Questions tagged [reference-request]

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

1,327 questions
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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 ...
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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 ...
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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 ...
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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?
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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 $P\neq NP$) ...
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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 $k$ ...
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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 ...
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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 $G^{'}$ (...
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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 ...
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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 ...
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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 ...
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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 ...
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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?
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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 ...
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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!...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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 ...
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Status of constant-depth isomorphism in $AC^0[\oplus]$

In , 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 ...
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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 "...
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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 $m$. ...
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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 ...
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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-...
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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 ...
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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. ...
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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 ...
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Was counting complexity first introduced by Valiant in 1979?

Was #P first introduced in ?  Valiant, Leslie G. "The complexity of computing the permanent." Theoretical computer science 8.2 (1979): 189-201.
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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 ...
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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 $u$ ...
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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 ...
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 ...