning resources on how to design concurrent data structures. I'm more interested in the design process (...
17
votes
0answers
502 views

Deeper look at Algorithmica?

Russell Impagliazzo published "A Personal View of Average-Case Complexity" (preprint) back in 1995. He presented five possible worlds we could be living in, depending on how P and NP were related. The ...
10
votes
1answer
192 views

Complexity of digraph homomorphism to an oriented cycle

Given a fixed directed graph (digraph) $D$, the $D$-COLORING decision problem asks whether an input digraph $G$ has a homomorphism to $D$. (A homomorphism of $G$ to $D$ is a mapping $f$ of $V(G)$ to $...
4
votes
2answers
111 views

Ordered-file maintenance

I am studying the Advanced Data Structures material and I'd like to implement the Ordered-file maintenance data structure. I have few questions in order to start. The papers rely on a static view, ...
9
votes
0answers
311 views

Upper Bound on Number of $n \times n$ Boolean matrices of Boolean rank at most $k$

An $n \times n$ Boolean matrix $B$ has Boolean rank $k$ if there exist matrices $L \in \{0,1\}^{n \times k}$ and $R \in \{0,1\}^{k \times n}$, s.t. $B = L \circ R$. Here $\circ$ denotes the Boolean ...
6
votes
2answers
229 views

Local Graph Isomorphism to construct Global Graph Isomorphism

Does there exist a Graph Isomorphism Algorithm that uses Local Isomorphism to construct a Global Isomorphism? For example, two graphs are given, say, $H, G$. it is asked to determine whether $G\simeq ...
7
votes
1answer
126 views

A word anticorrespondence problem

A problem instance is a finite list of 4-tuples $(\alpha_1, u_1, v_1, \beta_1), ..., (\alpha_N, u_N, v_N, \beta_N)$, where $\alpha_i, \beta_i \in X$ come from a finite set, and each $u_i,v_i \in A^*$ ...
1
vote
1answer
74 views

Normal form for deterministic (sub)sequential transducers with letter-by-letter outputs

For a project I'm working on, it would seem useful to have a normal form for deterministic (sub)sequential transducers in which the set of states, $Q$, is partitioned into states, $r \in Q_R$, that ...
1
vote
0answers
94 views

Minimizing a monotone submodular function under a cardinality constraint

I would like to know what the status of the following question is: Given query access to a non-decreasing, non-negative submodular function $f\colon 2^{[n]} \to \mathbb{R}$ and a parameter $0 \...
5
votes
0answers
129 views

The evaluation problem for AC$^0_d$ formulas is in FO

Let $d \in \mathbb{N}$ be arbitrary. Let $\mathsf{AC^0_d}$-Eval be the following promise problem: Input: A depth $d$ formula $\varphi(x)$ and a binary string $a$. Output: $\varphi(a)$ I am looking ...
5
votes
0answers
162 views

Is there an approximation algorithm for MAX k DOUBLE SET COVER?

Given a set system $(X,\mathcal S)$, let us say that a subset $\mathcal C\subseteq \mathcal S$ doubly covers a vertex $x$ in $X$ if $x$ is contained in at least two sets of $\mathcal C$. Let us define ...
1
vote
3answers
240 views

List of complexity classes closed under complement

Is there a list of 'natural' complexity classes closed under complement? Some that I could think of are P, ZPP, BPP, NP $\cap$ co-NP, PH, PP and PSPACE but surely there are others. Wikipedia and the ...
7
votes
1answer
232 views

Inexact labelled binary tree matching

Does anyone recognise the following problems? Do they have names? Are they hard? If we were looking for an exact match (0 mismatches), these would be solvable in polynomial time (using e.g. standard ...