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From Wikipedia, the free encyclopedia

The HAT-trie is a type of radix trie that uses array nodes to collect individual key–value pairs under radix nodes and hash buckets into an associative array. Unlike a simple hash table, HAT-tries store key–value in an ordered collection. The original inventors are Nikolas Askitis and Ranjan Sinha.[1][2] Askitis & Zobel showed that building and accessing the HAT-trie key/value collection is considerably faster than other sorted access methods and is comparable to the array hash which is an unsorted collection.[3] This is due to the cache-friendly nature of the data structure which attempts to group access to data in time and space into the 64 byte cache line size of the modern CPU.

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  • Did The Past Really Happen?
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Transcription

Hey, Vsauce. Michael here. The dog that played Toto in The Wizard of Oz was credited as Toto, but in reality the dog's name was Terry. And when Terry died in 1945 her owner and trainer Carl Spitz buried her on his ranch in Los Angeles. But in 1958 the Ventura Highway was constructed right through Terry's grave. Her remains were disturbed and have never been found. Fifty-three years later a memorial was erected in Hollywood Forever Cemetery in her honor but because she isn't burried there, the memorial is not a grave. It's what's known as a cenotaph, an empty tomb. I was reminded of Toto's cenotaph when I saw the cenotaph of Philopappos, atop the Hill of the Muses in Athens. You see, I was recently in Greece talking about YouTube with YouTube creators. The all seen eye of Guy came along and we visited the Acropolis, a Lion Gate - nearly a thousand years older than the Acropolis. The earliest known analog computer. Plenty of beautiful cats and I even took a selfie in Delphi. I've seen all of these things and how old they were, it made me wonder how will we be remembered. How will future archaeologists react to the ruins of today's society they find thousands of years from now. Will they do a good job piecing it together? Will anything about you in particular be remembered? And, for that matter, how do we even know that the past really happened? Not just the way we think it happened, but it all. Seriously, can you prove that the universe wasn't created last Thursday? That everything - every person, every memory you have, every photo you've taken didn't just pop in into existence last week or five minutes ago? Last Thursdayism is the belief that the universe was created last Thursday. It doesn't have actual followers or rituals but proving it wrong is impossible. Not because the universe actually was created last Thursday but because Last Thursdayism is not also falsifiable. It cannot be shown to be false. In the evidence you bring up against it can be explained away as part of the everything that was created last Thursday. Many people believe that in order for a theory and explanation to be scientific it must be possible to refute it, to prove it wrong, to test it. So, instead, Last Thursdayism falls into the domain of philosophy, where luckily there are razors - little rules of thumb that help shave off unlikely explanations. The most famous is Occam's Razor. When faced with the choice between explanations, choose the one that requires diffused assumptions. Occam's Razor can shave off last Thursdayism because it requires fewer assumptions to believe that, say, this beehive tomb was constructed way back in the Bronze Age and that I just visited it later than it does to believe that the tomb, my memories of it and this footage of me inside it just happen to coincidentally pop into existence at the same time last Thursday. One of my favourite philosophical razors cuts off so much stuff it's not even called a razor. It's called Newton's Flaming Laser Sword. It states if something cannot be settled by experiment, then it is not worthy of debate. So let's move on to the past. What does Newton's Flaming Laser Sword tell us about the past? I mean, it doesn't exist in the same way gravity or light or protons do. We can't do experiments on it, build control groups, run trials. The past just is what it was. We will one day be the past and no matter how well we try to record our stories ourselves, without time machines future archaeologists are going to have to make a lot of guesses about us. But that's kinda cool. Future humans will likely know way more than us today about medicine, about exoplanets, about physics. But one thing they almost surely will not know more about than we do is today. Will your great great great great grandkids know your name? Will aliens, who visit Earth millions of years after humans leave or go extinct, understand that Animorphs was just fiction, and not a history of our people? You are destined to become whatever the future thinks you were, if you're lucky. Vandals, fire, natural disaster, conquerors, thieves, all of these forces obscure facts overtime, but no matter how well we tried to preserve today for future history books, there's one type of fog we are unlikely to avoid. Apathy. Ira Glass put it well when he asked his listeners a simple question: name 10 people from the 15th century. We have records of more than 10 people but to most of us they don't matter. In five hundred years radio host will be making the same jokes but about us. However, there is a legacy leave behind that is irreversible. Immutable, and in a way, unforgettable. To conserve energy, turn off when not in use. Or just keep them on. Energy will be conserved no matter what you do. Even if you leave lights on all year, there will be no less or more energy in the universe. What's really being conserved when we turn off lights are the resources we turn into energy the lights can use. But if you counted up all the energy in the system, before and after turning the lights on, it would be the same. Energy also does something else. Unless hindered from doing so, energy will spread out - it will disperse. That is, in so few words, the Second Law of Thermodynamics. It's how our universe works. It's why things that happen spontaneously do. Energy spreads. Even when a process locally concentrates energy, like when a crystal forms or life grows, the Second Law isn't violated because these processes aren't independent from the larger world around them. They aren't 100 percent efficient. Hindrances can hold back the inevitable spread of energy for a long time. The Second Law doesn't say when energy will disperse - just that when it can, oh it will. Balloons will deflate, objects will fall, hot objects will cool down, and perfume sprayed across the room will eventually migrate to your nose even in really still air. How much or how widely energy has spread out is measured in entropy. Entropy is often called "disorder", "chaos". But entropy is very different from macroscopic messiness. This deck of cards is themed after Greek philosophers. It's also arranged by value and suit - the entire deck. But if I take the deck and shuffle it, that is, disorder it, I haven't actually increased the deck's entropy, because nothing about this deck of cards' energy is different than it was before. However, entropy in the greater world around us has increased because in order to shuffle the cards my body has to do work. It has to take energy concentrated in my cells and change and disperse that energy into kinetic energy, movement, and a little bit of heat from my body and from the cards, friction, and a little bit of sound energy - that rustling noise. So there's your real legacy. Your contribution to the universe's growing entropy. No process will be able to undo the net increase in entropy you accomplish in your life. History may forget you, or misinterpret your accomplishments, or what stood for. The ripples you leave behind may get redirected but the universe will never be able to forget the entropy you add. That's the law. The Second Law of Thermodynamics. Many scientists believe that this means that eventually energy - heat - will be completely spread out evenly throughout the universe. It will be the same temperature everywhere, and at that point nothing will be able to happen. Because in order for something to happen entropy needs to increase, energy needs to spread, the move to change. This may be the ultimate fate of the universe - thermodynamic equilibrium. The "Heat Death" of the universe. It's been estimated that at the rate things happen this end the universe will occur in about 8 googol years, and you're contributing to it by simply existing. A funny consequence of all this is the fact that people who aren't very active, people who don't do much but lay around aren't just being lazy. In a way they're being considerate. Sloth maybe of vice, but to the universe it's a fountain of youth. Choosing to do as little as possible means consciously limiting your contribution to the inevitable dispersal of energy and thus in a teeny-tiny way postponing the "Heat Death" of our universe. Relaxing adds time to the universe's life: in amount of time, to be fair, almost indistinguishable from zero, but still theoretically real. Being lazy will make the universe last longer. So thanks for chilling out. Thanks for taking it easy. And, as always, thanks for watching.

Description

A new HAT-trie starts out as a NULL pointer representing an empty node. The first added key allocates the smallest array node and copies into it the key/value pair, which becomes the first root of the trie. Each subsequent key/value pair is added to the initial array node until a maximum size is reached, after which the node is burst by re-distributing its keys into a hash bucket with new underlying array nodes, one for each occupied hash slot in the bucket. The hash bucket becomes the new root of the trie. The key strings are stored in the array nodes with a length encoding byte prefixed to the key value bytes. The value associated with each key can be stored either in-line alternating with the key strings, or placed in a second array, e.g., memory immediately after and joined to the array node.[4]

Once the trie has grown into its first hash bucket node, the hash bucket distributes new keys according to a hash function of the key value into array nodes contained underneath the bucket node. Keys continue to be added until a maximum number of keys for a particular hash bucket node is reached. The bucket contents are then re-distributed into a new radix node according to the stored key value's first character, which replaces the hash bucket node as the trie root[5] (e.g. see Burstsort[6]). The existing keys and values contained in the hash bucket are each shortened by one character and placed under the new radix node in a set of new array nodes.

Sorted access to the collection is provided by enumerating keys into a cursor by branching down the radix trie to assemble the leading characters, ending at either a hash bucket or an array node. Pointers to the keys contained in the hash bucket or array node are assembled into an array that is part of the cursor for sorting. Since there is a maximum number of keys in a hash bucket or array node, there is a pre-set fixed limit to the size of the cursor at all points in time. After the keys for the hash bucket or array node are exhausted by get-next (or get-previous) (see Iterator) the cursor is moved into the next radix node entry and the process repeats.[7]

References

  1. ^ described in an article published in Proc. Thirtieth Australasian Computer Science Conference (ACSC2007), Ballarat Australia. CRPIT, 62. Dobbie, G., Ed. ACS. 97-105
  2. ^ https://dl.acm.org/citation.cfm?id=1273761 HAT-trie: A Cache-conscious Trie-based Data Structure for Strings
  3. ^ Askitis, N. & Zobel, J. (2005), Cache-conscious collision resolution for string hash tables, in ‘Proc. SPIRE String Processing and Information Retrieval Symp.’, Springer-Verlag, pp. 92–104
  4. ^ Askitis, N. and Zobel, J. 2011. Redesigning the string hash table, burst trie, and BST to exploit cache. ACM J. Exp. Algor. 15, 1, Article 1.7 (January 2011)
  5. ^ Burst tries: a fast, efficient data structure for string keys ACM Trans. Inf. Syst., Vol. 20, No. 2. (April 2002), pp. 192-223, doi:10.1145/506309.506312 by Steffen Heinz, Justin Zobel, Hugh E. Williams
  6. ^ Sinha, R. and Wirth, A. 2010. Engineering burstsort: Toward fast in-place string sorting. ACM J. Exp. Algor. 15, Article 2.5 (March 2010)
  7. ^ http://www.siam.org/meetings/alenex03/Abstracts/rsinha.pdf Cache-Conscious Sorting of Large Sets of Strings with Dynamic Tries

External links

This page was last edited on 23 September 2023, at 13:19
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