a couple thoughts:

1) approximate randomized algorithms are your friend, especially when we talk about things like (RAN|MAP|MLE|M)SAC in model fitting. for some classes of problems, random approximate algorithms are the *only* attack that we have that are feasible in terms of time/space complexity.

2) your analysis fails to account for the hidden leading constant (otherwise there's no reason to consider quicksort when you have heapsort) and what happens when N gets to be large enough. the fact is that for big enough N or big enough S, the lower order algorithms will start to become dramatically faster, even if repeated applications are necessary to cross-validate results.

3) unless you're using arbitrary precision math, all of these algorithms are approximate anyway and great care must be taken to understand how these systems can be (pre)conditioned to minimize the compounded effects of fixed precision arightmetic.

touche.

how so?

let me summarize: the same math that drives google's search (spectral graph theory) has been shown to be really useful in solving a very common class of linear equations if you're willing to roll the dice (randomize algorithm).

not really.

the method applies to the _general_ (i.e. dense) case of diagonally dominant (i.e. |A_i,i| > |A_i,j| for all i,j) symmetric systems that show up all the time (grammian matrices, for example), not just the sparse case.

give me $30k in consulting fees and i'll tell you who to hire.

i was going to ask the same question. i've worked on projects where the idl generates about 100k sloc just by itself. add in all the other custom code generation and up that by another 200k lines.

here's the problem: every day, i make pretty heavy use of machine learning and the other bits and pieces that collectively get referred to as artificial intelligence. as a consequence, i deal with a very large number of fools who are each convinced that their $ALGORITHM is an earth shattering new paradigm for $TASK and clearly is the best thing evar. so you start reading and you realize that in 99.999% of cases, you're staring at something that is some combination of:

a) based on a fundamentally broken assumptions (usually never even stated)
b) bad analogies that obfuscate the fact that wheels are being re-invented (usually poorly)
c) narrowly defined special case
d) broken (provably non-optimal optimization routines)

that rare 0.001% for me consists of things like the ransac family of meta-algorithms, mean-shift tracking, markov random fields, quadratic correlation filters, and support vector machines.

the latter. the former would require, amongst other things, access to the source code (as required by the original critterdings license) and a lot of noise coming from the biological disciplines re: computationally tractable, useful models for the various signaling pathways involved in hallucinogen use.

exactly, although i suspect that the right answer depends on the kind of person you are.

for me, very few things piss me off more quickly than getting a request to stay late to finish something for a deadline without even a hint of an offer of help from my management. this usually means i turn into the bad guy asking my team to work extra hours to deal with the most recent crisis caused by one of the other teams on our project (conveniently located elsewhere in the country and impossible to contact after 4pm eastern) screwing up.

Quick: who are Robert Tarjan, Edsgar Dijkstra, Robert Floyd and Stephen Warshall and why would you care about their work?

Which brings me to my point: if you don't know what you're looking for, all the references in the world are essentially useless to you.

If I ever meet a person with DeVry / ITT / etc. "credentials" who has done any of the following:

(a) designed fully decentralized, distributed, scalable, robust, real-time systems and successfully implemented and deployed said systems in the real world
(b) built a compiler from the tokenizer up and understands every step of how code gets turned into bits and how those bits get executed on modern hardware
(c) had an opportunity to use Tarjan's disjoint union / find algorithms and can explain where those data structures / algorithms are appropriate

I'd be interested in hiring him/her. The problem is that I have yet to meet such a person, because DeVry / ITT / etc. are degree mills whose sole purpose is to get as many people to cross the lowest possible bar that could pass accreditation -- i.e. turn a profit. As a consequence, the DeVry / ITT / etc. grads that I've had the "pleasure" of working with all have very narrow and shallow areas of competency and essentially zero ability to work outside those areas. The benefit of a four year degree is that in spite of all the fluff:

(a) you have a far better opportunity to actually cover the full breadth of theory
(b) there is enough time to mature enough intellectually to start to grok the zen nature of the theory
(c) you can't really choose between theory and practice; you have to demonstrate a degree of proficiency in both

one of the benefits of an ironkey --- when you're done washing it, it will will both smell good *and* continue to work.

not saying that it's necessarily worth the $350 odd for a 4gb stick tho...