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On modern hardware the min-max heap beats a binary heap

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Re: On modern hardware the min-max heap beats a binary heap

#11

I have used a min-max heap once. I don't remember why I needed it at the time--it was a previous job--but I do remember that I had to roll my own, because it's just not that popular of a data structure, and it was the obvious and only good solution to the problem at the time. So, it's nice to see a detailed analysis of the structure like this! Perhaps if it becomes more popular, I will find more places to use it.

I used a min heap in a FANG interview. It's an obvious/good solution if the problem has a mix of reading/removing the smallest number in a data structure and writing new numbers to the data structure.

Re: On modern hardware the min-max heap beats a binary heap

#12
post #11

I have used a min-max heap once. I don't remember why I needed it at the time--it was a previous job--but I do remember that I had to roll my own, because it's just not that popular of a data structure, and it was the obvious and only good solution to the problem at the time. So, it's nice to see a detailed analysis of the structure like this! Perhaps if it becomes more popular, I will find more places to use it.

I used a min heap in a FANG interview. It's an obvious/good solution if the problem has a mix of reading/removing the smallest number in a data structure and writing new numbers to the data structure.

A min heap is different from a min-max heap. A min-max heap supports the operations of both a min heap and a max heap (essentially by interleaving the two). A normal min heap is a standard data structure, a min-max heap less so.

Re: On modern hardware the min-max heap beats a binary heap

#13
post #10

Earlier quoted context omitted.

Surely you should ve able to just use a different comparator instead (> instead of <).

Not in python! But I guess using negatives is the same as using different key (which is what python uses instead of comparators). The real problem is if you need min/max at the same time. Then you not only need a min heap and max heap, you also need to track what was already popped from either heap! This is because in python you can't delete an element if it's not at the root. So tracking "tombstones" will let you po…

Sounds like python is not batteries included compared to other languages in this regard!

Re: On modern hardware the min-max heap beats a binary heap

#14
And if you only need a monotone priority queue (i.e. priority queue where the popped elements are monotonically increasing/decreasing) you should consider using a radix heap. This monotone requirement can be satisfied more than you would expect when eg. using time as key or in pathfinding. I have a simple radix heap implementation here: https://github.com/mpdn/radix-heap

Re: On modern hardware the min-max heap beats a binary heap

#15

I have used a min-max heap once. I don't remember why I needed it at the time--it was a previous job--but I do remember that I had to roll my own, because it's just not that popular of a data structure, and it was the obvious and only good solution to the problem at the time. So, it's nice to see a detailed analysis of the structure like this! Perhaps if it becomes more popular, I will find more places to use it.

IIRC it's used in chess programs to evaluate moves.

Re: On modern hardware the min-max heap beats a binary heap

#16

It would be neat to fire this up on an older processor which doesn’t have modern instruction-level parallelism and verify the difference in performance

On x86 you'd have to search pretty far back before the available ILP really dropped off. Some of the lower-end OoO ARMs might be a good testing ground, though. Say, a Raspberry Pi 4? Earlier-gen RPi used in-order cores.

Re: On modern hardware the min-max heap beats a binary heap

#17
post #5

In certain domains, the trend has been to give up constant factors in order to increase programmer productivity (e.g., python pays a 10x slowdown but is batteries included). So in that case I would use this data structure even if it weren't faster. I can't count the number of times I have had to mess with inserting negative priorities into a min heap to create a max heap! We should just have one data structure that d…

So, kind of a non sequitur, but I occasionally think about Qt's QList. When introduced, it was odd for reserving space at the beginning as well as the end, so you had constant-time inserts/removals at the beginning. That and storing pointers for any T larger than a pointer also reduced the constant factor on insertion/deletions from the middle. Since it was always stored as a list of pointer-sized items, some code could be shared between implementations for different types, so your program's binary could be a bit smaller. I think they said at the initial release that they benchmarked a bunch of options in some real code and this won.

That was waaay at odds with the mindset of the STL, which seemed to me and I think a lot of folks like the state-of-the-art of containers at the time: with the STL if you prepend/insert much you need to use a deque/linked list, you decide pointer vs. value each time you declare a type, and if you want to know about the constant factor on an insert in the middle of the list you probably already lost.

(Qt has/had some other fun pragmatic things, like copy-on-write types in a lot of places. I didn't really do nearly enough with it to discover the pitfalls, but was fun to read.)

So I think about that, about how there are likely some trees out there that could just as well be sorted arrays, about adaptive structures that change their behavior based on dynamically observing how they're used (one recently discussed here: http://blog.erlang.org/the-new-scalable-ets-ordered_set/), even about tricks in in JS string implementations and VMs. I don't have answers, but I sometimes wonder if we should be thinking more in terms of tools that may not be perfect on all axes but soften or eliminate performance cliffs we take for granted. Not that the zero-overhead fine-tuned types are going away, just that they aren't the only imaginable approach.

I wonder if we'll see progress in those sort of imperfect-but-resilient tools over time. I think the long-run trend is towards some form of programming being accessible to more people more easily (like how, as you note, folks do real work in Python now). That certainly fits with trying to make your tools resilient to "misuse"--or, better, properly supporting more patterns so they're not even misuse. No conclusions, just hand-waving, but I do wonder if anyone working in software construction tools will eventually more usefully wave their hands in that direction :P

Re: On modern hardware the min-max heap beats a binary heap

#18
post #5

In certain domains, the trend has been to give up constant factors in order to increase programmer productivity (e.g., python pays a 10x slowdown but is batteries included). So in that case I would use this data structure even if it weren't faster. I can't count the number of times I have had to mess with inserting negative priorities into a min heap to create a max heap! We should just have one data structure that d…

So, kind of a non sequitur, but I occasionally think about Qt's QList . When introduced, it was odd for reserving space at the beginning as well as the end, so you had constant-time inserts/removals at the beginning. That and storing pointers for any T larger than a pointer also reduced the constant factor on insertion/deletions from the middle. Since it was always stored as a list of pointer-sized items, some code c…

You would probably enjoy reading about an alternative implementation for STL's std::deque, called a tier vector[1][2].

It supports O(1) push_front/pop_front/push_back/pop_back/operator[]/at (like you would expect from a deque) but also O(sqrt(N)) insert and remove from middle!!!

The paper was from 1999 and 2001 but I only learned about it from a recent HN post[3] where some guy rediscovered it (20 years too late). I still wonder why this design lost to the std::deque we have in STL today.

[1] http://www.cphstl.dk/Report/Deque-first-attempt/cphstl-repor...

[2] https://www.ics.uci.edu/~goodrich/pubs/wads99.pdf

[3] https://news.ycombinator.com/item?id=20872696

Re: On modern hardware the min-max heap beats a binary heap

#19

Like folks mentioned there, I wonder if a higher-fanout heap (people asked about 4-ary) might also do well in practice. Looking at Wikipedia ( https://en.wikipedia.org/wiki/D-ary_heap ), it looks like maybe so -- the growth in number of comparisons isn't that bad, and it mentions 4-ary heaps working well specifically. (Like how linear search wins for small N, or insertion sort helps with small subarrays in introsort:…

I've tried D-ary heaps before (even min-max d-ary heap). Somehow my memory was that D = 3 or 4 sometimes performed better than 2, but now that I checked, in my code (which I spent a lot of times optimizing) I settled on plain binary heap at the end. So maybe my memory was faulty? Though I could swear I saw a performance improvement for D > 2 at some point. Sadly I don't recall why I reverted to binary heap exactly, or even whether it was related to speed or something else. Anybody tried it and remembered how it turned out?

Re: On modern hardware the min-max heap beats a binary heap

#20

Like folks mentioned there, I wonder if a higher-fanout heap (people asked about 4-ary) might also do well in practice. Looking at Wikipedia ( https://en.wikipedia.org/wiki/D-ary_heap ), it looks like maybe so -- the growth in number of comparisons isn't that bad, and it mentions 4-ary heaps working well specifically. (Like how linear search wins for small N, or insertion sort helps with small subarrays in introsort:…

I remember doing tests years ago and find that the extra comparison and loop control can tank the performance for n-ary when n>2. But that was >10 years ago.
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