LEWIN, D. Consistent hashing and random trees: Algorithms for caching in distributed networks. Master's thesis, Department of EECS, MIT, 1998. Available at the MIT Library, http://thesis.mit.edu/.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....mappings are instead consistent which means that for each different configuration of the hash table, the hash function does not completely reshuffle the mapping of keys to cells. Consistent hashing can be implemented by mapping keys and peers to points on a circle using a base hash function [13]. In Chord this is accomplished by assigning each peer and each key a probabilistically unique bit identifier generated by a base hash function such as the cryptographic hash function SHA 1. An identifier for a peer is obtained by hashing a unique identifier of the peer such as its IP address ....

D. M. Lewin. Consistent hashing and random trees: Algorithms for caching in distributed networks. Master's thesis, Massachusetts Institute of Technology (MIT), May 1998.

....means that node n executes procedure f( and n:x denotes the value of the variable x stored at node n. The Chord protocol supports a single operation: given a key, it maps the key onto the node responsible for that key. Chord implements a distributed hash table, based on consistent hashing [5, 7]; keys are mapped onto nodes by a hash function that can be resolved by any node in the system, via queries to other nodes. In a steady N node network, each node needs routing information about O(log N) other nodes, and resolves the hash function by communicating with O(log N) nodes. We now ....

....(and keys) and their hashed identifiers. To maintain the mapping when a node n joins, certain keys previously assigned to n s successor are reassigned to n. When node n leaves the network, all of its keys are reassigned to n s successor. No other changes in assignment need to occur. Previous work [5, 7] has shown that consistent hashing does a good job of load balancing keys onto nodes. Intuitively, this follows since the use of an appropriate base hash function means that node and key identifiers can be treated as independent, uniformly distributed random points on the circle. This intuition ....

LEWIN, D. Consistent hashing and random trees: Algorithms for caching in distributed networks. Master's thesis, Department of EECS, MIT, 1998. Available at the MIT Library, http://thesis.mit.edu/.

....then B can route to A) and transitive (if A can route to B and B can route to C, then A can route to C) A. Overview At its heart, Chord provides fast distributed computation of a hash function mapping keys to nodes responsible for them. Chord assigns keys to nodes with consistent hashing [12] [14], which has several desirable properties. With high probability the hash function balances load (all nodes receive roughly the same number of keys) Also with high probability, when an N node joins (or leaves) the network, only an O(1 N) fraction of the keys are moved to a different ....

....No other changes in assignment of keys to nodes need occur. In the example above, if a node were to join with identifier 26, it would capture the key with identifier 24 from the node with identifier 32. The following results are proven in the papers that introduced consistent hashing [12] [14]: Theorem IV.1: For any set of N nodes and K keys, with high probability: 1. Each node is responsible for at most (1 #)K N keys 2. When an (N 1) node joins or leaves the network, responsibility for O(K N) keys changes hands (and only to or from the joining or leaving node) When ....

LEWIN, D. Consistent hashing and random trees: Algorithms for caching in distributed networks. Master's thesis, Department of EECS, MIT, 1998. Available at the MIT Library, http://thesis.mit.edu/.

....the locations of keys, how new nodes join the system, and how to recover from the failure (or planned departure) of existing nodes. 4.1 Overview At its heart, Chord provides fast distributed computation of a hash function mapping keys to nodes responsible for them. It uses consistent hashing [11, 13], which has several desirable properties. With high probability the hash function balances load (all nodes receive roughly the same number of keys) Also with high probability, when an N node joins (or leaves) the network, only an O(1 N) fraction of the keys are moved to a di#erent ....

....successor. No other changes in assignment of keys to nodes need occur. In the example above, if a node were to join with identifier 26, it would capture the key with identifier 24 from the node with identifier 32. The following results are proven in the papers that introduced consistent hashing [11, 13]: Theorem 4.1. For any set of N nodes and K keys, with high probability: 1. Each node is responsible for at most (1 #)K N keys 2. When an (N 1) node joins or leaves the network, responsibility for O(K N) keys changes hands (and only to or from the joining or leaving node) 7 When ....

Lewin, D. Consistent hashing and random trees: Algorithms for caching in distributed networks. Master's thesis, Department of EECS, MIT, 1998. Available at the MIT Library, http://thesis.mit.edu/.

....5 describes enhancements to the base protocol to handle concurrent joins and leaves, and node failures. 4.1 Overview At its heart, chord provides fast distributed computation of a hash function mapping keys to machines responsible for them. We use a previously developed consistent hash function [11, 13], which has several good properties. With high probability 1 the hash function balances load (all machines receive at most (1 ffl) times the average number of keys) Also with high probability, when an N th machine joins (or leaves) the network, only an O(1=N) fraction of the keys are moved ....

....theorem refers to the choice of random seed. In practice, any good hash function (such as SHA 1) should be sufficient to achieve the claimed bounds. To achieve the (1 ffl)K=N bound on load with small ffl, each node actually needs to run log N virtual nodes, each with its own hashed identifier [13]. For simplicity, in the remainder of this section we dispense with the assumption of virtual nodes. In this case, the load on a machine may exceed the average by (at most) an O(log N) factor with high probability. 6 Notation Definition finger[k] start (n 2 k Gamma1 ) mod 2 m , 1 k m ....

LEWIN, D. Consistent hashing and random trees: Algorithms for caching in distributed networks. Master's thesis, MIT, 1998. Available at the MIT Library, http://thesis.mit.edu.

....here, these algorithms do not require a hierarchical structure in the underlying data. Some of these schemes are based on ooding [1] and thus do not scale due to their high resource usage. A particularly elegant algorithm is described in [43] it is based upon the idea of consistent hashing [28], and provides both excellent load balancing and bounded worst case access latencies. The CAN scheme [37] also provides bounded 22 latencies, and by using di erent number of CAN dimensions, is able to trade o latency versus the amount of state at a server. Both Chord [43] and CAN [37] implement ....

D. Lewin. Consistent hashing and random trees: Algorithms for caching in distributed networks. Master's thesis, MIT, 1998.

....not handle concurrent joins or failures. Section 5 describes enhancements to the base protocol to handle concurrent joins and failures. 4.1 Overview At its heart, Chord provides fast distributed computation of a hash function mapping keys to nodes responsible for them. It uses consistent hashing [11, 13], which has several good properties. With high probability the hash function balances load (all nodes receive roughly the same number of keys) Also with high probability, when an node joins (or leaves) the network, only an fraction of the keys are moved to a different ....

.... s successor. No other changes in assignment of keys to nodes need occur. In the example above, if a node were to join with identifier 7, it would capture the key with identifier 6 from the node with identifier 0. The following results are proven in the papers that introduced consistent hashing [11, 13]: THEOREM 1. For any set of nodes and keys, with high probability: 1. Each node is responsible for at most keys 3 2. When an node joins or leaves the network, responsibility for keys changes hands (and only to or from the joining or leaving ....

LEWIN, D. Consistent hashing and random trees: Algorithms for caching in distributed networks. Master's thesis, Department of EECS, MIT, 1998. Available at the MIT Library, http://thesis.mit.edu/.

....servers. As a result, none of the proposed methods is both highly scalable and robust. In addition, load balance is hard to achieve as the content of each cache depends heavily on the query pattern. Cache Resolver [30] like CFS, uses consistent hashing to evenly map stored data among the servers [12, 14]. However, Cache Resolver assumes that clients know the entire set of servers; maintaining an up to date server list is likely to be difficult in a large peer to peer system where servers join and depart at unpredictable times. 3. Design Overview CFS provides distributed read only file storage. ....

LEWIN, D. Consistent hashing and random trees: Algorithms for caching in distributed networks. Master's thesis, MIT, 1998.

....servers. As a result, none of the proposed methods is both highly scalable and robust. In addition, load balance is hard to achieve as the content of each cache depends heavily on the query pattern. Cache Resolver [30] like CFS, uses consistent hashing to evenly map stored data among the servers [12, 14]. However, Cache Resolver assumes that clients know the entire set of servers; maintaining an up to date server list is likely to be difficult in a large peer to peer system where servers join and depart at unpredictable times. 3. Design Overview CFS provides distributed read only file storage. ....

LEWIN, D. Consistent hashing and random trees: Algorithms for caching in distributed networks. Master's thesis, MIT, 1998.

....servers. As a result, none of the proposed methods is both highly scalable and robust. In addition, load balance is hard to achieve as the content of each cache depends heavily on the query pattern. Cache Resolver [34] like CFS, uses consistent hashing to evenly map stored data among the servers [13, 16]. However, Cache Resolver assumes that clients know the entire set of servers; maintaining an up to date server list is likely to be dicult in a large peer to peer system where servers join and depart at unpredictable times. 15 16 Chapter 3 Design Overview CFS provides distributed read only ....

Daniel Lewin. Consistent hashing and random trees: Algorithms for caching in distributed networks. Master's thesis, MIT, 1998.

....not handle concurrent joins or failures. Section 5 describes enhancements to the base protocol to handle concurrent joins and failures. 4.1 Overview At its heart, Chord provides fast distributed computation of a hash function mapping keys to nodes responsible for them. It uses consistent hashing [11, 13], which has several good properties. With high probability the hash function balances load (all nodes receive roughly the same number of keys) Also with high probability, when an N th node joins (or leaves) the network, only an O(1=N) fraction of the keys are moved to a different location ....

....n s successor. No other changes in assignment of keys to nodes need occur. In the example above, if a node were to join with identifier 7, it would capture the key with identifier 6 from the node with identifier 0. The following results are proven in the papers that introduced consistent hashing [11, 13]: THEOREM 1. For any set of N nodes and K keys, with high probability: 1. Each node is responsible for at most (1 ffl)K=N keys 3 2. When an (N 1) st node joins or leaves the network, responsibility for O(K=N) keys changes hands (and only to or from the joining or leaving node) When ....

LEWIN, D. Consistent hashing and random trees: Algorithms for caching in distributed networks. Master's thesis, Department of EECS, MIT, 1998. Available at the MIT Library, http://thesis.mit.edu/.

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LEWIN, D. Consistent hashing and random trees: Algorithms for caching in distributed networks. Master's thesis, Department of EECS, MIT, 1998. Available at the MIT Library, http://thesis.mit.edu/.

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LEWIN, D. Consistent hashing and random trees: Algorithms for caching in distributed networks. Master's thesis, Department of EECS, MIT, 1998. Available at the MIT Library, http://thesis.mit.edu/.

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D. M. Lewin. Consistent hashing and random trees: Algorithms for caching in distributed networks. Master's thesis, Massachusetts Institute of Technology (MIT), May 1998. 131

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D. Lewin. Consistent Hashing and Random Trees: Algorithms for Caching in Distributed Networks. Master's thesis, Massachusetts Institute of Technology, Cambridge, MA, USA, March 1998.

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D. Lewin. Consistent Hashing and Random Trees: Algorithms for Caching in Distributed Networks. Master's thesis, Massachusetts Institute of Technology, Cambridge, MA, USA, March 1998.

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LEWIN, D. Consistent hashing and random trees: Algorithms for caching in distributed networks. Master's thesis, Department of EECS, MIT, 1998. Available at the MIT Library, http://thesis.mit.edu/.

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D. M. Lewin. Consistent hashing and random trees: Algorithms for caching in distributed networks. Master's thesis, Massachusetts Institute of Technology (MIT), May 1998.

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