332 karma · joined November 12, 2012
Professor at UESTC, works on theoretical computer science and operations research.
Research interests: algorithms, combinatorial optimization, computational geometry and problem-solving in general.
It is reasonable enough to see what's happening, but obviously, I'm not going to watch a movie on that.
2. Visual snow syndrome: Many had their first experience of visual snow after staring into the screen for too long. People who believe in that is the cause of visual snow would want a screen that does not emit light.
It has a few different ways of display. For example: Floyd–Steinberg dithering: essentially only black and white with dithering, and the speed pretty good. A16: uses 16 shades of grey, but the speed is horrible for moving images. So I wonder if a mix of the two can do much better (e.g. moving objects using floyd-steinberg until it stops moving)
Before doing that, I need to know the exact limit of eink. Are some operations slow because the microcontroller or because it is the limit of the display module itself? This article shows such a question is not that easy to answer using the openly available information.
Also, I'm interested if there are algorithmic problems to be solved in this space. (I do research in theoretical computer science). If you are in NYC and knowledgeable I'm very interested to chat (I know little, but I have the monitor you can play with).
I had a similar problem in my earlier career, because I try to be as precise as possible. But for conciseness, I don't bother to explain anything. Later on I learned to say things in English, or give intuition, before writing out the formal definitions.
Fortunately, papers the reviewers cannot understand have a hard time getting into top conferences in my area (CS theory).
Otherwise, for people who learned functional programming from the start, it's much easier to understand.
If I teach an undergrad course, I would model after Michel Goemans's course. http://www-math.mit.edu/~goemans/18433S15/18433.html I will also introduce some submodular functions(and touches submodular flow). It captures half of the things encountered in the course, and general and simple enough to be the first thing to try. For example, the following problem might be difficult if one tries to create an algorithm by modify the standard matching algorithms. However, one can easily show it is polynomial time solvable by proving some submodular property.
http://cstheory.stackexchange.com/questions/20245/subset-of-...
Efficient Algorithms for Envy-Free Stick Division With Fewest Cuts http://arxiv.org/abs/1502.04048
The Algorithm Design Manual had the following(page ix in second edition) "Any errors, deficiencies, or problems in this book are somebody else’s fault, but I would appreciate knowing about them so as to determine who is to blame."
Hence the joke.
Source: Steve told me.
The hw is basically"given you've learned this, can you apply them?" I found many students like this style of problems.
I personally prefer the homework problems of Sariel har-Peled(who teaches in the same university, and I'm TAing for) http://sarielhp.org/teach/ His hw problems guides one to figure out important materials that's not covered in class by breaking it down to small steps. (Say, a hw problem that introduces parametric search) I definitely recommend solve some sariel style problems once one mastered the basic material.
But anyway, coin change problem can be solved much faster. http://link.springer.com/article/10.1007%2Fs00453-007-0162-8
If Σ(S) is the set of all subset sums of S, where S={s_1,...,s_n}, then
Σ(S) = Σ(s_1)+Σ(s_2)+...+Σ(s_n).
Here A+B = {a+b|a in A, b in B} + is associative and commutative. Now we want to add parenthesis on that formula in a way such that it is fast. Similar to matrix chain multiplication. We make sure + can be fast if certain property are satisfied(Theorem 2), and the rest is just figuring out the right way to add parenthesis.
One can transform the problem to the following, and solve it in around O(n^7) time. http://dl.acm.org/citation.cfm?id=73853
There probably exist faster algorithm for this special case using smarter parametric search...
I still don't know which field you are from, thus I kindly request you to give me a definite reference where convex hull is defined that way. I'm cornered in the world of computational geometry, and doesn't know how other fields use the word.
In fact, I don't even know what definition you are talking about. You said 'elastic band', but do you mean the 'elastic band' that bounds the points freely and somehow still convex(which is what the "convex hull" meant in the author's article), or do you mean the tightened 'elastic band'. Thus asking for seeing this definition is important for me to even understand what you are talking about.
"Perhaps you are not as knowledgeable about this field as you think." Perhaps. This is why having definitive references help.
This is the top 5 links that contains the definition of convex hull when I searched "convex hull" in google. (These exclude the wikipedia(wikibooks) pages because I have already use them)
1. http://mathworld.wolfram.com/ConvexHull.html (The convex hull of a set of points S in n dimensions is the intersection of all convex sets containing S.)
2. http://doc.cgal.org/latest/Convex_hull_2/ (A subset S⊆ℝ^2 is convex if for any two points p and q in the set the line segment with endpoints p and q is contained in S. The convex hull of a set S is the smallest convex set containing S. )
3. http://www.cs.uu.nl/docs/vakken/ga/slides1.pdf (For any subset of the plane (set of points, rectangle, simple polygon), its convex hull is the smallest convex set that contains that subset)
4. http://www.cs.jhu.edu/~misha/Fall05/09.13.05.pdf (Given a finite set of points P={p1,…,pn}, the convex hull of P is the smallest convex set C such that P⊂C)
5. http://geomalgorithms.com/a10-_hull-1.html (The most common form of this algorithm involves determining the smallest convex set (called the "convex hull") containing a discrete set of points.)
All of the definitions are not equivalent to the authors, but equivalent(or a special case when restricted to finite set/R^2) to each other. I also have book excerpts if you really need them.
"I found it rude of you to simply trash the author's article when they spent time preparing an extremely good resource" I did not have object of their work, just particular terminology. I pointed out specific flaws in the article and constructively offered how to fix them. In fact it took out a huge amount of my time in order to come up with equivalent definition that also preserve the author's intuition. My definition is not obviously equivalent to the ones I presented above. It requires a proof, and I can only prove the case when there is only a finite number of points, which works great because that's the exact case the author is thinking about.
" - and I don't agree that your correction was useful. " If you always take convex hull of a set of point S to mean "a convex curve that bounds a set of points S" then you won't think the correction is useful because my definition doesn't equal yours.
"You did the author a disservice on that site and should consider an apology." I do not agree.
But in standard terminology, convex hull of a set S is the smallest convex set containing the set of points. The convex hull is always minimal because it's unique.
The name convex hull is related to linear hull and conic hull, therefore defining it to not contain the interior is strange, but reasonable because in many applications we only care about the description of the convex hull by describing the polygon.