CS计算机代考程序代写 cache algorithm distributed system data structure file system Consistent Hashing
Consistent Hashing
Organization‐Based Analysis of Web‐Object Sharing and Caching Alec Wolma et al.
• Five cache nodes
• Client determines node
Cache hit: Serve from cache
to contact
Client
Server
Caching
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Cache miss: Serve from server &
populate cache
Problem: Mapping objects to caches
• Given a number of caches (e.g., cooperative caching, CDNs, etc.)
• Each cache should carry an equal share of objects
• Clients need to know what cache to query for a given
object
• Horizontally partition (shard) object ID space
– Doesn’t work with skewed distributions: e.g., 10 servers, each handles 100 IDs, but all objects have IDs between 1‐100 or 900‐ 1000
• Caches should be able to come and go without disrupting the whole operation (i.e., non‐effected caches)
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Solution attempt: Use hashing
• Map object ID (e.g., URL u) into one of the caches
• Use a hash function that maps u to node h(u)
– Forexample,h(x)=(ax+b)modp,wherepisrangeofh(x),i.e.,the number of caches
– InterpretuasanumberbasedonbitpatternofobjectID(orURL)
• Hashing tends to distribute input uniformly across range of hash function
– Objects(URLs)areequallybalancedacrosscaches,evenifobjectIDs are skewed (i.e., highly clustered in ID space)
• No one cache responsible for an uneven share of objects/URLs
• No disproportionately loaded node (potential bottleneck)
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h(u) = (7u + 4) mod 5 Assume, we have five
caches, numbered 0, …, 4.
C0
Objects
Client
h(4) C h(2)
Server
h(6) C1 6
h(5)
24 C3 2
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5
C4
5
Removing a cache changes location
Old New
Client
4
1 2
Server
h(u) = (7u + 4) mod 4 (now have to map across 4 caches)
of almost every objects! C0
Now: h(6)=2 C1 Now: h(4)=0
Now: h(2)=2
Now: h(5)=3
6
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C2
2
6, 2
C3
55
mapping
mapping 4
3
4
Client
1
h(u) = 7u + 4 mod 4 (mapped across 4 nodes)
h(4)=0 0 4
h(2)=2 h(6)=2
2
6, 2 5
h(5)=3
3
Objects
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Client
1
6 6, 2 4 52 5
Adding a cache changes the location
4
of almost every object!
h(u) = (7u + 4) mod 5 (adding a cache again)
Old New h(4)=2 0 4
h(2)=3 h(6)=1
2
h(5)=4
3
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• Goals
Consistent hashing
– Uniform distribution of objects across nodes
– Easily find objects
– Let any client perform a local computation mapping a URL to node that contains referenced object
– Allow for nodes to be added/removed without much disruption – remap only n/m objects (n objects, m slots)
• D. Karger et al., MIT, 1997
• Basis for Akamai
– CDN company (content distribution network) – Web cache as a service
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slot via h(..)
• Each cache is mapped to a
m‐2
m‐1 0 1
2
slot via h(..)
• Assign each object to the closest
m‐3 …
3 …
Consistent hashing Key idea intuition
• Select a base hash function that maps input identifier to the number range [0, …, m‐1]
• E.g.,h(x)=(ax+b)modm
• Interpret range of h(..) as array that wraps around (i.e., a circle)
• h(..) gives slot in array (circle) and wraps around at m‐1 to 0
• Each object is mapped to a
cache slot in clockwise direction on the circle
Clockwise
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point on unit circle via h(..) • Each cache is mapped to a
6
point on unit circle via h(..) • Assign each URL to closest
Cache Object
1
Consistent hashing Original interpretation
• Select a base hash function that maps input identifier to the number range [0, …, M]
• Divide by M, re‐mapping [0,…,M] to [0, 1]
• Interpret this interval as the unit circle: Here, circle with
circumference 1 (normally radius 1) • Each object is mapped to a
C
7
A
cache point in clockwise direction on the circle
4
B
2 3
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5
6 5
A
4
2 3
Cache Object
Mapping items to caches
C
7
1
Items Items Items
2, 3
4, 5, 6 7, 1
mapped to B mapped to C mapped to A
B
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6 5
Items
4, 5, 6 7, 1
mapped to C mapped to A
4
2 3
C
7
1
Items Items
2, 3, 7, 1 mapped to B
B
Removing a cache
A
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6 5
7, 1, 2
C
4, 5, 6
mapped to C mapped to A
4
B3
A
Adding a cache
7
1
Items Items Items
37, 1, 2, 3 mapped to B
2
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Node
Lookup(key)
C
Retrieve object with key from A
Processing a Lookup(key)
A B
Information about
node addition & removal (e.g., via gossiping or via a coordination service)
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Cache lookup data structure at each node
• Store cache points in a binary tree
• Find clockwise successor of a URL point by single search in
tree (takes O(log n) time)
• For a constant time technique, cf. Karger et al., 1997
key[left(x)] key[x] key[right(x)] F BH
ADK
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Client wants to read key k1 (from table t1)
4
Cassandra global read‐path
Cassandra
Coordinator 2
Cassandra •Disks •Zone A
Client sends request to any node
•Disks
•Zone C
Coordinator determines
responsible replica & forwards request
Key range for k1
Cassandra •Disks •Zone C
Cassandra •Disks •Zone B
3
Replica queries local file system, Returns value
Cassandra •Disks •Zone A
1 Client Request
Cassandra •Disks •Zone B
Replica
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Base hash function: MD5
• Message Digest 5 (MD5), R. Rivest, 1992 (MD1, …, MD6)
• Hash function that produces a 128‐bit (16‐byte) hash value
• Maps variable‐length message into a fixed‐length output
• MD5 hash is typically expressed as a hex number (32 digits)
• It’s been shown that MD5 is not collision resistant
• US‐CERT about MD5 “should be considered cryptographically broken and unsuitable for further use” (for security, not for caching)
• SHA‐2 is a more appropriate cryptographic hash function
• For consistent hashing, MD5 is sufficient
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MD5 examples
• MD5(“Thequickbrownfoxjumpsoverthelazy dog”) = 9e107d9d372bb6826bd81d3542a419d6
• MD5(“Thequickbrownfoxjumpsoverthelazy dog.”) = e4d909c290d0fb1ca068ffaddf22cbd0
• MD5(“”)=d41d8cd98f00b204e9800998ecf8427e http://en.wikipedia.org/wiki/MD5#Algorithm
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Self‐study questions
• HowwouldyouuseMD5andSHA2insteadofh(..) from our slides for consistent hashing?
• Applyh(..),MD5,SHA2toaURL,wheredoesthe output map on the unit circle?
• Discussprosandconsofhavingagivencaching server map to one vs. more points on the unit circle.
• Whataretheimplicationsofaslash‐doteffecton consistent hashing?
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