Patent Application: US-48242300-A

Abstract:
the routing address lookup problem is one of the major bottlenecks in high performance routers and deals with forwarding of packets . in the internet domain it is known as “ ip address lookup problem .” this invention provides a new and easy way to preprocess routing tables which gives efficient packet / message forwarding and is feasible in the time and the space it consumes . more precisely , the method for m - bit ip addresses gives a balanced trade - off between performing a binary search on t with o accesses , where | t | is the number of entries in t , and executing a single access on a table of 2 m entries obtained by fully expanding t . while the prior art starts out from space - efficient data structures and aim at lowering the o access cost , the invention starts out from the expanded table with 2 m entries and aim at compressing it without an excessive increase in the number of accesses . the embodiment results in a lookup which takes exactly three memory accesses in tables which occupy o space in the worst case . since the internet is more structured real routing tables for ip with m = 32 bits , should take even much smaller space . for most routers the cache is sufficient to include our tables whereas dedicated routers need only a few megabytes cache for large tables . the impact of fast lookup is increased network bandwidth .

Description:
we describe our embodiment of the invention solving the ip address lookup problem in terms of m - bit addresses . 2 . the message / packet forwarding part , where given the destination , the tables are used to determine the output port / next hop of that message / packet . 1 . in the expansion phase , we implicitly derive the output interfaces for all the 2 m possible addresses . 2 . in the compression phase , we fix a value 1 ≦ k ≦ m and find two statistical parameters α k and β k related to some combinatorial properties of the items in the routing table at hand . these two parameters characterize the space occupancy of the embodiment . when our tables fit into an l2 cache , the method is extremely fast and a 1 megabyte such cache will suffice for most of backbone and enterprise routers . for dedicated routers , it is expected to have a few megabytes dedicated cache memory for the tables and dedicated hardware which can easily implement our tables and lookups . we need precise notation describing strings of bits , which are common in the literature . given the binary alphabet σ ={ 0 , 1 }, we denote the set of all binary strings of length k by σ k . we indicate the length of a string x by | x |. given two strings α and β , we say that α is a prefix of β ( of length | α |) if | α |≦| β | and the first | α | bits of β are equal to those in α ( e . g ., 101110 is a prefix of 1011101101110 ). moreover , we denote by α · β the concatenation of α and β , that is , the string whose first | α | bits are equal to α and whose last | β | bits are equal to β ( e . g ., the concatenation of 101110 and 1101110 is 1011101101110 ). finally , given a string α and a string set s , we define α · s ={ x | x = α · β with βεs } as the concatenation of α and each string β in s . a routing table t relative to m - bit addresses is a sequence of pairs ( p , h ) where the route p is a string with | p |≦ m and the next hop h is an integer in [ 1 . . . h ], with h denoting the number of next hops . in the following we will denote by | t | the size of t , that is , the number of pairs in the sequence . moreover , we will assume that t always contains the pair ( ε , h ε ) where ε denotes the empty string and h ε corresponds to the default next hop . the ip address lookup problem can now be stated as follows . given a routing table t and xεσ m , compute the next hop h x corresponding to address x . we have to uniquely identify a pair ( p x , h x ) for which p x is the longest prefix of x appearing in t . that is , ( a ) p x is a prefix of x , and there exists h x such that ( p x , h x ) εt ; ( b ) | p x |& gt ;| p | for any other pair ( p , h ) εt , such that p is a prefix of x . conditions ( a )-( b ) are well defined since t contains the default pair ( ε , h ε ) and so h x always exists . we now describe the preprocessing part of the invention formally . the first step intuitively extends the routes of t that are shorter than m in all possible ways by preserving the information regarding their corresponding next - hop interfaces . we say that t is in decreasing ( respectively , increasing ) order if the routes in its pairs are lexicographically sorted in that order ( lexicographic sorting is known in the art ). we take t in decreasing order and number its pairs according to their ranks , obtaining a sequence of pairs t 1 , t 2 , . . . , t | t | such that t i precedes t j if and only if i & lt ; j . as a result , if p j is a prefix of p i then t i precedes t j . we use this property to suitably expand the pairs . with each pair t i =( p i , h i ) we associate its expansion set , denoted exp ( t i ), to collect all m - bit strings that have p i as a prefix . formally , exp ( t i )=( p i · σ m −| p i | )×{ h i }, for 1 ≦ i ≦| t |. ( using portions other than the prefix is possible and understood to those skilled in the art ). we then define the expansion of t on m bits , denoted t ′, as the union t ′=∪ i = 1 | t | t ′ i where the sets t ′ i are inductively defined and computed as follows : t ′ 1 = exp ( t 1 ), and t ′ i = exp ( t i )⊖∪ 1 ≦ j & lt ; i t ′ j , where the operator ⊖ removes from exp ( t i ) all pairs whose routes already appear in the pairs of ∪ 1 ≦ j & lt ; i t ′ j . in this way , we fill the entries of the expanded table t ′ consistently with the pairs in the routing table t , as stated by the following fact . if ( p x , h x ) εt is the result of the ip address lookup for any m - bit string x , then ( x , h x ) εt ′. since we took all expansions t ′ is made up of 2 m pairs and that , if we had enough space , we could solve the ip address lookup problem with a single access to t ′. we therefore need to compress t ′ somehow . this phase heavily relies on a parameter k to be fixed later on , where 1 ≦ k ≦ m . we are given the expanded table t ′ and wish to build three tables row , col and next_hop to represent the same information as t ′ in less space by a simple run length encoding ( rle ) scheme ( see nelson , m ., the data compression book , m & amp ; t books , san mateo , calif ., 1992 ). we note that other encoding schemes may be possible and are within the scope of the current invention . we begin by clustering the pairs in t ′ according to the first k bits of their strings . the cluster corresponding to a string xεσ k is t ′ ( x ) ={( y , h xy )| yεσ m − k and ( x · y , h xy ) εt ′}. note that | t ′ ( x ) |= 2 m − k . we can define our first statistical parameter to denote the number of distinct clusters . given a routing table t with m - bit addresses , the row k - size of t for 1 ≦ k ≦ m is parameter α k is the first measure of a simple form of compression . although we expand the prefixes shorter than k , we do not increase the number of distinct clusters as the following fact shows . for a routing table t , let r k be the number of distinct next - hop interfaces in all the pairs with routes of length at most k , and let n k be the number of pairs whose routes are longer than k , where 1 ≦ k ≦ m . we have α k ≦ r k + n k ≦| t |. we now describe the compression based upon the rle scheme . it takes a cluster t ′ ( x ) and returns an rle sequence s ( x ) in two logical steps : 1 . sort t ′ ( x ) in ascending order ( so that the strings are lexicographically sorted ) and number its pairs according to their ranks , obtaining t ′ ( x ) ={( y i , h i )} 1 ≦ i ≦ 2 m − k . 2 . transform t ′ ( x ) into s ( x ) by replacing each maximal run ( y i , h i ), ( y i + 1 , h i + 1 ), . . . , ( y j , h i + l ), such that h i = h i + 1 = . . . = h i + l , by a pair & lt ; h i , l + 1 & gt ;, where l + 1 is called the run length of h i . the previous steps encode the 2 m − k pairs of strings and interfaces of each cluster t ′ ( x ) into a single and ( usually ) shorter sequence s ( x ) . note that , by definition 2 , α k is the number of distinct rle sequences s ( x ) so produced . we further process them to obtain an equal number of equivalent rle sequences s ′ ( x ) . the main goal of this step is to obtain sequences such that , for any i , the i - th pair of any two such sequences have the same run length value . we show how to do it by means of an auxiliary function φ ( s , t ) defined on two nonempty rle sequences s =& lt ; a , f & gt ;· s 1 and t =& lt ; b , g & gt ;· t 1 as follows : ϕ  ( s , t ) = { t if   s 1 = t 1 = ε , 〈 b , f 〉 · ϕ  ( s 1 , t 1 ) if   f = g   and   s 1 , t 1 ≠ ε , 〈 b , f 〉 · ϕ  ( s 1 , 〈 b , g - f 〉 · t 1 ) if   f & lt ; g   and   s 1 , t 1 ≠ ε , 〈 b , g 〉 · ϕ  ( 〈 a , f - g 〉 · s 1 , t 1 ) if   f & gt ; g   and   s 1 , t 1 ≠ ε . the purpose of φ is to “ unify ” the run lengths of two rle sequences by splitting some pairs & lt ; b , f & gt ; into & lt ; b , f 1 & gt ;, . . . , & lt ; b , f r & gt ;, such that f = f 1 + . . . + f r . the unification defined by is φ a variant of standard merge , except that it is not commutative as it only returns the ( split ) pairs in the second rle sequence . in order to apply unification to a set of rle sequences s 1 , s 2 , . . . , s q , we define function φ ( s 1 , . . . , s q ) that returns rle sequences s ′ 1 , s ′ 2 , . . . , s ′ q as follows . first , s ′ q = φ ( φ ( . . . φ ( φ ( φ ( s 1 , s 2 ), s 3 ), s 4 ) . . . , s q − 1 ), s q ). as a result of this step , we obtain that the run lengths in s ′ q are those common to all the input sequences . then , s ′ i = φ ( s ′ q , s i ) for i & lt ; q : in this way , the pairs of the set of rle sequences s 1 , s 2 , . . . , s q are equally split . we are now ready to define the second statistical parameter . given an rle sequence s , let its length | s | be the number of pairs in it . regarding the routing table t , let us take the α k rle sequences s 1 , s 2 , . . . , s α k obtained by the distinct clusters t ′ ( x ) with xεσ k , and apply the unification φ ( s 1 , s 2 , . . . , s α k ) defined above . given a routing table t with m - bit addresses , the column k - size β k of t , for 1 ≦ k ≦ m , is the ( equal ) length of the rle sequences resulting from φ ( s 1 , s 2 , . . . , s α k ). that is , although we increase the length of the original rle sequences , we have that β k is still linear in | t |. the embodiment achieves a compact representation which is easy to search as we will show now . it stores a routing table t in a sufficiently compact way to guarantee always a constant number of accesses . here is a summary of the main computational steps for building t : 1 . find the α k distinct clusters without their explicit construction . 3 . unify the rle sequences by applying φ and number the resulting sequences , all of length β k , from 1 to α k . 4 . store the next hops of the r - th lre sequence in row r of table next_hop , which hence has αk rows and β k columns . 5 . set row [ x [ 1 . . . k ]]= r for each string x such that cluster t ′ ( x [ 1 . . . k ]) has been encoded by the r - th rle sequence . 6 . let f 1 , . . . , f β k be the run lengths in any lre sequence , and let sum ( c )= σ i = 1 c f i denote the sum of the first c run lengths ( where sum ( 0 )= 0 ). set col [ x [ k + 1 . . . m ]]= c for each string x , such that x [ k + 1 . . . m ] encodes an integer q with sum ( c − 1 )≦ q & lt ; sum ( c ). the time complexity of the above procedure is bounded by o ( 2 k + 2 m − k +| t | 2 ) because we use simple sorting , merging and scanning . we let # bytes ( n ) denote the number of bytes necessary to store an integer n , and a word be sufficiently large to contain the involved integers . we achieve the following : given a routing table t with m - bit addresses and h next - hop interfaces , we can store t into three tables row , col and next_hop of total size 2 k ·# bytes ( α k )+ 2 m − k ·# bytes ( β k )+ α k · β k ·# bytes ( h ) in o ( 2 k + 2 m − k +| t | 2 ) worst - case time , for 1 ≦ k ≦ m , so that an ip address lookup for a string x of m bits takes exactly three accesses given by the following calculation per message / packet ( which is three table accesses ): h x = next_hop [ row [ x [ 1 . . . k ]], col [ x [ k + 1 . . . m ]]] where x [ . . . j ] denotes the substring of x starting from the i - th bit and ending at the j - th bit . we wish to point out that the result represents a reasonable trade - off between performing a binary search on t with o ( log | t |) accesses and executing a single access on a table of 2 m entries obtained by t . note that once the next hop is determined the router places the message on the output port corresponding to the next hop . implementing the method as a software program or as a hardware device combined with software program at a hosting computer are known to those who are skilled in the art . in fact , numerous implementations in software , hardware , firmware and combination thereof , are possible which represent applications of the principles and paradigms of the present invention . all variation on the treatment and processing of message destination addresses prior , during and after the lookup stage are possible and the embodiment is merely one example of address processing . further , combining the invention with alternate routing mechanisms and devices can readily be devised by those who are skilled in the art without departing from the scope of the present invention . next we describe a small example of the application of our invention to a routing table . this illustrates the applicability of the suggested approach to a destination domain made out of binary strings and output interfaces ( next hops ) domain named by single letters . this and its generalizations to other domains are apparent to those skilled in the art . as our example , let us consider the routing table t shown in table 2 where m = 4 and h = 3 . the first step of the expansion phase consists of sorting t in decreasing order . the result of this step is shown in table 3 . this table is now expanded as shown in table 4 : the third column of this table shows the corresponding sub - tables t ′ i according to the definition of the expanded table t ′. let us now enter the compression phase : to this aim , we choose k = 2 . we then have the following four clusters and the corresponding rle sequences ( shown between square brackets ): t ′ ( 00 ) ={( 00 , a ),( 01 , a ),( 10 , c ),( 11 , b )} [ s 1 =& lt ; a , 2 ×& lt ; c , 1 & gt ;& lt ; b , 1 & gt ;] t ′ ( 01 ) ={( 00 , c ),( 01 , c ),( 10 , c ),( 11 , c )} [ s 2 =& lt ; c , 4 & gt ;] t ′ ( 10 ) ={( 00 , b ),( 01 , b ),( 10 , b ),( 11 , b )} [ s 3 =& lt ; b , 4 & gt ;] t ′ ( 11 ) ={( 00 , c ),( 01 , c ),( 10 , c ),( 11 , c )} [ s 4 = s 2 ] in this case α k = 3 ( since t ′ ( 01 ) = t ′ ( 11 ) , r k = 3 and n k = 2 . we now unify the rle sequences by applying function φ . in particular , we have that s ′ 3 = φ ( φ ( s 1 , s 2 ), s 3 )= φ (& lt ; c , 2 & gt ;& lt ; c , 1 & gt ;& lt ; c , 1 & gt ;, s 3 )=& lt ; b , 2 & gt ;& lt ; b , 1 & gt ;& lt ; b , 1 & gt ; s ′ 2 = φ ( s ′ 3 , s 2 )=& lt ; c , 2 & gt ;& lt ; c , 1 & gt ;& lt ; c , 1 & gt ; s ′ 1 = φ ( s ′ 3 , s 1 )=& lt ; a , 2 & gt ;& lt ; c , 1 & gt ;& lt ; b , 1 & gt ;= s 1 . clearly , β k = 3 . thus , # bytes ( α k )=# bytes ( β k )=# bytes ( h )= 1 so that the memory occupancy is equal to 4 + 4 + 9 = 17 bytes ( observe that the original table t occupies 6 + 6 = 12 bytes ). in summary , the overall data structures is shown in fig1 . we can observe the network traffic and investigate how the choice of the parameters above ( say k ) is affecting the actual performance based on destination statistics . this information can be used in recomputing the table adaptively . as the network changes , routing information changes since new network nodes are added or old one are eliminated . there are known method to collect the topology and determine routing information per destination . as the routing table information gets renewed , the methods here may be extended to work on - line . first , if the number of changes is small ( one or two addition , for example ), the ip lookup can first identify whether a package belongs to this set of newly added / deleted addresses and act accordingly : follow the new rule for the added nodes otherwise consult the prepared lookup tables . in case there are many changes , the above tables computed by the expansion compression phases has to be repeated . it is possible that the method we disclose will be used only partially in a node and for certain destinations , a separate table or other data structure will be maintained , especially for frequent destinations whose next hop information can be made available , say to a parallel process . such variations and combination of use are familiar to the skilled in the art and do not depart from the basic invention . the destination addresses on packets and messages may be shifted , masked , encrypted or hashed . in each case a possible preprocessing of the address is needed to first move the packet into the representation according to which the routing tables were defined . the pre - processing may involve adjusting the destination tag , since some routing methods apply such swapping as part of the routing between different parts of the network . mcauley , a ., tsuchiya , p ., and wilson , d . fast multilevel hierarchical routing table using content - addressable memory . u . s . patent application ser . no . 034 , 444 , 1995 . deering , s ., and hinden , r . internet protocol , version 6 ( ipv6 ). rfc 1883 , ( http :// www . merit . edu / internet / documents / rfc / rfc1883 . txt ) 1995 . degermark , m ., brodnik , a ., carlsson , s ., and pink , s . small forwarding tables for fast routing lookups . acm computer communication review 27 , 4 ( october 1997 ), 3 - 14 . fuller , v ., li , t ., yu , j ., and varadhan , k . classless inter - domain routing ( cidr ): an address assignment and aggregation strategy . rfc 1519 ( http :// www . merit . edu / internet / documents / rfc / rfc1519 . txt ), 1993 . lampson , b ., srinivasan , v ., and varghese , g . ip lookups using multiway and multicolumn search . in acm infocom conference ( april 1998 ). morrison , d . patricia — practical algorithm to retrieve information coded in alfanumeric . journal of acm 15 , 4 ( october 1968 ), 514 - 534 . nelson , m . the data compression book . m & amp ; 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