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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How to find the asymptotically tight upper bounds for T(n) in the recurrences?

I am wonder how to exactly find the tight upper bound for T(n)? for one example below: T(n)=T( n/2 + n(1/2)) + n. I am not sure can I approximately consider T(n) as T(n)=T( n/2 ) + n. ...
-2
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44 views

Running time on deterministic vs non-deterministic Turing machine [on hold]

I came across the following statement: If a program $P$ for Non Deterministic Turing Machine solves a decision problem in time limited by a polynomial $p(S)$, where $S$-size of instance, then it can ...
3
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1answer
336 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 ...
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1answer
61 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
35 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 ...
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0answers
82 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
196 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
166 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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117 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
136 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
94 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 ...
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69 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
60 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 ...
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3answers
89 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
101 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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36 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
96 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
343 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 ...
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3answers
250 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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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
160 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
178 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
160 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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129 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
1k 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
198 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?
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44 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 ...
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1answer
125 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 ...
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4answers
356 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
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1answer
120 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
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3answers
118 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
369 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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209 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
102 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 ...
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1answer
109 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
167 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
115 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 ...
6
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1answer
226 views

Distinguishing between two coins

It is well known that the complexity of distinguishing an $\epsilon$ biased coin from a fair one is $\theta(\epsilon^{-2})$. Are there results for distinguishing a $p$ coin from a $p+\epsilon$ coin? I ...
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2answers
262 views

Lower-bound of a decision problem [closed]

What's the lower-bound of the decision problem that decides: Whether there is at least one element A[i] such that A[i] = i in a sorted array A of non-negtive integers? (An example is A = ...
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0answers
21 views

What's the official name for time-driven parallel informed sorting methods?

If you have a set $\Delta = \{A,B,C,D,E,...\}$ and you want to sort $\Delta$ based on a certain quality of the elements $\in \Delta$, then you can use a certain classification or ranking algorithm $R$ ...
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476 views

Most efficient algorithm to search an unsorted array with a very precise data structure

(I apologize in advance if this question sounds a bit practical, but I suspect it might have an interesting theoretical aspect.) I have a (large) array of data, not completely sorted, but with which ...
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197 views

Does Kannan's theorem imply that NEXPTIME^NP ⊄ P/poly?

I was reading a paper of Buhrman and Homer “Superpolynomial Circuits, Almost Sparse Oracles and the Exponential Hierarchy”. On the bottom of page 2 they remark that the results of Kannan imply that ...
8
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1answer
168 views

Consequences of nondeterminism speeding up deterministic computation

If $\mathsf{NP}$ contains a class of superpolynomial time problems, i.e. for some function $t \in n^{\omega(1)}$, $\mathsf{DTIME}(t) \subseteq \mathsf{NP}$, then if follows from the ...
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0answers
194 views

Does $P\neq NP$ imply any larger separation?

I've asked a similar question in cs.se, but didn't get a satisfying answer. Assuming $P\neq NP$, what can we say about the runtime of any algorithm for an $NP$-complete problem? Obviously, it means ...
4
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0answers
119 views

Deciding transitivity of a directed acyclic graph [duplicate]

Is there any algorithm that decides whether a given directed acyclic graph is transitive or not, in time-complexity asymptotically better than boolean matrix multiplication?
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3answers
1k views

How much time to recognize palindromes in logarithmic space?

It is well-known that palindromes can be recognized in linear time on $2$-tape Turing machines, but not on single-tape Turing machines (in which case the time needed is quadratic). The linear-time ...
4
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1answer
63 views

Complexity of generically inverting a class of near linear monotonic functions

Given a monotonic increasing function $f(\mathbb{N}) \rightarrow \mathbb{N}$ and a slack function $a(\mathbb{N})\rightarrow \mathbb{N}$, where $f(n) = n \pm O(a(n))$; how many calls to $f$ do we ...