As an example, look at what the AI consensus might have been 30 years ago for championship chess programs, and compare it to the massive database searches used by Deep Blue to pummel human opponents. I think you’ll find that things haven’t worked out quite the way they were expected to.

The feeling of the hoi polloi, of course, is that Artificial Intelligence is dead, and that’s probably the best thing that could happen to what is still a pretty exciting field. But it’s quite a rarity for the public to get a hands-on look at exciting developments in AI.

Unfortunately, the public beta of the Swingly search engine is not going to be the exception to this rule.
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In the case of New Zealand developer Philip Whitley, not understanding the Pigeonhole Principle led to a $NZ 5.3M fine, and up to five years in jail.
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These days the stakes are much higher when it comes to calculating the values of constants. Alexander Yee and Shigeru Kondo have just announced the calculation of pi to 5 trillion digits. And oddly enough, this was accomplished on a desktop machine running Windows server, not the Linux cluster I would have expected.

Here are some of key stats:

Operating System

Windows Server 2008 R2 Enterprise x64

Software

y-cruncher

Processor

2 Intel Xeon X5680 @3.33 GHz offering 24 hyperthreaded processors

Disk Space

The computation required roughly 22TB of disk space, and the compressed result takes another 3.8TB

Time

The task took 90 days to complete, and 66 hours to verify

The y-cruncher software package that broke this record also holds records for several other constants, including one trillion digits of e. So in 30 years, more or less, the desktop PC has gone from constant calculations under a million digits to over a trillion digits. That growth rate of 1.7x per year maps pretty well to Moore’s Law, suggesting that we can expect these numbers to continue climbing for at least a few more years.

Kudos to Alexander Yee and Shigeru Kondo on a smashing accomplishment!

The loose version of this principle says “After placing n pigeons into m compartments, if n is greater than m, you will find that some compartment must contain more than one pigeon.”

Seems obvious, and perhaps it is, but at least in the world of data compression it must be trotted out from time to time in order to bludgeon dreams back to reality.
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In honor of the often puzzling topics I’ve been working on, here’s a little crossword with an algorithms theme.

The java applet that lets you solve online has a bit of lameness, but it’s not mine and so it’s kind of out of my hands. I’d love to have a higher quality engine, but the free choices are limited. In particular, there doesn’t appear to be a free javascript crossword engine for the taking, so I’m stuck with Java, as are you.
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As I’ve confessed in the past, I’m a sucker for word puzzles. My recent post on a Will Shortz puzzle from NPR Morning Edition ended up provoking a surprising amount of comment, much of it in the vein of Watch me solve it better, faster, and with more style using language XXX.

I certainly enjoyed watching other people solve the problem, and found their solutions instructive. As the XP crowd has figured out, we programmers spend too much time working on our own problems and not enough time watching how other people work. There’s a lot to learn, both good and bad, from getting a peek inside another person’s head.

Out of the Blue

Which brings me to the puzzle at the center of this article.
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Finding the Convex Hull of a set of points is an interesting problem in computational geometry. It is useful as a building block for a diverse set of applications, including thing such as:

• Collision detection in video games, providing a useful replacement for bounding boxes.
• Visual pattern matching/object detection
• Mapping
• Path determination

Just as an example, if one of the Mars rovers has to chart a path around a boulder, the convex hull can be used to provide the shortest path past the obstacle, given a map that shows the points where the boulder abuts the ground.

This article will go over the definition of the 2D convex hull, describe Graham’s efficient algorithm for finding the convex hull of a set of points, and present a sample C++ program that can be used to experiment with the algorithm.

The Convex Hull

There are many ways to draw a boundary around a set of points in a two-dimensional plane. One of the easiest to implement is a bounding-box, which is a rectangle that spans the set from its minimum and maximum points in the X and Y planes.

Creating a bounding-box is easy, but it doesn’t form as tight a wrapper as we might like around a set of points. Consider the bounding box around the three points shown in Figure 1.

Figure 1 - A standard bounding box around three points

Figure 2 - A convex hull around the three points from Figure 1

This article discusses the use of C++ hash containers to improve storage of subproblem results when using dynamic programming (DP.) Memoization is a key part of dynamic programming, which is conventionally done by storing subproblem results in simple tables or lists. Using hash tables instead of these simpler structures will allow you to use dynamic programming while retaining your algorithm’s natural recursive structure, simplifying design and making your code easier to follow. I’ll provide a fully-developed example of an algorithm, and show how it can be adapted to use hash table memoization.
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Nobody wants to face the fact that Linux, Mac OS X, Microsoft Windows XP, and Vista are based on OS designs that are as old as the hills …

Meanwhile, none of these operating systems has the power to make multicore chips work as advertised. In the end, these chips are little more than novelties. Intel actually has the gall to claim that its extra cores can save power by automatically shutting down when they’re not in use. This just means they’ll be shut down most of the time. If the software could take advantage of these extra cores, there wouldn’t be any need to shut them down….

Why can’t operating systems simply dedicate extra cores to housekeeping chores and cool background tasks? It’s simple enough to work. Here are a few choice uses for core dedication. There are six of them, since we may see a six-core chip on the road ahead.

According to this piece in Wired, things are even more dire than that:

The problem is that many software applications weren’t written for chips with multiple cores, and the hardware is advancing so fast that the software runs the risk of being left behind.

“You can imagine a scenario where people stop buying laptops and PCs because we can’t figure this out,” said David Patterson, a computer-architecture expert and computer science professor at the University of California, Berkeley.

People are going to stop buying computers? Panic indeed!
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