Stratified B-Trees and Versioned Dictionaries
Stratified B-trees and Versioned Dictionaries.
Andy Twigg, Andrew Byde, Grzegorz Miło´s, Tim Moreton, John Wilkesy and Tom Wilkie
Acunu, yGoogle firstname@acunu.com Abstract
External-memory versioned dictionaries are fundamental to file systems, databases and many other algorithms.
The ubiquitous data structure is the copy-onwrite
(CoW) B-tree. Unfortunately, it doesn’t inherit the
B-tree’s optimality properties; it has poor space utilization, cannot offer fast updates, and relies on random IO to scale. We describe the ‘stratified B-tree’, which is the first versioned dictionary offering fast updates and an optimal tradeoff between space, query and update costs.
1 Introduction
The (external-memory) dictionary is at the heart of any file system or database, and many other algorithms. A dictionary stores a mapping from keys to values. A versioned dictionary is a dictionary with an associated version tree, supporting the following operations:
update(k,v,x): associate value x to key k in leaf version v;
range query(k1,k2,v): return all keys (and values) in range [k1,k2] in version v;
clone(v): return a new child of version v that inherits all its keys and values.
Note that only leaf versions can be modified. If clone only works on leaf versions, we say the structure is partially-versioned; otherwise it is fully-versioned.
2 Related work
The B-tree was presented in 1972 [1], and it survives because it has many desirable properties; in particular, it uses optimal space, and offers point queries in optimal
O(logB N) IOs1. More details can be found in [7].
1We use the standard notation B to denote the block size, andN the total number of elements inserted. For the analysis, we assume entries
(including pointers) are of equal size, so B is the number of entries per block. A versioned B-tree is of great interest to storage and file systems. In 1986, Driscoll et al. [8] presented the ‘path-copying’ technique to make
Andy Twigg, Andrew Byde, Grzegorz Miło´s, Tim Moreton, John Wilkesy and Tom Wilkie
Acunu, yGoogle firstname@acunu.com Abstract
External-memory versioned dictionaries are fundamental to file systems, databases and many other algorithms.
The ubiquitous data structure is the copy-onwrite
(CoW) B-tree. Unfortunately, it doesn’t inherit the
B-tree’s optimality properties; it has poor space utilization, cannot offer fast updates, and relies on random IO to scale. We describe the ‘stratified B-tree’, which is the first versioned dictionary offering fast updates and an optimal tradeoff between space, query and update costs.
1 Introduction
The (external-memory) dictionary is at the heart of any file system or database, and many other algorithms. A dictionary stores a mapping from keys to values. A versioned dictionary is a dictionary with an associated version tree, supporting the following operations:
update(k,v,x): associate value x to key k in leaf version v;
range query(k1,k2,v): return all keys (and values) in range [k1,k2] in version v;
clone(v): return a new child of version v that inherits all its keys and values.
Note that only leaf versions can be modified. If clone only works on leaf versions, we say the structure is partially-versioned; otherwise it is fully-versioned.
2 Related work
The B-tree was presented in 1972 [1], and it survives because it has many desirable properties; in particular, it uses optimal space, and offers point queries in optimal
O(logB N) IOs1. More details can be found in [7].
1We use the standard notation B to denote the block size, andN the total number of elements inserted. For the analysis, we assume entries
(including pointers) are of equal size, so B is the number of entries per block. A versioned B-tree is of great interest to storage and file systems. In 1986, Driscoll et al. [8] presented the ‘path-copying’ technique to make
References: 1(3):173–189, 1972. 5(4):264–275, 1996. New York, NY, USA, 2007. ACM. [4] Jeff Bonwick and Matt Ahrens. The zettabyte file system, 2008. In USENIX Annual Technical Conference, pages 43–60, 1992. McGraw-Hill Higher Education, 2nd edition, 2001. In STOC ’86, pages 109–121, New York, NY, USA, 1986 USA, 1999. IEEE Computer Society. [11] Dave Hitz and James Lau. File system design for an nfs file server appliance, 1994. SIGMOD Rec., 20(2):426–435, 1991. Berkeley, CA, USA, 2003. USENIX Association.