Questions tagged [worst-case]
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12
questions
1
vote
0answers
46 views
Asymptotic time required to simulate a Turing machine M for k steps
Problem: Given an encoding of a Turing machine M and a natural number k as input, find the output of M (given a blank tape) after k steps.
Wikipedia's page on EXPTIME-complete says it takes O(k) time ...
4
votes
0answers
127 views
Worst-Case and Average-Case running-time equal with universal p-distribution with kolmogorov-complexity any applications of this theory?
at the moment I'm reading "Gems of Theoretical Computer Science" from Schöning and Pruim.
In Chapter 8 the book defines a "universal probability distribution" in a way that the Average-Case running-...
27
votes
3answers
894 views
Did “Where the really hard problems are” hold up? What are current ideas on the subject?
I found this paper to be very interesting. To summarize: it discusses why in practice you rarely find a worst-case instance of a NP-complete problem. The idea in the article is that instances usually ...
6
votes
2answers
402 views
How powerful is $ACC^0$ circuit class in average case?
We know that $NEXP$ is not in $ACC^0$ .
Does the result that $NEXP$ is not in $ACC^0$ also hold in average case?
That is given a boolean function in $NEXP$ is it known that for every input length $...
-3
votes
1answer
277 views
Are Graph and Group Isomorphism problems random self-reducible?
Are Graph and Group Isomorphism problems known to be random self-reducible? If so is there a good proof?
Are there other non-trivial examples of random self-reducibility? Is there a good reference?
12
votes
2answers
2k views
What is worst case complexity of number field sieve?
Given composite $N\in\Bbb N$ general number field sieve is best known factorization algorithm for integer factorization of $N$. It is a randomized algorithm and we get an expected complexity of $O\Big(...
3
votes
1answer
132 views
Number of different longest common substrings
Given an alphabet $\Sigma$ of size $k$ and two strings $w_1,w_2\in \Sigma^n$ of length $n$. The longest common substring problem asks for a longest string in the set $A(w_1,w_2)$ of all common ...
22
votes
3answers
1k views
Justifying asymptotic worst-case analysis to scientists
I've been working on on introducing some results from computational complexity into theoretical biology, especially evolution & ecology, with the goal of being interesting/useful to biologists. ...
3
votes
2answers
131 views
How well can we do with this variable assignment problem?
Given in this problem is a set of values $0 \le c_{a,b} < n$, where $0 \le a < n$ and $0 \le b < n$.
The problem is to find the following sum as quickly as possible:
$$\sum_{a,b}{c_{a,b}x^a ...
7
votes
2answers
402 views
What are the current best upper bounds of #P?
#P is the class of counting problems for problems in NP. In other words, a solution to #P returns the number of solutions to a particular problem in NP.
I'm wondering if there have been any studies ...
21
votes
1answer
737 views
How close can we get to linear multiply, add, and compare (on integers)?
Accoring to K. W. Regan's article "Connect the Stars", he mentions at the end that it is still an open problem to find a representation of integers such that the addition, multiplication, and ...
9
votes
1answer
928 views
What is the worst case of the randomized incremental delaunay triangulation algorithm?
I know that the expected worst-case runtime of the randomized incremental delaunay triangulation algorithm (as given in Computational Geometry) is $\mathcal O(n \log n)$.
There is an exercise which ...
