# Questions tagged [worst-case]

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### Proof of SPFA's worst-case complexity?

I am trying to prove the worst-case asymptotic time complexity of the Shortest Path Faster Algorithm (SPFA). I know the complexity is the same as the "original" Bellman-Ford (BF) algorithm, ...
65 views

### Worst to average case reductions for quantum complexity classes

I am studying worst to average case reductions for different complexity classes. Consider quantum complexity classes like QMA, QSZK, or QIP. Is it known or believed that these classes are amenable to ...
74 views

### When was the dynamic array first used as an example for amortized analysis?

I'm writing a report on amortized analysis, and I'm using the example of a dynamic array to explain each method. I think it would be nice to add a reference to when this example was first used, as it ...
1 vote
133 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 ...
183 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-...
1k 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 ...
484 views

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 $... -2 votes 1 answer 365 views ### Are Graph and Group Isomorphism problems random self-reducible? Are Graph and Group Isomorphism problems known to be random self-reducible? If so is there a good proof? Are there other non-trivial examples of random self-reducibility? Is there a good reference? 14 votes 2 answers 4k views ### What is worst case complexity of number field sieve? Given composite$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(... 147 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 ...
2k 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. ...
133 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 ...
425 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 ...
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 ...