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1500 questions
13
votes
1 answer
Generate scale-free networks with power-law degree distributions using Barabasi-Albert
I'm trying to reproduce the synthetic networks (graphs) described in some papers.
It is stated that the Barabasi-Albert model was used to create "scale-free networks with power-law degree distributions, $P_A(k) ∝ k^{-λ}$".
$P_A$ is a probability…
Agostino
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13
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2 answers
Time Complexity proof for Segment Tree implementation of the ranged sum problem
I understand that segment trees can be used to find the sum of sub array of $A$. And that this can done in $\mathcal{O}(\log n)$ time according to the tutorial here.
However I'm not able to prove that the querying time is indeed $\mathcal{O}(\log…
Arijit Choudhury
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13
votes
5 answers
is it possible to minimize pushdown automata?
is it possible to minimize pushdown automata?
If no, why?
Is it because for minimization the equivalence classes need to have a finite index and we cannot guarantee that for CFG?
Tom J.
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13
votes
0 answers
Choosing a subset of binary variables to maximize the sum of the highest $K$
Consider the following problem:
Input:
integers $n > m > k$;
$n$ numbers $0 \leq p_1, \ldots, p_n \leq 1$;
$n$ numbers $r_1, \ldots, r_n$ where ($r_i \geq 0$).
Let $X_1,\dots,X_n$ be $n$ independent random variables with distribution $X_i \sim…
Scarlet
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13
votes
2 answers
Group isomorphism to graph ismorphism
In reading some blogs about computational complexity (for example here)I assimilated the notion that deciding if two groups are isomorphic is easier than testing two graphs for isomorphism. For example, on the stated page it says that graph…
Jernej
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13
votes
3 answers
Why Term Rewriting?
I've done a bit of googleing and have come up a bit short.
I am wondering what are the main reasons for computing scientists, programmers,
to study term rewriting, and/or term graph rewriting.
As far as I can tell, it just helps for basic reasoning…
Musa Al-hassy
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13
votes
4 answers
Has the graph isomorphism problem been solved?
Wikipedia's graph isomorphism problem page would seem to indicate that, no, it has not been solved. However, a friend of mine pointed out A Polynomial Time Algorithm for Graph Isomorphism . I am not sophisticated enough to follow the reasoning in…
Tyler Spaeth
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13
votes
1 answer
NP-complete proof from Dasgupta problem on Kite
I am trying to understand this problem from Algorithms. by S. Dasgupta, C.H. Papadimitriou, and U.V. Vazirani, chapter8, Pg281. Problem 8.19
A kite is a graph on an even number of vertices, say $2n$, in which $n$ of the vertices form a clique
and…
John
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13
votes
4 answers
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" which gave me this but it is too mathy. I just want a…
Nathvi
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13
votes
4 answers
NFA with exponential number of states when determinized
How can I build an example of a regular language where the minimal DFA has $2^n$ states and the minimal NFA has $n$ states? Obviously the DFA's state-set should contain all subsets of the the NFA's state-set, but I don't know how to start. Any…
mrk
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13
votes
1 answer
Why aren't we researching more towards compile time guarantees?
I love all that is compile time and I love the idea that once you compile a program a lot of guarantees are made about it's execution. Generally speaking a static type system (Haskell, C++, ...) seems to give stronger compile-time guarantees than…
sh03
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13
votes
2 answers
Is there an efficient algorithm for expression equivalence?
e.g. $xy+x+y=x+y(x+1)$ ?
The expressions are from ordinary high-school algebra, but restricted to arithmetic addition and multiplication (e.g. $2+2=4; 2.3=6$), with no inverses, subtraction or division. Letters are variables.
If it helps, we can…
hyperpallium
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13
votes
9 answers
What exactly is an algorithm?
I know that this may sound a bit out of the box, in fact i used to always think inside the box, but recently i've been thinking, possibly because computer science provides an high degree of freedom, about ways to devise programs other than the ones…
Devian Dover
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13
votes
1 answer
Are all system calls blocking?
I was reading an article that describes the switch between user-space and kernel-space that happens upon a system call. The article says
An application expects the completion of the system call before resuming user-mode execution.
Now, until now…
Ankit
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13
votes
3 answers
Why larger input sizes imply harder instances?
Below, assume we're working with an infinite-tape Turing machine.
When explaining the notion of time complexity to someone, and why it is measured relative to the input size of an instance, I stumbled across the following claim:
[..] For example,…
user20