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001 Ai Topological Sort

127-persistent-data-structures-introduction

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How Persistent Data Structures Work

Source: https://arpitbhayani.me/blogs/persistent-data-structures-introduction Date: 2021-02-07

Explore persistent data structures - access historical versions, understand partial, full, and confluent persistence, and see real-world applications.

Ordinary data structures are ephemeral implying that any update made to it destroys the old version and all we are left with is the updated latest one. Persistent Data Structures change this notion and allow us to hold multiple versions of a data structure at any given instant of time. This enables us to go back in “time” and access any version that we want.

In this essay, we take a detailed look into the world of Persistent Data Structures and see the basics of its implementation along with where exactly we can find them in action. This essay is meant to act as an exhaustive introduction to the topic and in future essays, we will dive deeper into the specifics of each data structure.

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002 Temporal Primer
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003 Rag Production
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004 Structure Of Llm Chat
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005 How Llms Work
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006 Monolith Is Distributed System
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007 Defensive Databases
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008 Bm25
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009 Join Algorithms
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010 Venting At Work
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011 Half Life
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012 Multi Paxos
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013 Mysql Replication Internals
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014 Bloom Filters
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015 Clock Sync Nightmare
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016 Kafka Partitions
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017 Product Quantization
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018 Qkv Matrices
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019 Deleted Production
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020 How Llm Inference Works
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021 Blocking Queues
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022 Heartbeats In Distributed Systems
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023 Cassandra Writes
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024 Redis Replication
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025 Arrogant People At Work
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029 Grpc Http2
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030 Meetings With No Agenda Are A Waste Of Time
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031 Growth Is Not About Doing Everything
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033 Stay Relevant At Higher Salary Levels
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034 Why Consensus
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035 Database Deadlocks
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036 Cpu Cache Locality
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037 Eventual Consistency
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038 Dns Udp Tcp
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039 Masters
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040 Empathy Makes Great Engineers Unstoppable
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041 Good Mentors Build People
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042 Always Have Back Burner Projects
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043 Before You Push Back Know What Youre Standing On
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044 Be The One They Can Count On
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045 How Much People Bet On You
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046 How To Get Leadership To Say Yes To Your Project
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047 Dont Let Your Best Ideas Die In Silence
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048 Be Someone Others Want To Work With
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049 Dont Fall For Xy Problem Ask Right Questions
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050 Biggest Lie Startups Tell Engineers
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051 Promotions Are Proactive Not Reactive
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052 Not Enough To Be Right Learn To Be Heard
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053 No One Ships Alone
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054 Not Every Mistake Needs A Correction
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055 Build Influence At Work
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056 Your Soft Skills Arent Soft At All
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057 Experience Before Forming Opinion
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058 Curiosity And High Bias For Action
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073 Shiny Object Syndrome In Tech
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074 3p
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075 Leverage The Equilibrium
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076 On Demand Container Loading In Aws Lambda
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077 Sql Has Problems We Can Fix Them Pipe Syntax In Sql
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078 Nanolog A Nanosecond Scale Logging System
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079 Best Resource Is Mythical
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080 Wtf The Who To Follow Service At Twitter
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081 Know A Lot
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082 Out Of Syllabus
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083 Negotiate The Offer
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084 Never Bad Mouth Your Ex Exployer
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085 Culture Fit
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086 Quantification In Resume
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087 Hiring Is Unfair
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088 Questions For Interviewers
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089 Collaboration Communication
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090 Out Of Vicious Interview Cycle
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091 Pitch Projects Not Ideas
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092 Read Design Docs
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093 Read Rca Docs
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094 Start Generalist
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095 Do Not Rely On Summaries
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096 Structure Your Design Interviews
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097 Title Inflation
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098 Find Your Own Project
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099 Six Pointers To Crack Coding And Design Interviews
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100 Keep Yourself Unblocked
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101 Genetic Knapsack
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102 Pseudorandom Number Generation Lfsr
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103 How Indexes Work On Partitioned And Sharded Data
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104 Some Data Partitioning Strategies For Distributed Data Stores
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105 Data Partitioning
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106 Leaderless Replication
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107 Conflict Resolution
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108 Conflict Detection
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109 Multi Master Replication
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110 Monotonic Reads
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111 Read Your Write Consistency
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112 Handling Outages Master Replica
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113 Replication Formats
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114 Replication Strategies
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115 Master Replica Replication
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116 Durability
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117 Isolation
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118 Atomicity
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119 Consistency
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120 Architectures In Distributed Systems
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121 Mistaken Beliefs Of Distributed Systems
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122 Fork Bomb
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124 Taxonomy On Sql
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125 The Weird Walrus
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126 Fully Persistent Arrays
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127 Persistent Data Structures Introduction
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128 Constant Folding Python
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129 String Interning Python
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130 Recursion Visualizer Python
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131 Flajolet Martin
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132 2q Cache
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133 Israeli Queues
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134 1d Terrain
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135 Jaccard Minhash
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136 Ts Smoothing
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137 Lfu
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138 Morris Counter
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139 Slowsort
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141 Phi Accrual
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142 10x Engineer
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144 Decipher Single Xor
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145 Python Iterable Integers
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146 Inheritance C
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147 Rum
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148 Consistent Hashing
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149 Python Caches Integers
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150 Fractional Cascading
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151 Copy On Write
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152 Midpoint Insertion Caching Strategy
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153 Fsm Python
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154 Bayesian Average
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157 Better Programmer
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158 Python Prompts
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159 Rule 30 Cellular Automata
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160 Function Overloading
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161 Isolation Forest
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162 Image Steganography
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163 Long Integers Python
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164 I Changed My Python
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168 Making Http Requests Using Netcat
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This essay is loosely based on the iconic paper published in 1986 titled Making Data Structures Persistent by James R. Driscoll, Neil Sarnak, Daniel D. Sleator, and Robert E. Tarjan.

Persistence

Persistent Data Structures preserve previous versions of themselves allowing us to revisit and audit any historical version. Depending on the operations allowed on the previous versions, persistence is classified into three categories

Partially Persistent

Partially Persistent Data Structures allows access to all the historical versions but allows modification to only the newest one. This typically makes historical versions of the data structure immutable (read-only).

https://user-images.githubusercontent.com/4745789/107117960-e4a66480-68a3-11eb-97a0-c8c412527471.png

Fully Persistent

Fully Persistent Data Structures allows access and modification to all the historical versions. It does not restrict any modifications whatsoever. This means we can typically revisit any historical version and modify it and thus fork out a new branch.

https://user-images.githubusercontent.com/4745789/107117958-e112dd80-68a3-11eb-971b-58034e693f44.png

Confluently Persistent

Confluently Persistent Data Structures allow modifications to historical versions while also allowing them to be merged with existing ones to create a new version from the previous two.

https://user-images.githubusercontent.com/4745789/107117954-da846600-68a3-11eb-9c34-b9489c170710.png

Applications of Persistent Data Structures

Persistent Data Structures find their applications spanning the entire spectrum of Computer Science, including but not limited to - Functional Programming Languages, Computational Geometry, Text Editors, and many more.

Functional Programming Languages

Functional Programming Languages are ideal candidates for incorporating Persistent Data Structures as they forbid, while some discourage, the mutability of underlying structures. These languages pass around states within functions and expect that they do not update the existing one but return a new state. Programming languages like Haskell, Clojure, Elm, Javascript, Scala have native Persistent implementations of data structures like Lists, Maps, Sets, and Trees.

Computational Geometry

One of the fundamental problems in Computational Geometry is the Point Location Problem which deals with identifying the region where the query point lies. A simpler version of the problem statement is to find if a point lies within or outside a given polygon. A popular solution to determine a solution to the Point Location problem statement uses Persistent Red-Black Trees.

Text and File Editing

The most common operation required by any Text or File editing tool is Undo and Redo and having persisted all historical versions through a persistent data structure makes these most frequent operations very efficient and a breeze.

Implementing Partial Persistence

There are a few generic techniques that help in implementing Partial Persistence. Just to reiterate, partial persistence allows access to all the historical versions but allows modification to only the newest one, to create a newer updated copy of data.

Copy on Write Semantics

A naive way to implement Partial Persistence is by utilizing the Copy-on-Write semantics and naively creating a deep copy upon every update. This technique is inefficient because upon every writes the entire data structure is deep copied.

There are certain methods built upon certain storage paradigms that copy only what matters making the entire CoW efficient. I have already gone in-depth of Copy-on-Write semantics and I encourage you to check that out.

The Fat Node Method

Instead of creating copies of the entire data structure, the Fat Node method suggests that each cell holding the value within the data structure is modified to hold multiple values (one for each version) making it arbitrarily fat. Each value node thus holds a value and a version stamp.

Plain text

The Node-Copying Method

The Node-Copying method eliminates all the problems with the Fat Node method. It allows each node to hold only a fixed number of values in it. Upon exhaustion of space, a new copy of Node is created and it holds only the newest values in it. The old node also holds pointers to the newly created node allowing browsing.

Having this structure helps in making update operation slightly efficient by reducing the number of nodes to be copied during writes, considering the in-degrees to each node is bounded.

Path-Copying Method

The path-copying method copies all the nodes coming in the path from the root to the node being modified. This way it tries to minimize the copy and promotes reusing some of the unmodified data. This method comes in super handy in Linked Data Structures like Lists and Trees.

https://user-images.githubusercontent.com/4745789/107144006-33b0d000-695e-11eb-9e13-959eaeba44f4.png

Implementation of Full Persistence is a mammoth of a topic on its own and deserves its own essay. Hence skipping it from the scope of this one.

Reducing the memory footprint

Since persistent data structures thrive on high memory usage, they require some garbage collection system to prevent memory leaks. Algorithms like Reference Counting or Mark and Sweep serves the purpose pretty well.

Thus when a historical version is not referenced anymore in the program space, the corresponding objects and nodes are freed up.

References

  • Making Data Structures Persistent
  • Persistent data structure - Wikipedia
  • Geometric Data Structures
  • Point Location Problem - Wikipedia
  • Text Editor: Data Structures - HackerNews