Questions tagged [reference-request]

Questions requesting papers in the literature on specific, narrow issues.

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Dealing with intractability: NP-complete problems

Assume that I am a programmer and I have an NP-complete problem that I need to solve it. What methods are available to deal with NPC problems? Is there a survey or something similar on this topic?
16k views

How not to solve P=NP?

There are lots of attempts at proving either $\mathsf{P} = \mathsf{NP}$ or $\mathsf{P} \neq \mathsf{NP}$, and naturally many people think about the question, having ideas for proving either direction....
2k views

What classes of data structures can be made persistent?

Persistent data structures are immutable data structures. Operations on them return a new "copy" of the data structure, but altered by the operation; the old data structure remains unchanged ...
4k views

Is there a method for automatic runtime analysis of algorithms?

I am wondering, is there a method for automatic runtime analysis that works at least on a relevant subset of algorithms (algorithms that can be analyzed)? I googled "Automatic algorithm analysis" ...
1k views

Is there a sometimes-efficient algorithm to solve #SAT?

Let $B$ be a boolean formula consisting of the usual AND, OR, and NOT operators and some variables. I would like to count the number of satisfying assignments for $B$. That is, I want to find the ...
1k views

Universal simulation of Turing machines

Let $f$ be a fixed time-constructable function. The classical universal simulation result for TMs (Hennie and Stearns, 1966) states that there is a two-tape TM $U$ such that given the description of ...
2k views

Algorithm books on a range of topics

I've been tasked with building a library of books on algorithms for our small company (about 15 people). The budget is more than 5k, but certainly less than 10k, so I can buy a fair number of books. ...
732 views

Recipe book for SAT encodings?

SAT solvers are getting more and more efficient in solving large instances and are being used as back-ends in various contexts. Every time one wants to use them to solve a problem in a specific domain,...
788 views

References on comparison between quantum computers and Turing machines

I was told that quantum computers are not computationally more powerful than Turing machines. Could someone kindly help in giving some literature references explaining that fact?
848 views

Are there established complexity classes with real numbers?

A student recently asked me to check an NP-hardness proof for them. They performed a reduction along the lines of: I reduce this problem $P'$ that is known to be NP-complete to my problem $P$ (with ...
953 views

Decision problems in $\mathsf{P}$ without fast algorithms

What are some examples of difficult decision problems that can be solved in polynomial time? I'm looking for problems for which the optimal algorithm is "slow", or problems for which the fastest known ...
489 views

How to scale down parallel complexity results to constantly many cores?

I have had problems accepting the complexity theoretic view of "efficiently solved by parallel algorithm" which is given by the class NC: NC is the class of problems that can be solved by a ...
2k views

Decidable restrictions of the Post Correspondence Problem

The Post Correspondence Problem (PCP) is undecidable. The bounded version of the PCP is $\mathrm{NP}$-complete and the marked version of the PCP (the words of one of the two lists are required to ...
941 views

How to enumerate minimal covers of a set

I have a set $S$ and a set $P = \{P_{1},...,P_{n}\}$ with $\bigcup P_{i} = S$. I want to find all the inclusion-minimal subsets of $P$ that are covers of $S$. What is the best algorithm for ...
1k views

Why are all problems in FPTAS also in FPT?

According to the Wikipedia article on polynomial-time approximation schemes: All problems in FPTAS are fixed-parameter tractable. This result surprises me - these classes seem to be totally ...
1k views

Are context-free languages in $a^*b^*$ closed under complement?

The context-free languages are not closed under complement, we know that. As far as I understand, context-free languages that are a subset of $a^*b^*$ for some letters $a,b$ are closed under ...
665 views

What are some interesting applications of the skyline problem?

You are given a set of $n$ rectangles in no particular order. They have varying widths and heights, but their bottom edges are collinear, so that they look like buildings on a skyline. For each ...
11k views

Book for algorithms beyond Cormen

I've finished most of the material in Cormen's Intro to Algorithms book and I am looking for an algorithms book that covers material beyond Corman's book. Are there any recommendations? NOTE: I asked ...
286 views

Splicing squares on a Turing Machine finite tape

Trying to explain a problem, I thought of a variant of Turing Machines. It is unlikely to be new, but I do not recall ever seing it before, and I wonder whether it has been used or has a name. The ...
65k views

What is tail recursion?

I know the general concept of recursion. I came across the concept of tail recursion while studying the quicksort algorithm. In this video of quick sort algorithm from MIT at 18:30 seconds the ...
29k views

Which machine learning algorithms can be used for time series forecasts?

Currently I am playing around with time series forecasts (specifically for Forex). I have seen some scientific papers about echo state networks which are applied to Forex forecast. Are there other ...
2k views

Quantum lambda calculus

Classically, there are 3 popular ways to think about computation: Turing machine, circuits, and lambda-calculus (I use this as a catch all for most functional views). All 3 have been fruitful ways to ...
8k views

Worst case $O(n \ln n)$ in place stable sort?

I am having trouble finding good resources that give a worst case $O(n \ln n)$ in place stable sorting algorithm. Does anyone know of any good resources? Just a reminder, in place means it uses the ...
4k views

Fast k mismatch string matching algorithm

I am looking for a fast k-mismatch string matching algorithm. Given a pattern string P of length m, and a text string T of length n, I need a fast (linear time) algorithm to find all positions where P ...
662 views

Deterministic linear time algorithm to check if one array is a sorted version of the other

Consider the following problem: Input: two arrays $A$ and $B$ of length $n$, where $B$ is in sorted order. Query: do $A$ and $B$ contain the same items (with their multiplicity)? What is the ...
2k views

Can we construct a Karp reduction from a Cook reduction between NP problems?

We have had several questions about the relation of Cook and Karp reductions. It's clear that Cook reductions (polynomial-time Turing reductions) do not define the same notion of NP-completeness as ...
2k views

Finding shortest paths in undirected graphs with possibly negative edge weights

The book "Algorithms" by Robert Sedgewick and Kevin Wayne hinted that (see the quote below) there are efficient algorithms for finding shortest paths in undirected graphs with possibly ...
528 views

Proving the (in)tractability of this Nth prime recurrence

As follows from my previous question, I've been playing with the Riemann hypothesis as a matter of recreational mathematics. In the process, I've come to a rather interesting recurrence, and I'm ...
1k views

Efficiently sampling shortest $s$-$t$ paths uniformly and independently at random

Let $G$ be a graph, and let $s$ and $t$ be two vertices of $G$. Can we efficiently sample a shortest $s$-$t$ path uniformly and independently at random from the set of all shortest paths between $s$ ...
7k views

Time complexity of base conversion

Why can't arbitrary base conversion be as fast as converting from base $b$ to base $b^k$ ? Seems to be a big time complexity difference! I am also interested in reading material about it. Old. ...
11k views

Practical application of Finite State Machines

I am looking for practical applications of Finite State Machines like DFA, NFA, Moore, Mealy machines... It would be helpful if someone point to examples from Linux Kernel. I know that DFA is used in ...
632 views

What is the name of this logistic variant of TSP?

I have a logistic problem that can be seen as a variant of $\text{TSP}$. It is so natural, I'm sure it has been studied in Operations research or something similar. Here's one way of looking at the ...
581 views

How to prove the emptiness of intersection of two context free languages is undecidable?

Where can I find a proof that the emptiness problem for the intersection of two context free languages is undecidable? I searched on the internet but could not find anything helpful. Do you maybe ...
412 views

Reconstructing a screen of permuted pixels

Reconstructing a screen of permuted pixels Summary Given a video with the pixel locations randomly permuted (once, for the entire video), can we (efficiently) reconstruct the original picture? Let: ...
396 views

Existence of NP problems with complexity intermediate between P and NP-hard

Assuming P!=NP, there is a result that there are decision problems intermediate between P and NP-complete. That is, the class NP cannot be a union of two disjoint subsets: P and NP-complete. I could ...
253 views

Compare regex in programming languages with regular expression from automata/formal language?

I'm trying to reconcile the differences/similarities between regular expression from formal language theory and automata, and the "regex" offered by programming languages. These two differ not just ...
98 views

What kind of formal language is generated by Parsing Expression Grammars?

I've been unable to find what class of languages is recognized by PEGs. The original paper [1] only conjectures that there are some Context-Free Grammars that are unrecognizable by PEGs. It also ...
239 views

Measures and probability in formal language theory

I am looking for references for the following problem: I have a very special class of regular languages and my aim is to express (and to justify my conjecture) that this class itself is very small in ...
157 views

Complexity of space density and sequentiality

I'm looking for some standard terminology, metrics and/or applications of the consideration of density and sequentiality of algorithms. When we measure algorithms we tend to give the big-Oh notation ...
274 views

Unbiasing of sequences

There is the well-known method of unbiasing of bit sequences due to von Neumann. Are there similar schemes applicable to other sequences, e.g. the result of throwing a normal die?
2k views

A reference for pseudocode for Monge-Elkan algorithm?

Does anyone have a good reference to pseudocode for Monge-Elkan string comparison algorithm? I have access to the two original papers, but they do not show the pseudocode of the actual algorithm. ...
5k views

Undecidable unary languages (also known as Tally languages)

An exercise that was in a past session is the following: Prove that there exists an undecidable subset of $\{1\}^*$ This exercise looks very strange to me, because I think that all subsets are ...
6k views

What use are groups, monoids, and rings in database computations?

Why would a company like Twitter be interested in algebraic concepts like groups, monoids and rings? See their repository at github:twitter/algebird. All I could find is: Implementations of ...
3k views

I started reading more and more language research papers. I find it very interesting and a good way to learn more about programming in general. However, there usually comes a section where I always ...
652 views

Studying Programming Language Theory

I have recently become extremely interested in understanding and proving aspects of (functional) programming languages. However as I dive deeper in, things like $\lambda$ calculus, category theory, ...
531 views

Finding an $st$-path in a planar graph which is adjacent to the fewest number of faces

I am curious whether the following problems has been studied before, but wasn't able to find any papers about it: Given a planar graph $G$, and two vertices $s$ and $t$, find an $s$-$t$ path $P$ ...
1k views

Computer Science Book for Young Adults

What is a good beginner computer science book for a young adult, say, a 15 year old? I want to get started in CS, but have no idea where to start. I have limited experience in programming.
1k views

Theoretical foundations of Divide and Conquer

When it comes to the design of algorithms, one often employs the following techniques: Dynamic Programming The Greedy-Strategy Divide-and-Conquer While for the first two methods, there are well-...