The
Luleå algorithm, designed by , is a
patentA patent is a set of exclusive rights granted by a state to an inventor or their assignee for a limited period of time in exchange for a public disclosure of an invention....
ed technique for storing and searching
internetThe Internet is a global system of interconnected computer networks that use the standardized Internet Protocol Suite to serve billions of users worldwide...
routing tableIn computer networking a routing table, or Routing Information Base , is an electronic table or database type object that is stored in a router or a networked computer. The routing table stores the routes to particular network destinations...
s efficiently. It is named after the
Luleå University of TechnologyLuleå University of Technology or Luleå tekniska universitet is Scandinavia's northernmost university of technology. It has four campuses, located in Luleå , Kiruna , Skellefteå and Piteå .- History :The university was founded on June 1 1971 at Porsön in Luleå as...
, the home institute of the technique's authors. The name of the algorithm does not appear in the original paper describing it, but was used in a message from Craig Partridge to the
Internet Engineering Task ForceThe Internet Engineering Task Force develops and promotes Internet standards, cooperating closely with the W3C and ISO/IEC standard bodies and dealing in particular with standards of the TCP/IP and Internet protocol suite...
describing that paper prior to its publication.
The key task to be performed in internet routing is to match a given
IPv4Internet Protocol version 4 is the fourth revision in the development of the Internet Protocol and it is the first version of the protocol to be widely deployed. Together with IPv6, it is at the core of standards-based internetworking methods of the Internet...
addressAn Internet Protocol address is a numerical label that is assigned to devices participating in a computer network utilizing the Internet Protocol for communication between its nodes....
(viewed as a sequence of 32 bits) to the longest
prefixA prefix is an affix which is placed before the stem of a word. Particularly in the study of Semitic languages, a prefix is called a preformative, as they can alter the form of the words to which they are fixed.Examples of prefixes:...
of the address for which routing information is available.
The
Luleå algorithm, designed by , is a
patentA patent is a set of exclusive rights granted by a state to an inventor or their assignee for a limited period of time in exchange for a public disclosure of an invention....
ed technique for storing and searching
internetThe Internet is a global system of interconnected computer networks that use the standardized Internet Protocol Suite to serve billions of users worldwide...
routing tableIn computer networking a routing table, or Routing Information Base , is an electronic table or database type object that is stored in a router or a networked computer. The routing table stores the routes to particular network destinations...
s efficiently. It is named after the
Luleå University of TechnologyLuleå University of Technology or Luleå tekniska universitet is Scandinavia's northernmost university of technology. It has four campuses, located in Luleå , Kiruna , Skellefteå and Piteå .- History :The university was founded on June 1 1971 at Porsön in Luleå as...
, the home institute of the technique's authors. The name of the algorithm does not appear in the original paper describing it, but was used in a message from Craig Partridge to the
Internet Engineering Task ForceThe Internet Engineering Task Force develops and promotes Internet standards, cooperating closely with the W3C and ISO/IEC standard bodies and dealing in particular with standards of the TCP/IP and Internet protocol suite...
describing that paper prior to its publication.
The key task to be performed in internet routing is to match a given
IPv4Internet Protocol version 4 is the fourth revision in the development of the Internet Protocol and it is the first version of the protocol to be widely deployed. Together with IPv6, it is at the core of standards-based internetworking methods of the Internet...
addressAn Internet Protocol address is a numerical label that is assigned to devices participating in a computer network utilizing the Internet Protocol for communication between its nodes....
(viewed as a sequence of 32 bits) to the longest
prefixA prefix is an affix which is placed before the stem of a word. Particularly in the study of Semitic languages, a prefix is called a preformative, as they can alter the form of the words to which they are fixed.Examples of prefixes:...
of the address for which routing information is available. This prefix matching problem may be solved by a
trieIn computer science, a trie, or prefix tree, is an ordered tree data structure that is used to store an associative array where the keys are usually strings. Unlike a binary search tree, no node in the tree stores the key associated with that node; instead, its position in the tree shows what key...
, but trie structures use a significant amount of space (a
nodeA node is an abstract basic unit used to build linked data structures such as trees, linked lists, and computer-based representations of graphs. Each node contains some data and possibly links to other nodes. Links between nodes are often implemented by pointers or references.A node can be thought...
for each bit of each address) and searching them requires traversing a sequence of nodes with length proportional to the number of bits in the address. The Luleå algorithm shortcuts this process by storing only the nodes at three levels of the trie structure, rather than storing the entire trie.
The main advantage of the Luleå algorithm for the routing task is that it uses very little memory, averaging 4–5 bytes per entry for large routing tables. This small memory footprint often allows the entire data structure to fit into the routing processor's cache, speeding operations. However, it has the disadvantage that it cannot be modified easily: small changes to the routing table may require most or all of the data structure to be reconstructed.
First level
The first level of the data structure consists of
- A bit vector consisting of 216 = 65536 bits, with one entry for each 16-bit prefix of an IPv4
Internet Protocol version 4 is the fourth revision in the development of the Internet Protocol and it is the first version of the protocol to be widely deployed. Together with IPv6, it is at the core of standards-based internetworking methods of the Internet...
address. A bit in this table is set to one if there is routing information associated with that prefix or with a longer sequence beginning with that prefix, or if the given prefix is the first one associated with routing information at some higher level of the trie; otherwise it is set to zero.
- An array of sixteen-bit words for each nonzero bit in the bit vector. Each datum
A geodetic datum is a reference from which measurements are made. In surveying and geodesy,a datum is a set of reference points on the earth's surface against which position measurements are made, and an associated model of the shape of the earth to define a geographic coordinate system...
either supplies an index that points to the second-level data structure object for the corresponding prefix, or supplies the routing information for that prefix directly.
- An array of "base indexes", one for each consecutive subsequence of 64 bits in the bit vector, pointing to the first datum associated with a nonzero bit in that subsequence.
- An array of "code words", one for each consecutive subsequence of 16 bits in the bit vector. Each code word is 16 bits, and consists of a 10-bit "value" and a 6-bit "offset". The sum of the offset and the associated base index gives a pointer to the first datum associated with a nonzero bit in the given 16-bit subsequence. The 10-bit value gives an index into a "maptable" from which the precise position of the appropriate datum can be found.
To look up the datum for a given address
x in the first level of the data structure, the Luleå algorithm computes three values:
- the base index at the position in the base index array indexed by the first 10 bits of x
- the offset at the position in the code word array indexed by the first 12 bits of x
- the value in maptable[y][z], where y is the maptable index from the code word array and z is bits 13–16 of x
The sum of these three values provides the index to use for
x in the array of items.
Second and third levels
The second and third levels of the data structure are structured similarly to each other; in each of these levels the Luleå algorithm must perform prefix matching on 8-bit quantities (bits 17–24 and 25–32 of the address, respectively). The data structure is structured in "chunks", each of which allows performing this prefix matching task on some subsequence of the address space; the data items from the first level data structure point to these chunks.
If there are few enough different pieces of routing information associated with a chunk, the chunk just stores the list of these routes, and searches through them by a single step of binary search followed by a sequential search. Otherwise, an indexing technique analogous to that of the first level is applied.