Principles of Reliable Distributed Systems Lecture 2: Distributed Hash Tables (DHT), Chord

1Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2008

Principles of Reliable Distributed Systems

Lecture 2: Distributed Hash

Tables (DHT), Chord

Spring 2008 Idit Keidar


Today’s Material

• Chord: A Scalable Peer-to-peer Lookup Service for Internet Applications– Stoica et al.


Reminder: Peer-to-Peer Lookup

• Insert (key, file)• Lookup (key)

– Should find keys inserted in any node


Reminder: Overlay Networks

• A virtual structure imposed over the physical network (e.g., the Internet)– over the Internet, there is a

(IP level) link between every pair of nodes

– an overlay uses a fixed subset of these

• Why restrict to a subset?


Routing/Lookup in Overlays

• How does one route a packet to its destination in an overlay?

• How about lookup (key)?• Unstructured overlay: (last week)

– Flooding or random walks• Structured overlay: (today)

– The links are chosen according to some rule– Tables define next-hop for routing and lookup


Structured Lookup Overlays• Many academic systems –

– CAN, Chord , D2B, Kademlia, Koorde, Pastry, Tapestry, Viceroy, …

• OverNet based on the Kademlia algorithm• Symmetric, no hierarchy• Decentralized self management• Structured overlay – data stored in a defined place,

search goes on a defined path• Implement Distributed Hash Table (DHT)

abstraction


Reminder: Hashing

• Data structure supporting the operations:– void insert( key, item ) – item search( key )

• Implementation uses hash function for mapping keys to array cells

• Expected search time O(1)– provided that there are few collisions


Distributed Hash Tables (DHTs)

• Nodes store table entries– The role of array cells

• Good abstraction for lookup? – Why?


The DHT Service Interface

lookup( key ) returns the location of the node currently

responsible for this keykey is usually numeric (in some range)


Using the DHT Interface

• How do you publish a file?• How do you find a file?• Requirements for an application being able

to use DHTs?– Data identified with unique keys– Nodes can (agree to) store keys for each other

• location of object (pointer) or actual object (data)


What Does a DHT Implementation Need to Do?

• Map keys to nodes– Needs to be dynamic as nodes join and leave– How does this affect the service interface?

• Route a request to the appropriate node– Routing on the overlay


Lookup Example

K V

K V

K V

K V

K V

K V

K V

K V

K V

K V

K V

insert(K1,V1)

K V(K1,V1)

lookup(K1)


Mapping Keys to Nodes

• Goal: load balancing– Why?

• Typical approach: – Give an m-bit id to each node and each key

(e.g., using SHA-1 on the key, IP address)– Map key to node whose id is “close” to the key

(need distance function) – How is load balancing achieved?


Routing Issues

• Each node must be able to forward each lookup query to a node closer to the destination

• Maintain routing tables adaptively– Each node knows some other nodes– Must adapt to changes (joins, leaves, failures)– Goals?


Handling Join/Leave

• When a node joins it needs to assume responsibility for some keys – Ask the application to move these keys to it– How many keys will need to be moved?

• When a nodes fails or leaves, its keys have to be moved to others– What else is needed in order to implement this?


P2P System Interface

• Lookup• Join• Move keys


Chord

Stoica, Morris, Karger, Kaashoek, and Balakrishnan


Chord Logical Structure

• m-bit ID space (2m IDs), usually m=160.• Think of nodes as organized in a logical ring

according to their IDs.N1

N8

N10

N14

N21

N30N38

N42

N48

N51N56


Consistent Hashing: Assigning Keys to Nodes

• Key k is assigned to first node whose ID equals or follows k – successor(k)

N1N8

N10

N14

N21

N30N38

N42

N48

N51N56

K54


Moving Keys upon Join/Leave

• When a node joins, it becomes responsible for some keys previously assigned to its successor – Local change– Assuming load is balanced, how many keys

should move?• And what happens when a node leaves?


Consistent Hashing Guarantees• For any set of N nodes and K keys, w.h.p.:

– Each node is responsible for at most (1 + )K/N keys– When an (N + 1)st node joins or leaves,

responsibility for O(K/N) keys changes hands (only to or from the joining or leaving node)

• For the scheme described above, = O(logN) can be reduced to an arbitrarily small constant

by having each node run (logN) virtual nodes, each with its own identifier


Simple Routing Solutions

• Each node knows only its successor – Routing around the circle– Good idea?

• Each node knows all other nodes– O(1) routing– Cost?


Chord Skiplist Routing• Each node has “fingers” to nodes ½ way around the ID

space from it, ¼ the way…• finger[i] at n contains successor(n+2i-1)• successor is finger[1]

N0N8

N10

N14

N21

N30N38

N42

N48

N51N56

How many entries in the finger table?


Example: Chord FingersN0

N10

N21

N30

N47

finger[1..4]

N72

N82

N90

N114

finger[5]

finger[6]

finge

r[7]

m entrieslog N distinct fingers with high probability


Chord Data Structures (At Each Node)

• Finger table• First finger is successor• Predecessor


Forwarding Queries

• Query for key k is forwarded to finger with highest ID not exceeding k

K54 Lookup( K54 )N0

N8N10

N14

N21

N30N38

N42

N48

N51N56


How long does it take?

Remote Procedure Call (RPC)


Routing Time• Node n looks up a key stored at node p• p is in n’s ith interval:

p ((n+2i-1)mod 2m, (n+2i)mod 2m] • n contacts f=finger[i]

– The interval is not empty (because p is in it) so: f ((n+2i-1)mod 2m, (n+2i)mod 2m]

– RPC f• f is at least 2i-1 away from n• p is at most 2i-1 away from f• The distance is halved: maximum m steps


Routing Time Refined

• Assuming uniform node distribution around the circle, the number of nodes in the search space is halved at each step: – Expected number of steps: log N

• Note that:– m = 160 – For 1,000,000 nodes, log N = 20


What About Network Distance?K54

Lookup( K54 )N0N8

N10

N14

N21

N30N38

N42

N48

N51N56

Haifa

Texas

China


Joining Chord

• Goals?• Required steps:

– Find your successor– Initialize finger table and predecessor– Notify other nodes that need to change their

finger table and predecessor pointer• O(log2N)

– Learn the keys that you are responsible for; notify others that you assume control over them


Join Algorithm: Take II

• Observation: for correctness, successors suffice – Fingers only needed for performance

• Upon join, update successor only• Periodically,

– Check that successors and predecessors are consistent

– Fix fingers


Creation and Join


Join Examplejoiner finds successor

getskeys

stabilizefixes

successor

stabilizefixes

predecessor


Join Stabilization Guarantee

• If any sequence of join operations is executed interleaved with stabilizations,– Then at some time after the last join – The successor pointers form a cycle on all the

nodes in the network• Model assumptions?


Performance with Concurrent Joins

• Assume a stable network with N nodes with correct finger pointers

• Now, another set of up to N nodes joins the network, – And all successor pointers (but perhaps not all

finger pointers) are correct, • Then lookups still take O(logN) time w.h.p.• Model assumptions?


Failure Handling

• Periodically fixing fingers • List of r successors instead of one successor• Periodically probing predecessors:


Failure Detection

• Each node has a local failure detector module• Uses periodic probes and timeouts to check

liveness of successors and fingers– If the probed node does not respond by a designated

timeout, it is suspected to be faulty• A node that suspects its successor (finger) finds a

new successor (finger)• False suspicion - the suspected node is not faulty

– Suspected due to communication problems


The Model?• Reliable messages among correct nodes

– No network partitions• Node failures can be accurately detected!

– No false suspicions• Properties hold as long as failure is bounded:

– Assume a list of r = (logN) successors– Start from stable state and then each node fails with prob. 1/2– Then w.h.p. find successor returns the closest living successor to

the query key– And the expected time to execute find successor is O(logN)


What Can Partitions Do?

N0N8

N10

N14

N21N38

N42

N51N56

Suspect successor

N30Suspect

successor

N48

Suspect successor


What About Moving Keys?

• Left up to the application• Solution: keep soft state, refreshed

periodically– Every refresh operation performs lookup(key)

before storing the key in the right place• How can we increase reliability for the time

between failure and refresh?


Summary: DHT Advantages

• Peer-to-peer: no centralized control or infrastructure

• Scalability: O(log N) routing, routing tables, join time

• Load-balancing• Overlay robustness


DHT Disadvantages

• No control where data is stored• In practice, organizations want:

– Content Locality – explicitly place data where we want (inside the organization)

– Path Locality – guarantee that local traffic (a user in the organization looks for a file of the organization) remains local

• No prefix search

Principles of Reliable Distributed Systems Lecture 2: Distributed Hash Tables (DHT), Chord

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