The Luleå algorithm of computer science, designed by Degermark et al. (1997), is a technique for storing and searching internet routing tables efficiently. It is named after the Luleå University of Technology, 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 Force describing that paper prior to its publication.
Contents
The key task to be performed in internet routing is to match a given IPv4 address (viewed as a sequence of 32 bits) to the longest prefix of the address for which routing information is available. This prefix matching problem may be solved by a trie, but trie structures use a significant amount of space (a node 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.
The Luleå algorithm is patented in the United States (Degermark et al. 2001).
First level
The first level of the data structure consists of
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.