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Know Your Algorithms


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Dear KV,

My team and I are selecting a new server platform for our project and trying to decide whether we need more cores or higher-frequency CPUs, which seems to be the main trade-off to make on current server systems. Our system is deployed on the highest-end systems and, therefore, the highest-frequency systems we could buy two years ago. We run these systems at 100% CPU utilization at all times. Our deployment does not consume a lot of memory, just a lot of CPU cycles, and so we are again leaning toward buying the latest, top-of-the-line servers from our vendor. We have looked at refactoring some of our software, but from a cost perspective, expensive servers are cheaper than expensive programmer time, which is being used to add new features, rather than reworking old code. In your opinion, what is more important in modern systems: frequency or core count?

Richly Served

Dear Served,

I really wish I knew who your vendor is, so I could get a cut of this incredibly lucrative pie. As the highest-end servers currently enjoy a massive markup, your salesperson probably appreciates every time you call.

The short answer to your question about frequency vs. core count is, "You tell me." It seems as if you have spent little or no time trying to understand your own workload and have simply fallen for the modern fallacy of "newer will make it better." Even apart from the end of frequency scaling, it has rarely been the case that just adding more oomph to a system is the best way to improve performance. The true keys to improving performance are measurement and an understanding of algorithms.

Knowing your CPU is in use 100% of the time does not tell you much about the overall system other than it is busy, but busy with what? Maybe it is sitting in a tight loop, or someone added a bunch of delay loops during testing that are no longer necessary. Until you profile your system, you have no idea why the CPU is busy. All systems provide some form of profiling so you can track down where the bottlenecks are, and it is your responsibility to apply these tools before you spend money on brand-new hardwareespecially given how wacky new hardware has been in the past five years, particularly as a result of NUMA (non-uniform memory access) and all the convoluted security mitigations that have sapped the life out of modern systems to deal with Spectre and the like. There are days when KV longs for the simplicity of a slow, eight-bit microprocessor, something one could understand by looking at the stream of assembly flying by. But those days are over, and, honestly, no one wants to look at cat videos on a Commodore 64, so it is just not a workable solution for the modern Internet.

Since I have discussed measurement before, let's discuss now the importance of algorithms. Algorithms are at the heart of what we as software engineers do, even though this fact is now more often hidden from us by libraries and well-traveled APIs. The theory, it seems, is that hiding algorithmic complexity from programmers can make them more productive. If I can stack boxes on top of boxeslike little Lego bricksto get my job done, then I do not need to understand what is inside the boxes, only how to hook them together. The box-stacking model breaks down when one or more of the boxes turns out to be your bottleneck. Then you will have to open the box and understand what is inside, which, hopefully, does not look like poisonous black goo.

A nuanced understanding of algorithms takes many years, but there are good references, such as Donald Knuth's book series, The Art of Computer Programming, which can help you along the way. The simplest way to start thinking about your algorithm is the number of operations required per unit of input. In undergraduate computer science, this is often taught by comparing searching and sorting algorithms. Imagine that you want to find a piece of data in an array. You know the value you want to find but not where to find it. A naive first approach would be to start from element 0 and then compare your target value to each of the elements in turn. In the best case, your target value is present at element 0, in which case you have executed a very small number, perhaps only one or two instructions. The worst-case scenario is that your target element does not exist at all in the array and you will have executed many instructionsone comparison for every element of the arrayonly to find that the answer to your search is empty. This is called a linear search.


Personally, I never bother with the best case, because I always expect that, on average, everything will be worst case.


For many data structures and algorithms, we want to know the best, worst, and average number of operations it takes to achieve our goal. For searching an array, best is 1, worst is N (the size of the array), and average is somewhere in the middle. If the data you are storing and searching is very smalla few kilobytesthen an array is likely your best choice. This is because even the worst-case search time is only a few thousand operations, and on any modern processor, that is not going to take a long time. Also, arrays are very simple to work with and understand. It is only when the size of the dataset grows into megabytes or larger that it makes sense to pick an algorithm that, while it might be more complex, is able to provide a better average number of operations.

One example might be to pick a hash table that has an average search time of one operation and a worst search time of Nagain the number of elements in the table. Hash tables are more complex to implement than arrays, but that complexity may be worth the shorter search time if, indeed, searching is what your system does most often. There are data structures and search algorithms that have been developed over the past 30 years with varying performance characteristics, and the list is too long, tedious, and boring to address in depth here. The main considerations are how long does it take, in the best, worst, and average cases, to:

  • Add an element to the data structure (insertion time).
  • Remove an element.
  • Find an element.

Personally, I never bother with the best case, because I always expect that, on average, everything will be worst case. If you are lucky, there is already a good implementation of the data structure and algorithm you need in a different box from the one you are using now, and instead of having to open the box and see the goo, you can choose the better box and move on to the next bottleneck. No matter what you are doing when optimizing code, better choice of algorithms nearly always trumps higher frequency or core count.

In the end, it comes back to measurement driving algorithm selection, followed by more measurement, followed by more refinement. Or you can just open your wallet and keep paying for supposedly faster hardware that never delivers what you think you paid for. If you go the latter route, please contact KV so we can set up a vendor relationship.

KV

q stamp of ACM QueueRelated articles
on queue.acm.org

KV the Loudmouth
https://queue.acm.org/detail.cfm?id=1255426

10 Optimizations on Linear Search
Thomas A. Limoncelli
https://queue.acm.org/detail.cfm?id=2984631

Computing without Processors
Satnam Singh
https://queue.acm.org/detail.cfm?id=2000516

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Author

George V. Neville-Neil (kv@acm.org) is the proprietor of Neville-Neil Consulting and co-chair of the ACM Queue editorial board. He works on networking and operating systems code for fun and profit, teaches courses on various programming-related subjects, and encourages your comments, quips, and code snips pertaining to his Communications column.


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