Questions tagged [reference-request]

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

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1answer
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How to benchmark #2-SAT counting algorithms?

Are there any libraries of #2-SAT instances that are hard to solve with state-of-the-art exact solvers (sharpSAT, cachet, ...)? Alternatively: are there practical ways to generate hard #2-SAT ...
7
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0answers
155 views

A class of functions on a lattice that are easy to optimize

Let $({\cal P}(X),\subseteq)$ be the subset lattice for a finite set $X$. Consider a function $f:{\cal P}(X)\to \mathbb{R}$ with the following property: Given any element $I_0\in {\cal P}(X)$, there ...
3
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0answers
296 views

Book Recommendations for a General Introduction to (Theoretical) Computer Science

After perusing the web and cstheory.stackexchange in particular, I've come across many different wonderful resources in Computer Science - from Sipser's "Introduction to the Theory of Computation" to ...
4
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1answer
175 views

Have fixed parameter integer program algorithms ever been implemented for research use?

Have any fixed parameter integer programming algorithms described in Integer programming with a fixed number of variables been implemented? Is there a reference code that researchers can use?
2
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1answer
214 views

Deformation of finite regular languages [closed]

Let $L \subseteq \{0,1\}^n$ be any finite regular language s.t it has an acyclic DFA. Let $C$ be some class of acyclic DFAs. Let $\sigma \in S_n$ be a permutation on $n$ symbols. We can apply $\...
2
votes
2answers
226 views

Maximum Treewidth of a Graphs with $m$ Edges

What is the maximum treewidth of a graph with $m$ edges? In other words, what is the correct growth for the following function? $\alpha(m) = max\{\mathrm{treewidth}(G): G \mbox{ has $m$ edges}\}$. ...
1
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0answers
63 views

Complexity of Proportional Sampling

Let $p_1,...,p_n$ be a list of numbers, each specified by $n^{O(1)}$ bits. Let $\mu = \sum_{i} p_i$ be the sum of all numbers in the list. I want to sample from the set $\{1,...,n\}$ where each $j$ is ...
5
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0answers
110 views

Graceful labeling completion problems

A graceful labeling of a graph with $m$ edges is a labeling of its vertices with some subset of the integers between $0$ and $m$ inclusive, such that no two vertices share a label, and such that each ...
2
votes
1answer
267 views

Is Isomorphism of bounded degree hyper-graphs in P?

Informally, hypergraph is a generalization of a graph in which an edge can join any number of vertices. A hyper graph G=(V,E) is a two tuple, where $V$ is the set of vertices and $E$ is a set contain ...
5
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0answers
158 views

Is E.M Luks algorithm for trivalent graph isomorphism parallelizable?

It is still open whether also Luks’ efficient GI algorithm for graphs with bounded degree is parallelizable i.e. NC. I get this from the survey "On Graph Isomorphism for Restricted Graph Classes" by ...
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Easy instances for coset intersection problem

Coset Intersection Problem Given : $K,H \le S_n$, and $\sigma \in S_n$ Find : $K \cap H\sigma$ Known results are : $n^{O(\sqrt n )}$ time algorithm by L.Babai. $n^{O(1)} m^{O(\sqrt m )}$, where $...
3
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0answers
208 views

Is there any known strategy that avoids circuits and that respects believed separations to prove $P$ is not $NP$?

Vinay Deolalikar's approach tried to randomness is not strong enough, Blum's proof tried to show $P/poly$ is not strong enough, Mulmuley's and Smale's approach (while not enough to show $P\neq NP$) ...
1
vote
1answer
82 views

Practical/heuristic algorithm for multi set-cover

Consider a universe $N$ containing $n$ elements, and a collection of sets $\mathcal{C}$, over $N$. The $k$-multiset multicover (MSMC) problem is to cover all elements of the universe $N$ at least $k$ ...
3
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0answers
46 views

Correlated random models of game trees

Say we want to understand a game tree search algorithm in a theoretical context. Thus, we want a parameterized family of problem instances, separate from actual games such as a chess, so that ...
4
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1answer
183 views

How to find largest supergroup in polynomial time?

Let $G \le S_n$, and G acts on set $[n]$ via a map $\pi$: $$\pi : G \times [n]\mapsto [n] $$ In Input generating set of $G$ is given. Question : I need to find the largest supergroup $G^{'}$ (...
0
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1answer
120 views

Different algorithms for longest increasing subsequence

The longest increasing subsequence problem has a simple and elegant $O(n \log n)$ time solution via patience sorting. Such a basic and well-studied problem, however, should have a number of different ...
6
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0answers
126 views

Book/ Monograph on graph minor theory [Reference request]

I want to learn graph minor theory. Now i have read the very basic things and the overview from the book of R.Diestel but proceeding further is getting difficult. Currently, I am also following the ...
4
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0answers
181 views

What exactly did Lenstra prove on mixed integer linear program?

I studied Lenstra's paper https://www.jstor.org/stable/3689168. I have no clue what complexity he provides on Mixed Integer Programming (it is too terse and it is not a stand alone paper as he assumes ...
4
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0answers
143 views

On status of Valiant's $NC^2=P^{\#P}$ provability program?

In here it is written 'A most interesting/controversial talk was by Leslie Valiant. He explored paths to try to prove that $NC^2=P^{\#P}\dots$'.... This was a decade back. What is the rationale (at ...
9
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1answer
260 views

Are there protein-based computational models?

Is there an framework/formalism which defines computational models based on proteins other than Adleman's DNA model or this work by Cherry and Qian?
4
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1answer
237 views

Textbook/resources for a beginning researcher in (Machine) Learning Theory

I'm looking to begin understanding basic concepts, notions, results and definitions in the area of Computational Learning Theory (or the theory of Machine Learning), as is done in the theoretical ...
7
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2answers
711 views

Sources of open problems?

I'm wondering if there are some known sources of open TCS problems? I'm a junior studying math/CS and would like to know of some accessible problems that I could start thinking about! Thanks so much!...
2
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1answer
560 views

Is simply typed lambda calculus equivalent to primitive recursive functions

It's well known that the computation models untyped lambda calculus and $\mu$-recursive function are equivalent in terms of computability (in fact they are both Turing complete.) It is also well known ...
5
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0answers
134 views

reference clarification: Whitney's theorem on unique embeddability of 3-connected planar graphs?

This is a question about the correct reference for a result that seems to appear frequently in the literature on planar graph isomorphism. In "A $V \log V$ Algorithm for Isomorphism of Triconnected ...
10
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2answers
271 views

Complexity of Homogenizing a String

Motivation: While developing tools for data versioning, we ended up looking into algorithms for "diff"ing two sets of integers, by coming up with a sequence of transformations that take one set of ...
4
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0answers
158 views

On earlier references for $P=BPP$ and Kolmogorov's possible view on modern breakthroughs involving randomness?

Kolmogorov and Uspenskii in this paper 'http://epubs.siam.org/doi/pdf/10.1137/1132060' speculate P=BPP in 1986. They do this without getting into circuit lower bounds and from a different view which ...
2
votes
1answer
210 views

On $NP$ and $XP$ classes?

On page 33 venn diagram in http://tcs.rwth-aachen.de/~sanchez/slides/Raleigh2014.pdf it is implied that $XP\subseteq NP$. Below this there is a statement which says $XP\not = NP$ unless $P=NP$. Is ...
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0answers
49 views

Counting multiplicative closures

Given a set $S$, its multiplicative closure is the set $$ \mathcal{M}(S) = \{s_1s_2\cdots s_k: k\in\mathbb{N},s_i\in S\} $$ of products of zero or more elements of $S$. So the multiplicative closure ...
7
votes
1answer
176 views

Composition of $FP$ and $\#P$ functions

Let $f_i \in FP$ and $g_i \in \#P$ for $i \in \mathbb{N}$. It is known that: $f_1(f_2(x)) \in FP$ and that $g_1(f_1(x)) \in \#P$. Is it known whether or not $f_1(g_1(x)) \in \#P$ or maybe $f_1(g_1(...
5
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0answers
97 views

Structures obtained by gluing simplices

I'm looking for the correct name of geometric structures obtained as follows. 2-structures: A collection $X$ of triangles is a $2$-structure. If $X$ is a $2$-structure and $Y$ is obtained from $X$ ...
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0answers
285 views

Reference request: exponential growth rates of subsequence-closed languages are integers

This question is migrated from MathOverflow, where it did not receive any answers a year ago. For a language $L$ over the finite alphabet $\Sigma$, let $L_n$ denote the set of words in $L$ of length $...
5
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0answers
117 views

Status of constant-depth isomorphism in $AC^0[\oplus]$

In [1], Agrawal proved the following: For any complexity class $\mathcal{C}$ closed under $NC^1$ reductions, problems complete for $\mathcal{C}$ under $FO$ reductions are isomorphic via an ...
3
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0answers
99 views

Notion of “total work” of a problem?

I apologize in advance if this question is outside the scope of this Exchange community; if so, perhaps someone can point me in the right direction. I am curious if there is a theoretical notion of "...
2
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0answers
80 views

Graphs for which the number of shortest paths between every pair of vertices is polynomially bounded

Let $G$ be a graph with $n$ vertices and $m$ edges, such that for every two vertices $u$ and $v$, the number of shortest paths from $u$ to $v$ is bounded by some polynomial $poly(n,m)$ in $n$ and $m$. ...
10
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1answer
154 views

Name for “uniformly polynomial” subclass of XP?

Suppose $L$ is a parameterized language with respect to some alphabet $\Sigma$. The $k$-slice of $L$ is $L_k = L \cap \{(x,k) \mid x \in \Sigma^{*}\}$, the set of instances in $L$ which have parameter ...
5
votes
1answer
103 views

Inference in typed lambda calculus theories

I'd like to do automated inference, say solving word problems or reducing to normal form, in an equational theory of the typed lambda calculus (with product and unit types). Equivalently, in category-...
14
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1answer
970 views

Is there a relationship between relational algebra/calculus and category theory?

I am aware of at least two different theoretical approaches for understanding relational databases: Codd's relational algebra/calculus, and category theory. Is there any relationship between these ...
16
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2answers
414 views

Is intersection of $k \ge 3$ graphic matroids in P?

It is known that intersection of three general matroids is NP-hard (source), which is done via reduction from Hamiltonian cycle. The reduction uses one graphic matroid and two connectivity matroids. ...
3
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0answers
249 views

A sequence wherein the Kolmogorov complexity of the terms does not increase

I am looking for an algorithm $A$ - which for any non-null input string $s_1$ produces a sequence $s_1, s_2...$ such that : It can be proved in some axiomtic system $S$ that: $\...
6
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0answers
101 views

Deterministic approximation algorithms for treewidth

As far as I understand, the factor $O(\sqrt{\log OPT})$ approximation algorithm for treewidth of Feige, Hajiaghayi, and Lee is randomized, and no deterministic approximation algorithm with this factor ...
16
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2answers
1k views

“Almost sorting” integers in linear time

I am interested in sorting an array of positive integer values $L = v_1, \ldots, v_n$ in linear time (in the RAM model with uniform cost measure, i.e., integers can have up to logarithmic size but ...
5
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2answers
232 views

Log space algorithms for modular decomposition tree

Can we have log space algorithms for modular decomposition tree (see definition) for any graph? If not, can we have log space algorithms for modular decomposition tree for any particular graph class? ...
2
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0answers
64 views

How to extend Solomonoff Induction to continuous domain

Informally speaking, Solomonoff Induction provides an Bayesian optimal way to predict the next symbol from observed symbol sequences $S_1S_2S_3...S_n$ where each $S_i$ belongs to a finite symbol set $\...
5
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0answers
87 views

Using epsilon biased sets for circuit lower bounds

I have seen instances of how the technique of epsilon biased sets can be used to construct hard functions against a circuit class - like how in the recent paper of Kane-Williams this was used to ...
8
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1answer
191 views

Was counting complexity first introduced by Valiant in 1979?

Was #P first introduced in [1]? [1] Valiant, Leslie G. "The complexity of computing the permanent." Theoretical computer science 8.2 (1979): 189-201.
8
votes
1answer
221 views

Vertex isoperimetric number of a graph - NP-hard?

The vertex isoperimetric number of a graph $G=(V,E)$ is $i_V(G) = \min\{\frac{|N(S)|}{|S|} : S \subseteq V, 1\le |S|\le \frac{|V|}{2}\}$. Several academic papers state that the problem of computing ...
9
votes
1answer
262 views

Complexity of checking if two words have an interleaving in a language

For a fixed language $L$ on some alphabet $A$, let us consider the following problem, that I call $L$-INTERLEAVING: Input: two words $u, v \in A^*$ Output: whether there exists an interleaving of $u$ ...
6
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0answers
90 views

Looking for an easy/pedantic exposition of Renegar's famous result on polynomial optimization

In September $1989$, Renegar had this famous sequence of 3 papers titled, "On the Computational Complexity and Geometry of the First-order Theory of the Reals, Part I/II/III". I was wondering if ...
7
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2answers
221 views

Efficiently ordering typed programs

Sometimes it is useful to enumerate in increasing order programs that have a given type. A simple example is test generation for compilers: we want to test a new optimising phase and are ...
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0answers
111 views

Transferring results on coalgebras in one category to another

Let $F$ and $G$ be endofunctors over categories $C$ and $ D$, respectively. Suppose that there is a forgetful functor $C \to D$ that has a left adjoint. Can we infer properties of $F$-coalgebras ...