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001 Ai Topological Sort

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The 2Q Algorithm - Addressing LRU's Sub-Optimality

Source: https://arpitbhayani.me/blogs/2q-cache Date: 2020-11-29

Explore the 2Q cache eviction algorithm, an improvement over LRU, used in databases like Postgres. Learn how it optimizes performance!

LRU is one of the most widely used cache eviction algorithms that span its utility across multiple database systems. Although popular, it suffers from a bunch of limitations especially when it is used for managing caches in disk-backed databases like MySQL and Postgres.

In this essay, we take a detailed look into the sub-optimality of LRU and how one of its variants called 2Q addresses and improves upon it. 2Q algorithm was first introduced in the paper - 2Q: A low overhead high-performance buffer management replacement algorithm by Theodore Johnson and Dennis Shasha.

001-ai-topological-sort.md
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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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026 Cdn Content Replication
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028 Emotions 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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032 Career Longevity Vs Job Hopping
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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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059 Worklog
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060 Mistakes And Growth
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061 Own It Instead Of Sweeping It Aside
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062 Dont Wait Step Up
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064 Interview Bias And What Sets You Apart
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065 Saying This Isnt My Problem Is A Problem
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066 Okr
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067 Miscommunication
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068 When In Doubt Code It Out
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070 Lead Projects That Land
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071 Abstract Thinking Skill Next Decade
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072 We Engineers Suck At Task Estimation
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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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123 Chained Operators Python
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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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140 Bitcask
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141 Phi Accrual
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142 10x Engineer
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143 Decipher Repeated Key Xor
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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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153 Fsm Python
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154 Bayesian Average
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156 Idf
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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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165 Benchmark And Compare Pagination Approach In Mongodb
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166 Mongodb Cursor Skip Is Slow
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167 Fast And Efficient Pagination In Mongodb
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168 Making Http Requests Using Netcat
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LRU

The LRU eviction algorithm evicts the page from the buffer which has not been accessed for the longest. LRU is typically implemented using a Doubly Linked List and a Hash Table. The intuition of this algorithm is so strong and implementation is so simple that until the early ’80s, LRU was the algorithm of choice in nearly all the systems. But as stated above, there are certain situations where LRU performs sub-optimal.

https://user-images.githubusercontent.com/4745789/100534745-43ae8400-3238-11eb-8855-752a6ef2f3c6.png

Sub-optimality during DB scans

If the database table is bigger than the LRU cache, the DB process, upon scanning the table will wipe out the entire LRU cache and fill it with the pages from just one scanned table. If these pages are not referenced again, this is a total loss and the performance of the database takes a massive hit. The performance will pickup once these pages are evicted from the cache and other pages make an entry.

Sub-optimality in evictions

LRU algorithm works with a single dimension - recency - as it removes the pages from the buffer on the basis of recent accesses. Since it does not really consider any other factor, it can actually evict a warmer page and replace it with a colder one - a page that could and would be accessed just once.

2Q Algorithm

2Q addresses the above-illustrated issues by introducing parallel buffers and supporting queues. Instead of considering just recency as a factor, 2Q also considers access frequency while making the decision to ensure the page that is really warm gets a place in the LRU cache. It admits only hot pages to the main buffer and tests every page for a second reference.

The golden rule that 2Q is based on is - Just because a page is accessed once does not entitle it to stay in the buffer. Instead, it should be decided if it is accessed again then only keep it in the buffer.

Below we take a detailed look into two versions of the 2Q algorithm - simplified and improved.

Simplified 2Q

Simplified 2Q algorithm works with two buffers: the primary LRU buffer - Am and a secondary FIFO buffer - A1. New faulted pages first go to the secondary buffer A1 and then when the page is referenced again, it moves to the primary LRU buffer Am. This ensures that the page that moves to the primary LRU buffer is hot and indeed requires to be cached.

https://user-images.githubusercontent.com/4745789/100536835-41a0f100-3249-11eb-920b-0bcaff905906.png

If the page residing in A1 is never referenced again, it eventually gets discarded, implying the page was indeed cold and did not deserve to be cached. Thus this simplified 2Q provides protection against the two listed sub-optimality of the simple LRU scheme by adding a secondary buffer and testing pages for a second reference. The pseudocode for the Simplified 2Q algorithm is as follows:

Plain text

Tuning Simplified 2Q buffer is difficult - if the maximum size of A1 is too small, the test for hotness becomes too strong and if it is too large then due to memory constraint Am will get relatively smaller memory making the primary LRU cache smaller, eventually degrading the database performance.

The full version 2Q algorithm remediates this limitation and eliminates tuning to a massive extent without taking any hit in performance.

2Q Full Version

Although Simplified 2Q algorithm does a decent job there is still scope of improvement when it comes to handling common database access pattern, that suggests, a page generally receives a lot of references for a short period of time and then no reference for a long time. If a page truly needs to be cached then after it receives a lot (not just one) of references in a short span it continues to receive references and hits on regular intervals.

To handle this common database access pattern, the 2Q algorithm splits the secondary buffer A1 into two buffers A1-In and A1-Out, where the new element always enters A1-In and continues to stay in A1-In till it gets accesses ensuring that the most recent first accesses happen in the memory.

Once the page gets old, it gets thrown off the memory but its disk reference is stored in the A1-Out buffer. If the page, whose reference is, residing in A1-Out is accessed again the page is promoted to Am LRU implying it indeed is a hot page that will be accessed again and hence required to be cached.

https://user-images.githubusercontent.com/4745789/100538168-0bb53a00-3254-11eb-8f69-ddcaf8d33a84.png

The Am buffer continues to be the usual LRU which means when any page residing in Am is accessed it is moved to the head and when a page is needed to be discarded the eviction happens from the tail end.

2Q in Postgres

Postgres uses 2Q as its cache management algorithm due to patent issues with IBM. Postgres used to have ARC as its caching algorithm but with IBM getting a patent over it, Postgres moved to 2Q. Postgres also claims that the performance of 2Q is similar to ARC.

References

  • LRU - Wikipedia
  • The Saga of the ARC Algorithm and Patent
  • 2Q: A low overhead high-performance buffer management replacement algorithm