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vzn
vzn
02:23
re group ad. isnt something better than nothing?
Analysis paralysis or paralysis of analysis is an anti-pattern, the state of over-analyzing (or over-thinking) a situation so that a decision or action is never taken, in effect paralyzing the outcome. A decision can be treated as over-complicated, with too many detailed options, so that a choice is never made, rather than try something and change if a major problem arises. A person might be seeking the optimal or "perfect" solution upfront, and fear making any decision which could lead to erroneous results, when on the way to a better solution. The phrase describes a situation where the...
02:58
0
Q: What's the dual problem of stable matching?

xiamxSo the dual problem of max-flow is min-cut. What's the dual problem of stable matching?

 
5 hours later…
08:05
@xiamx I was just about to post this. Should we close it? It's what we call a "dump": what have you tried, where did you get stuck?
08:58
hi
 
5 hours later…
13:37
@A.r.Naresh hi!
 
5 hours later…
18:45
Trying to play with symbols. If $T=\{T_i\}$ is the set of running times of every possible algorithm that solves a given problem $P$. Can we say that an algorithm $j$ is optimal if $T_j=\sup T$?
@Raphael
@saadtaame $\inf$, rather?
More importantly: optimal wrt what measure?
@saadtaame You could, then it's perhaps only optimal in terms of time
For other measures, we can use other sets.
But I think typically you'd simply show an (asymptotic) lower bound, and then give an algorithm achieving that bound. Then you could just claim you have an algorithm that is optimal, or in other words, the runtime of the algorithm can only be improved by constant factors
Now the question is: are there sets that are countable, uncountable?
@Juho
18:58
Huh? In general, yes. So what do you mean? How are you building your set?
No, I'm just asking if it's possible
@saadtaame Do these questions relate at all?
No, just curious
If your question is "are there countable and uncountable sets?" the answer is yes
(Note that \sup T may not exist, depending on your measure. There is always an algorithm that is faster on infinitely many inputs.)
19:00
How does that algorithm work, just returns the answer?
@Raphael
For finitely many, it's clear: store some values in a table, yes.
For infinitely many, I don't quite remember the proof. It may not have been constructive.
9
Q: Decision problem such that any algorithm admits an exponentially faster algorithm

RaphaelIn Hromkovič's Algorithmics for Hard Problems (2nd edition) there is this theorem (2.3.3.3, page 117): There is a (decidable) decision problem $P$ such that for every algorithm $A$ that solves $P$ there is another algorithm $A'$ that also solves $P$ and additionally fulfills $\qquad \forall...

@Raphael I, perhaps naively, thought we had already voted on and decided the issue of the homework policy. Frankly, I've seen behavior lately that goes against the policy, and I have taken action where I felt it was appropriate. We can rehash this old debate, but I'm not sure any of our positions have changed... but if you think there's a new audience, or that others' minds have been changed, we can definitely go through this again.
@Patrick87 In regard to what is this?
@saadtaame Were you successful with the planning problem?
@Raphael That seems really counter-intuitive indeed. Is that even true? From the abstract of the Blum paper: "We show that there is no effective procedure for going from an algorithm for f to another algorithm for f that is significantly faster on all but a finite number of inputs."
Doesn't that kinda sound like no, actually?
19:20
@Juho I took Kaveh's word on it. The sentence you cite does only say that we can't compute the faster algorithm, not that it does not exist.
Quite true of course
Tone of the phrase "problem dump" aside, I question the underlying assumption that all "problem dumps" are bad and bad for this site. Closing (or putting on hold, whatever they call it now) is an acceptable interim solution, but questions should get comments explaining how to make them suitable. I can't imagine any homework questions, copied verbatim from a textbook or otherwise, that would be of such low quality that they'd add no value here. Academic misconduct is not any more our concern than it is the police department's concern whether you brush your teeth twice a day. — Patrick87 8 mins ago
@Patrick87 The problem is that we don't know the question from a dump.
I can give the answer to the problem, but that does not (really) help the "asker".
(And they are a problem for a site of our size if they are allowed to take over, but you may disagree on that count.)
vzn
vzn
19:36
@Juho blums thms have long interested me. however they apparently deal with "pathological fns" acc to some (eg goldreich)
the proofs seem to possibly not apply to "time constructible" fns typically used for complexity analysis.
have always wanted more detail on how blums thms relate to actual day-to-day complexity use.
In complexity theory, a time-constructible function is a function f from natural numbers to natural numbers with the property that f(n) can be constructed from n by a Turing machine in the time of order f(n). The purpose of such a definition is to exclude functions that do not provide an upper bound on the runtime of some Turing machine. Time-constructible definitions There are two different definitions of a time-constructible function. In the first definition, a function f is called time-constructible if there exists a positive integer n0 and Turing machine M which, given a string 1n cons...
@Patrick87 Also, regarding "I can't imagine any homework questions, copied verbatim from a textbook or otherwise, that would be of such low quality that they'd add no value here." -- how does e.g. this one add anything? It's basic arithmetics in disguise of a computer engineering problem. And it's not alone.
@Patrick87 I'd appreciate it if we could discuss specific instances where you think wrong action was taken, instead of a general sentiment.

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