Time complexity of decision problems or relations among time-bounded complexity classes. (Use [tag:analysis-of-algorithms] for the time taken by particular algorithms.)

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77 views

Compute the integer part of y=sqrt(x) in O(n) arithmetical operations [on hold]

I'm nearing the end of the popular 'Nand To Tetris' course. In Chapter 12, an algorithm is presented which computes the integer part of y=sqrt(x), where x is an n-bit integer: In the accompanying ...
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22 views

How to compute Time Complexity [on hold]

please I want to ask about time complexity, how can I compute it? depending on my algorithm or my data? I have little information about complexity.
3
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2answers
136 views

Runtime of Tucker's algorithm for generating a Eulerian circuit

What is the time complexity of Tucker's algorithm for generating a Eulerian circuit? The Tucker's algorithm takes as input a connected graph whose vertices are all of even degree, constructs an ...
2
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0answers
106 views

Complexity of Knapsack-type problem with applications to computational workflows

Consider the following problem: Let there be a set A of $n$ items $A=\{z_1, ..., z_n\}$, and let $W$ be a strictly positive integer. Each item $z_i$ has a value $v_i$ and a weight $w_i$. Finding a ...
8
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1answer
166 views

Simple path on dag with backward edges

What is the complexity of the following problem ($\in$ P? NP-hard?): Input: a directed acyclic graph $D=(V,E)$, a set of backward edges $E'\subset V\times V$, and two distinct nodes $s$ and $t$. ...
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votes
1answer
122 views

Travelling sales man with Quantum Computers [closed]

I know that it takes billions of years to solve the travelling sales man when n = 25 (Number of cities). I am wondering how fast can a quantum computer solve the travelling sales man problem (for ...
7
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2answers
313 views

Generalized Geography on graphs of bounded treewidth

Generalized Geography (GG) is played on a directed graph where a token is moved along arcs alternatively by two players. The vertices from which the token leaves are deleted. When a player cannot play ...
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0answers
61 views

What is the minimal known space for polytime algorithms

Let L be a language whose minimal running time is $O(n^k)$ do we know of any bounds on the minimal amount of space necessary to compute L other than the trivial $n^k$? Are there any conjectured ...
8
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2answers
268 views

The hardness of generating an instance of a problem that is harder than the complexity of the resulting problem

In the movie Inception Cobb asks a asks Ariadne to design a maze that takes twice as much time to design. This lends itself to a generalized problem where we have an situation where we are resource ...
4
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0answers
96 views

Complexity of a naive algorithm for finding the longest Fibonacci substring

I already posted this question here but I didn't receive an answer, so I'm posting it here as well :) Given two symbols $\text{a}$ and $\text{b}$, let's define the $k$-th Fibonacci string as ...
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1answer
119 views

Algorithm to determine if given algorithm runs in polynomial time [duplicate]

In general, the undecidability of the halting problem prohibits the general determination of an algorithm's complexity. However, I can see no reason why the halting problem prohibits one from deciding ...
2
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0answers
72 views

number of iterations of this algorithm (upper bound)

Let $(A, dist)$ be a finite metric space. Consider the following "$p$-center problem": given a positive integer $p$, find a subset $B$of $A$ such that $|B| = p$ and which minimizes the number $\max_{a ...
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1answer
357 views

Is the following problem in P or in NP?

Given an integer $K$, a set of tasks $T=\{a_1,b_1,\dots,a_n,b_n\}$ with sequence dependent execution times $E:T \times T \rightarrow \mathbb{N}$ and precedence constraints on $T$ of the following ...
6
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1answer
76 views

Quanitifier Free Presburger Arithmetic: Upper bound on solution size?

DISCLAIMER: I had originally posted this to CS.SE, but I've deleted it and moved it here, since it received little attention, and I think it is a research level question. According to this paper, if ...
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0answers
41 views

Computational complexity of Initial Value Problems of ODEs

Are there known results on computational complexity of initial value problems of ODEs? As my question may be somewhat vague, I want to mention that I'm mainly interested for results on the ...
2
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0answers
86 views

Is the problem “Binary Sorted Min Sum” already known under an other name?

A computer scientist oriented toward applications gave me the following problem: Given a positive integer $n>0$, an increasing function function $f$ and a decreasing function $g$, both ...
8
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1answer
259 views

DFA intersection algorithm for special cases

I'm interested in efficient algorithms for DFA intersection for special cases. Namely, when the DFAs to intersect obey a certain structure and/or operates on limited alphabet. Is there any source ...
8
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0answers
64 views

Finding a median in a union of sets given as sorted arrays [duplicate]

You are given $k$ sorted arrays $A_1, A_2, ..., A_k$, each containing $n$ elements. How fast can you compute the median of $A_1 \cup A_2 \cup ... \cup A_k$ ? I have a solution running in ...
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1answer
182 views

Finding $x_1,x_2,…,x_k$ such that $n=x_1!+x_2!+…+x_k!$ and $k$ is minimal [closed]

Here is a problem I'm trying to solve: Given an integer $n$ return a list $[x_1,x_2,...,x_k]$ such that $n=x_1!+x_2!+...+x_k!$ and $k$ is as low as it can be. I'm thinking of creating a list of n ...
7
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0answers
363 views

Time complexity of a branching-and-bound algorithm

Theoretical computer scientists usually use branch-and-reduce algorithms to find exact solutions. The time complexity of such a branching algorithm is usually analyzed by the method of branching ...
2
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0answers
172 views

Subset sum solver. Worth continue working on this method? [closed]

I have been working in a subset sum problem solver for some time. The implementation is an exact/exhaustive search solver. The variable determining the asymptomatic growth rate is just $N$ (the ...
5
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1answer
124 views

What is the worst-case runtime complexity to transform a NFA to DFA via Rabin-Scott's power set construction?

What is the worst-case runtime complexity to transform a NFA to DFA via Rabin-Scott's power set construction? Why? Details: http://en.wikipedia.org/wiki/Powerset_construction states that the ...
6
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0answers
72 views

Complexity of solving vs verifying in P

Thinking of (seemingly) very different complexity of finding a solution to a NP problem and verifying it as the basis of practical cryptography, I am wondering if such separation is possible among ...
2
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0answers
84 views

Recent insights on algorithms for 1D bin packing

This is just a general question on recent algorithms for the 1D bin packing problem. I just want to collect some information on this issue, so I’m grateful for any information. Especially heuristics ...
4
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3answers
100 views

Fast high-dimensional K-nearest neighbors

I'm aware of this question http://stackoverflow.com/questions/4350215/fastest-nearest-neighbor-algorithm But it's not the same question as I'm asking. Because, Octree and its generalization are only ...
6
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1answer
104 views

What's the complexity of recognizing equivalence for the following relation?

Consider the set $\mathcal{M}_{m,n}(\mathbb{Z})$ of $m$-by-$n$ matrices over, e.g., integers. We say that two matrices $A$, $B \in \mathcal{M}_{m,n}(\mathbb{Z})$ are equivalent if $A$ can be obtained ...
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42 views

Little o Notation [closed]

I understand the little-oh notation a bit, but there is still some confusion. By definition, I get that f ∈ o(g) means that |f(x)/g(x)| approaches 0 as x approaches infinity. I also read somewhere ...
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1answer
100 views

Using master theorem when there is a constant in the recursive term [closed]

Is it possible to use the master theorem to find the asymptotic growth of a function of the form: $$T(n) = aT(\frac{n}{b}+c)+f(n)$$ Where $c$ is a constant. Can we safely ignore this constant and use ...
6
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1answer
2k views

Magic constant to solve NP-complete problem in polynomial time

Let's suppose that $P\ne NP$. Is that possible to solve all the instances of size $n$ of an NP-complete problem in polynomial time using some "universal magic constant" $C_n$ that has a polynomial ...
6
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2answers
348 views

Complexity of finding even cuts for a graph

Given a graph $G=(V,E)$, what is known about the classical computational complexity of finding a non-trivial cut which partitions the vertices into two sets $V_a$ and $V_b$ such that every vertex in ...
7
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3answers
256 views

Total orders which are the transitive closure of a set in P

I am wondering if there is an example of the following form. It seems highly plausible that there should be but I am struggling to come up with one. Consider $T \subseteq \mathbb{N}^2$, a set ...
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36 views

Limits of parallel computing with local connections?

There are successes with an increasing numbers of individual computational units in GPUs or as processor cores. Given someone made the effort to build a huge array of processors which - however - can ...
2
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1answer
167 views

Max flow: either saturate an edge or avoids

Is there a way to create a max flow graph such that it satisfies the condition that a flow either saturates an edge or completely avoids it. It can't have half its flow through one edge and half ...
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1answer
190 views

Is the running time of Boyer-Moore linear?

With pattern length $M$, text length $N$, and alphabet $\Sigma$, is the asymptotic running-time of Boyer-Moore $O(N/|\Sigma|)$ (even when $M$ grows larger than $|\Sigma|$)? Are there any sublinear ...
2
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1answer
170 views

Time complexity of d-dimensional convex hull

Consider the convex hull problem in $\Re^d$: Input: a list of $n$ points $S$ in $\Re^d$, Output: the vertices of the convex hull of $S$. What is the best lower bound on the time complexity of ...
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134 views

proving speedup phenomenon does not apply to any open complexity class separations

Aaronson recently wrote a blog refuting the idea that there could be some "glitch" in the formulation of the P vs NP conjecture[1] which reminds me of this following question. the Blum speedup ...
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3answers
2k views

Examples of problems where exponential algorithms run faster than polynomial algorithms for practical sizes?

Do you know of any problems (preferably at least somewhat well known), where, for a practical problem size, an exponential algorithm runs much faster than a best-known polynomial time counterpart. ...
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2answers
210 views

What is the asymptotic time complexity of the number of steps of “Half Or Triple Plus One” ( HOTPO)?

The "Half Or Triple Plus One" process goes as follows: start with $x=n$ for some value of $n$ if ($x$ is odd) $x = 3x+1$ else $x = \frac{x}{2}$ if ($x$ > 1) goto (2) ...
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0answers
49 views

Known time complexity advantage of quantum algorithms over classical algorithms [duplicate]

I know that this question may depend on how one formulates each complexity class, but in general, what time complexity advantage does quantum algorithms have over classical algorithms?
2
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1answer
97 views

Efficient Shamir secret sharing reconstruction

Shamir's secret sharing scheme is a well known way to convert a secret into a polynomial and distribute points in this polynomial. Some of these points can then be regrouped to reconstruct the ...
0
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1answer
164 views

maximum weighted 2D coverage problem by a rectangle

Let $P=\{p_1,\ldots,p_n\}$ be a set of $n$ points in a 2D plane, that is $p_i\in \mathbb{R}^2$, $\forall i=1,\ldots,n$. Each point, $p_i$, is associated with a weight, $w_i \geq 0$. Imagine a ...
13
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4answers
367 views

What notable automaton models have polynomially-decidable containment?

I'm trying to solve a particular problem, and I thought I might be able to solve it using automata theory. I'm wondering, what models of automata have containment decidable in polynomial time? i.e. if ...
2
votes
1answer
124 views

Is there an additive time hierarchy theorem?

I would like something like this to be true: Conjecture: There is a function $g(n)$ such that for all functions $f(n)$ (perhaps satisfying some reasonable properties, like time-constructability), ...
4
votes
3answers
126 views

Remove unneeded atoms in CNF minimalization (SAT preprocessing)

This might be a very basic question. I am interested in all atoms of a propositional formula that can be removed from a particular formula, while the derived formula has the same satisfiability ...
4
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3answers
496 views

Is it possible to optimize the calculation of $ax+b$ once I know $a$ and $b$?

An "algorithm" for calculating $ax+b$ would take the steps Calculate $a$ times $x$ Calculate $b$ plus the result of previous line. But if the values of $a$ and $b$ are known, can we create a more ...
8
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233 views

Linear space language that requires exponential time without ETH

The $\mathsf{P} \neq \mathsf{PSpace}$ conjecture means that There is a language $L \in \mathsf{DSpace}(O(n^t))$ for some $t>0$ such that for all positive integers $k$, $L$ requires ...
3
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1answer
133 views

Example of context-free grammar that triggers exponential behaviour without memoization in RD parsers

It is often said that memoization brings the complexity of recursive-descent parsers from exponential to polynomial. However, I had a hard time finding an example grammar that triggers the exponential ...
1
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1answer
145 views

Why does the construction step of Aho-Corasick take linear time in the number of nodes?

The original paper's analysis of this, as far as I can tell is this: "THEOREM 3. Algorithm 2 requires time linearly proportional to the sum of the lengths of the keywords. PROOF. Straightforward." ...
8
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1answer
173 views

Multidimensional arithmetic progression variant

For $\vec{d} \in \mathbb{N}^n$, let $Q(\vec{d}) \subset \mathbb{N}^n$ be the set of vertices of the $n$-dimensional cube scaled in the direction of the $i$-th coordinate by $d_i$, i.e. $Q(\vec{d} = ...
2
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2answers
128 views

Number of SAT checks that are needed to find all combinations of subset of boolean variables of a propositional formula

Please mind that I sometimes lack formal mathematical knowledge and English is not my first language, so I might miss the right words. Please change the tile if needed. Also, I have choosen this site ...