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Interconnections for Computer Communications and Packet Networks

Roberto Rojas-Cessa

Internet Protocol (IP) Address Lookup

Publication details https://www.routledgehandbooks.com/doi/10.1201/9781315373485-4 Roberto Rojas-Cessa Published online on: 06 Jan 2017

How to cite :- Roberto Rojas-Cessa. 06 Jan 2017, Internet Protocol (IP) Address Lookup from: Interconnections for Computer Communications and Packet Networks CRC Press Accessed on: 27 Sep 2021 https://www.routledgehandbooks.com/doi/10.1201/9781315373485-4

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Internet egress information called IP router’s next-hop is the just the process retrieve or This to router, of table. lookup, table forwarding or destination address the the node, (IP) in network between prefix Protocol matching a a to traversing prefix packet packet longest the a the port performing egress requires the out Finding Exercises Readings Additional 3.13 Memory Content-Addressable Scheme Ternary 3.12 Lookup Parallel-Search A Helix: 3.11 3.10 . ahCmrse Trie Path-Compressed 3.4 Trie Disjoint Tree Binary Basic 3.3 Introduction 3.2 3.1 CONTENTS Lookup Address (IP) Protocol Internet 3 . lo itrBsdAlgorithm Filter-Based Bloom 3.9 Algorithm Lulea Trie Level-Compressed 3.7 Trie Multibit 3.6 3.5 . 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IP con- of table forwarding set a a Specifically, prefix. of longest sists the to same matching the a becomes through reachable are aggregated. be and share may that (MSBs) port addresses bits router Those significant ports. addresses router. most different of a through ranges common at as reachable represented aggregation are prefix are given address prefixes, which a and of or networks, by different example prefix reachable figure, an are a this shows that In of 3.1 addresses Figure combination of of range port. the a router table summarize as includes forwarding to of prefix represented supernetting a The addresses objective called length. holding technique of the memory a range has a uses a addresses CIDR in router. of entries Internet of aggregation an aggregate number This to the used prefix. approach reducing as an is addresses IP [67] (CIDR) Routing Interdomain Classless Introduction 3.1 process. in lookup tables, the interrupt routing to in not changes as by accommo- so caused manner to table expeditious able forwarding an the be of should changes mechanisms date lookup IP Furthermore, mentable. 48 h opeiyo drs okpi ihbcue )pexlntsmybe may lengths prefix 1) because: high is lookup address of complexity The num- the minimize to addresses of aggregation the resolves CIDR Although ihCD,adesscnb grgtda rirr ees n Plookup IP and levels, arbitrary at aggregated be can addresses CIDR, With > necnetosfrCmue omnctosadPce Networks Packet and Communications Computer for Interconnections < ar h rfi eghidctstenme fsgicn isi the in bits significant of number the indicates length prefix The pair. 12.0.54.8/32 > , < 12.0.54.0/24 < > 12.0.54.2 and , < 12.0.0.0/16 > prefix , < > 12.0.54.0/24 fa incoming an If . < prefix/prefix > is Downloaded By: 10.3.98.104 At: 03:52 27 Sep 2021; For: 9781315373485, chapter3, 10.1201/9781315373485-4 ntero re euehr h em reo reitrhnebyi this in interchangeably trie or children of tree number terms the the does to here 0 so use from increases, We to numbers numbers 0 tree. be chapter. of numbers would from root set nodes numbers the the the those from sort in if of be could children that would we the Note children that and 9. first such tree), entry, the root an (as where 1 of tree units decimal a the this as and time tens the [2]. the by increase on be to reported continues to being number found is the be number but could written, This contents is prefixes. of the book number million lookup, the a or table. 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IP number memory which the of is number stride and the size memory both ue sssvrlsrtge ordc h eoyaon:1 small a 1) amount: memory the reduce to strategies several uses Lulea F orwading necnetosfrCmue omnctosadPce Networks Packet and Communications Computer for Interconnections P P P P P P P P P P 10 9 8 7 6 5 4 3 2 1 01* 10* 10* 1* 10* 10* 01* 0* 1* * table P10 0 P3 0 0 P3 1 0 0 1 P4 1 P4 P4 0 1 1 P3 P4 0 P1 1 h Cti svr ffciea reducing at effective very is trie LC The 0 P1 1 P9 0 P5 0 P1 0 1 P5 0 1 1 1 P6 0 P2 1 P2 P2 P2 P2 0 1 P2 0 0 1 1 1 P8 1 P2 1 P7 Downloaded By: 10.3.98.104 At: 03:52 27 Sep 2021; For: 9781315373485, chapter3, 10.1201/9781315373485-4 rfie rm001,a h i npsto ,t rfi 5.5/6 stebit the as 255.255/16, prefix to 1, position in 2 For bit position not. the in occu- as or decimal, 0.0/16, prefix in from 128.0/16 new prefixes or a binary, 2 in holds NHI. position 0000* position the pies 0000 in 0000 its 1000 stored whether prefix be indicate example, to a to needed is dedicated prefixes vector the is of 2 of bit number has objective The the bitmap The vector. show value. 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P5 10 P5 10 P6 P2 10 P2 P2 16 1 P2 − P2 0 0 .Hr,ec bit each Here, 1. 1 1 P8 1 P2 1 P7 59 Downloaded By: 10.3.98.104 At: 03:52 27 Sep 2021; For: 9781315373485, chapter3, 10.1201/9781315373485-4 atbet tr nomto bu h i-etr n ntr,frthe for turn, in and and array, bit-vector, index the base needed. about codeword, be information process. a would store lookup uses accesses be to scheme not memory maptable the may multiple a issue, described as as this 1s, vector overcome bit all To the counting storing However, for case. efficient bit this the in to 16 level 0 bits bit the from of ones prefix. bitmap matching the the a in prefix to 1’s once that equal way, of of or number this position than the In the smaller by lookup, trie). position addressed for multibit a is accessed with a table representing is in NHI bitmap, of as the the (instead respectively, in of respectively 1, bit 0, nodes and a the and 1, prefix, prefix, 0, same 1, 1, of the as to number bits belong them the the length 0011 prefix by and 0, considering 0010, represented to 0001, example, are For prefixes nodes small. bits duplicated kept if of is four, of table bits NHI setting the By in prefixes table. prefix as a NHI descendants, 0. of no the to and expansions in set These prefix not are length. no are prefix, prefix with 13 duplicated nodes longer and a Therefore, a 12, hold 1. have that 6, bit to nodes which Bits prefix, set presented 0. prefixes, same also is to of the are case 5 of bits ancestors Similar bit expansions are 0. are and are four they to they 1 bits to set but two expanded since to are these prefix but set they a Because prefix, is of 5. 0, 4 same bit and bit the first 4 in of the bits bits prefix is expansions in leaves; the it also 16 of as are has 1 duplicate 3 it to a to so set 1 is levels, bit 0 the Bits four set bit leaves. has to Here, subtree how 15. of This to example vector. 0 an bit shows 3.11 the Figure in 16. values level to up lengths 3.2. with Figure of tree binary the of representation trie LC Final 3.9 FIGURE 60 tsol ecernwta htLlade st on h ubrof number the count to is does Lulea what bitmap. a that in now nodes clear of representation be the should of It example an shows 3.11 Figure prefixes of number the to equal vector bit the in 1 to set bits of number The P10 P9 P8 P7 P6 P5 P4 P3 P2 P1 Forwading necnetosfrCmue omnctosadPce Networks Packet and Communications Computer for Interconnections 01 10 10 1 10 10 01 0* 1* * P3 P10 * * * * * * Table * 0 1 0 P4 P4 P3 01 x P1 01 where , P9 P1 01 P5 P6 x 10 orsod otemthn rfi at prefix matching the to corresponds 10 P2 P2 10 1 P2 P2 P8 P2 P7 Downloaded By: 10.3.98.104 At: 03:52 27 Sep 2021; For: 9781315373485, chapter3, 10.1201/9781315373485-4 or h onigo si h atbtms ssoe ntemaptable. must the 1s in stored of of is count set bit-mask the the last in However, the bit-masks) in wide. (three 1s of 2 6-bit of bit-mask offset is counting to The The 0 offset bit-masks. four. bit-mask the four from those as of all set 0, include each is in 0 ones bit-mask of number the accumulated where h ubro aeidxs.Teeoe h aeidxaryhas array index base reduces the (this Therefore, bit-masks indexes). consecutive base four of of set number bit each the for the allocated in is bit-mask index largest base possible the length, last considering The the by index. d for calculated bit accumulate is 2 and may index or offset, vector, that base code, 1s the the of of number of bits, use of number the in of example an shows of field offset The bit-mask. one only and one codeword to corresponds an codeword 1) fields: each two comprises and chunk code a as bits of ee 6comprises 16 level or larger the onto projected be can they level. and prefix levels selected different at found are Prefixes 3.10 FIGURE Lookup Address (IP) Protocol Internet i-ak o3 ffe onstenme f1 nBtms ,adcode and 4, Bit-mask in 1s in of 1s number of sixth the number counts (the the 5 5 counts offset Bit-mask 1 3, in index to is base which 0 Therefore, Bit-masks 92), left). corresponding bit the bit the (or from to bit-mask 01011101* points arrow 00000000 The prefix 3.12. Figure to in arrow the by index. pointer base a are for address bits destination 10 packet and a codeword of a bits access 12 to MSB used the Therefore, indexes. base log bit-masks oadte1 pt i-ak2 bit-mask to up 1s the add To h i etri emne nogop fsaladeulnme fbits, of number equal and small of groups into segmented is vector bit The sa xml,ltscnie htapce drs ace h i position bit the matches address packet arrays. a that index consider base let’s example, and an codeword As the shows 3.13 Figure 2 hrfr,tenme fcdwrsi h oeodaryi 06 where 4096, is array codeword the in codewords of number the Therefore, . (2 i 16 stebtms ftemthn pex i.Teostrcrsthe records offset The bit. (prefix) matching the of bit-mask the is − i 16) 16 niae h ubro si bit-masks in 1s of number the indicates h rgnlLlaagrtmue 6btbtmss Therefore, bit-masks. 16-bit uses algorithm Lulea original The . − Level 32 e Level 24 eas ffe onstenme foe ntrebtmss a bit-masks, three in ones of number the counts offset Because . 61 o ee 6 hrfr,tebs ne s1 isln (i.e., long bits 16 is index base the Therefore, 16. level for 1s 16 2 Level 16 2 16 4 06btmss oeodue h aenumber same the uses codeword A bit-masks. 4096 = 12 − ,a 2, aeindex base offset i − n )acombination a 2) and sue.Fgr 3.13 Figure used. is 3, i − and 2 2 2 16 6 1024 = i − 61 1, Downloaded By: 10.3.98.104 At: 03:52 27 Sep 2021; For: 9781315373485, chapter3, 10.1201/9781315373485-4 otebtcrepnigt h rfi.Tettlnme foe s2,which 22, bit-mask is the ones of of number beginning total the The from prefix. prefix the 1s to to of corresponds corresponding number bit the the counts to 5 Bit-mask in target the onto projected be can level target the than level. lower levels at Prefixes 3.11 FIGURE 62 xml fte1bt one ytedffrn fields. different the by counted bits 1 the of Example 3.12 FIGURE ( many as and codes different of number the as rows example. many our as for in maptable has position the table bit shows this each 3.14 The provides for Figure entry 1s bit-mask. This of bit-mask. maptable. corresponding number the a the accumulated in in the entry 1s showing an the by address of information to position used and is combination code the The indicates field Maptable code and The Field Code 3.7.2.1 4k each Prefixs bit 16 mask: bits) necnetosfrCmue omnctosadPce Networks Packet and Communications Computer for Interconnections 0 1 10 a b 1 0 c 2 34 0 10 d 0 e f v g . 1 h 1s counted 5678 i 0 j by 10 k 1 base index 1 1 910 10 l 0 m n 0 1112 0 o 10 1s 1 counted 13 ofset p 1 q by r 14 15 1 1s 10 s counted 1 Matching t by u code v Prefix Downloaded By: 10.3.98.104 At: 03:52 27 Sep 2021; For: 9781315373485, chapter3, 10.1201/9781315373485-4 ubro obntosare combinations of number ijitti) h ubro culcmiain htcnb rdcdin produced be the can (see that children combinations 2 no than or actual smaller two of is either expansion number has prefix node the each trie), where disjoint tree, 2 in a combinations than of completing smaller number to is the that bit-mask found 16-bit algorithm a Lulea the of authors The of Field number Code the to equal 3.7.2.2 is table this bitmap. in the entries) in (and 1s prefixes of number The 3.12. Figure of bitmap for maptable of Example 3.14 FIGURE lookup column. for maptable used the bits address address to packet used of are string 16) the level and of for rows bits 16) the 16 level address (e.g., for to log bits the used four 4 general, the are In (e.g., respectively. and address table, code destination the the packet’s of Therefore, columns a bit-mask. a in in bits bits LSB of number the as columns fields. index base and offset of values the of Example 3.13 FIGURE Lookup Address (IP) Protocol Internet Base Code (1k (4k (each 4k al . hw h H al sdi ue oietf h acigprefix. matching the identify to Lulea in used table NHI the shows 3.4 Table index word entris) entris) bit-mask: 16 ary: ary: bits) Bit 0 0 (6 10 Ofset (Code) bits) 0 0 (16 Bit-mask bits) (10 (r1) (r2) (r3) (r4) 0 adres bits) Code 3 57 r1 0 ones Bit 0 1 2 3 15 1 1 1 1 0 1 10 1 1 1 1 1 3 Bit 1 1 2 2 1 - mask 3 1 1 1 3 7 ones l r 1 10 2 1 1 where , 4 4 2 Bit 16 ones 0 1 1 4 31 5 2 steepnino rfie ssimilar is prefixes of expansion the As . 2 1 2 1 4 6 10 10 1 1 7 4 2 l Bit-mask stepexlvl pcfial,the Specifically, level. prefix the is 1 2 5 3 8 r3 1 2 9 5 3 2 10 1 3 5 3 1 1 3 5 3 3 2 10 1 btms ie S bits LSB size) (bit-mask 12 1 3 4 6 Bit- 13 1 4 6 3 mask 13 14 1 4 r1 7 3 ones 3 15 1 3 4 7 1 4 10 0 ( 16 Bit- bits) Example 0.72/16 14 mask r4 4 0 63 Downloaded By: 10.3.98.104 At: 03:52 27 Sep 2021; For: 9781315373485, chapter3, 10.1201/9781315373485-4 ethpidxtbeo i etri iue3.12. Figure in vector bit of table index hop Next 3.4 TABLE 64 mle ubro i hntoei h i-ak ngnrl h ieo the of size the general, with In but bit-mask. bit-mask the a in in those 0s than and bit code, of 1s number of smaller combination a the of information provides 2 as 2 with bit-masks for fteoiia 6bt.Te,ec obnto f0 n si i-akwith bit-mask a 2 in the 1s of and one 0s as of represented combination is each bits Then, 16 bits. ( 1), 16 + bits original (677 10 the combination only of need all-0s we the combinations, 678 considering represent After to [49]). considered been has hs xmlssosta h osbecmiain r nytoadfive, and two only are combinations possible the respectively. that shows examples These iue31 hw h obntoso opeetiswith tries complete of combinations the shows 3.15 Figure 4 6 and 16, = | code necnetosfrCmue omnctosadPce Networks Packet and Communications Computer for Interconnections | = d log a 4 7 a mrvmn ordc hsnme fcodes of number this reduce to improvement (an 677 = (4) 2 ( n a ( eoyaddress Memory is o xml,i h i-aki 6btwide, 16-bit is bit-mask the if example, For bits. n )) e nnme fbits. of number in , a 13 12 11 10 22 21 20 19 18 17 16 15 14 9 8 7 6 5 4 3 2 1 ( n + 1 = ) a 0 1 = (0) 10 obntos hssosta h code the that shows This combinations. a rfi d(NHI) Id Prefix ( n , − 1) m h d b u p n k v q g o a e c r s t 2 j f l i d log 2 (678) e 0 instead 10) = n n 2. and 1 = n (3.1) 4 = Downloaded By: 10.3.98.104 At: 03:52 27 Sep 2021; For: 9781315373485, chapter3, 10.1201/9781315373485-4 h isnee rmtepce etnto drs oacs h oeand code the access to of address summary destination a packet are the case) shows the tables. this 3.16 from NHI in Figure (16 needed maptable. level the bits the to the accessing of address for bits partial bits 4 address 10 as LSB the MSB The used the of the index. bits identify and base 12 bit-mask to corresponding MSB corresponding the address the the this, find IP For to destination table. used NHI the are the uses in Lulea NHI in corresponding process lookup Process The Matching Lulea codes. 3.7.2.3 Lulea bit two and one for trees complete of Combinations 3.15 FIGURE Lookup Address (IP) Protocol Internet ue erhprocess. search Lulea 3.16 FIGURE o xml,ltscnie Plou spromdfrapce ihdes- with packet a for performed is lookup IP consider let’s example, For B ase ary Bit index number Codewr ary 1 Disjoint treewithupto2levels(n=2) Disjoint treewithup to1level 0 31 Base 10 16 index Destinao Destinao 1 NHI 1 Ofset 2 0 1 6 0 table 4 IP IP adres Code adres adres 10 1 1 1 0 = 16 Maptble + adres

+ Number (n=1) prefixs Number Maptble chunk ; 1 0 0 1 in of 67 of 0 Column positn bits 0 1 index in 1 chunk) (bit 2 15 65 Downloaded By: 10.3.98.104 At: 03:52 27 Sep 2021; For: 9781315373485, chapter3, 10.1201/9781315373485-4 aeidxs atbe n H al a edt ealupdated. all be to need may the table to codewords, NHI continues as scheme, and matches this maptable, the in indexes, if costly base are time of updates lookup number table Forwarding the corresponding levels. similar to A other added A levels. prefix is simultaneously). larger accesses accessed other memory are for arrays performed is index process base and codeword the og.Telou opeiyo I-48i ()a h erho B2 is TBL24 on search TB- the in as stored matched O(1) is the is it DIR-24-8 TBL24, one, of at complexity to matched lookup not set The is Long). prefix is TBLlong. the bit to (if accesses pointer the to amount. memory a bit If memory is prefix and it prefix. otherwise a Speed a NHI; holds is the location) is entry (memory information the entry memories whether An two 32, logic. these indicate level shows to supporting 3.18 search Figure the the 32. directing level and on pointers prefixes or size. stores 24, memory TBLlong level that and on therefore, in prefixes fit stores and one that size, first those fixed to unknown a limited forwarding an given is for the is prefixes needed in memory of memory bits number level-32 the of 24 the the estimate idea than prefixes, to few the larger of difficult shows level prefixes number a is at 3.17 of it only intervals Figure number of Because vast, number 30. the table. too total on to The is 25 depends 32. levels 32 level 32 at at level are intervals prefix subtries, these at a representing or prefixes intervals, of these of descendant of expanded number the Each are large represented. 31 the are memory and intervals As 25 a 256-address levels 32. between uses than Prefixes smaller level 24 level. length to that Level with to prefixes level. expanded All are each prefixes. of 24 possible The for adoption all engine. The block represent lookup to 32. memory IP enough or the a 24 of uses prefix implementation level lengths) controlled the scheme either (or simplifies performs on greatly levels scheme prefixes levels two This two all algorithm. in represent Lulea to prefixes the expansion represent to to similar aims [75], scheme DIR-24-8 The Scheme DIR-24-8 3.8 this for address hop next the prefix provide to may corresponds so it to prefix and 2, This 1s matched number packet. of is number The the prefix set 14. the NHI stores = count a 16th 9 index can of base column reader bit-mask the and The and first maptable), where NHI=0+14+2=16. the 4 the in is of and row address 4 it 5 by the row (as Codeword addressed (or 0 matches r4 entry = is 0.72, maptable offset code address, 3.13). has the the (Figure four), 5 of example of Codeword an part 1. as bits index used 16 Base vector MSB bit the the Using in 0.72.0.0 address tination 66 o ee 6 ue efrsI okpi he eoyacse (where accesses memory three in lookup IP performs Lulea 16, level For I-48ue w eoybok,cle B2 n Bog hr the where TBLong, and TBL24 called blocks, memory two uses DIR-24-8 necnetosfrCmue omnctosadPce Networks Packet and Communications Computer for Interconnections Example ro nFgr .6adti stesm ubr The number. same the is this and 3.16 Figure in arrow I-48prom Plou nu otwo to up in lookup IP performs DIR-24-8 p nTbe34adFgr 3.12. Figure and 3.4 Table in Downloaded By: 10.3.98.104 At: 03:52 27 Sep 2021; For: 9781315373485, chapter3, 10.1201/9781315373485-4 vr lmn nlddi h set the in included element every zero. to the filter the 0 of where bit obtained, every initializing set from element given starts For a filter For Bloom set. a gramming a about information abstract expanded. are 3.19 prefixes Figure some NHI. where the to and bit 123, interval prefix the for stores example entry an The shows entry. an in used bits t opcns n ipiiy lo le san of is because filter applications Bloom various A in simplicity. used and widely compactness is its and [19] queries membership Theory. Algorithm Filter Filter-Based Bloom Bloom 3.9 however, 2 is TBLong, pointers in of similar number maximum is of process number The the bits. address and destination 32 packet address, instead a memory using of bits as MSB used 24 the is where access, prefix memory single by a created intervals prefix the and scheme DIR24-8 expansion. in levels Prefix 3.17 FIGURE Lookup Address (IP) Protocol Internet rdc fpexepnin.A a eddcdfo iue31,tetotal by the a 3.18, (as Figure (2 entries from is several deduced scheme accessing this be for can require of amount As identification may memory expansion). the it prefix simplifies but levels of updated of table product number The be prefixes. small to expanded the for entries as NHI simple of replicates is several update copy to need may it k L isidctdby indicated bits evl Levl 32 24 x j hr 1 where , ≤ 2 8 h i ( x h lo le sasaeecetdt tutr for structure data space-efficient a is filter Bloom A j i ≤ ( ) x m < j j r e ooe hspoeuei eetdfor repeated is procedure This one. to set are ) ≤ opormelement program To . n S , . k 24 ahindices hash 2 + 20 ) W where , S h m i = ( btaryta contains that array -bit x x { j j o 1 for ) x W noaBomfilter, Bloom a into 1 x , stenme of number the is 2 , · · · ≤ TBLlong TBL24 x , i ≤ n } 12 pro- , k and are 67 Downloaded By: 10.3.98.104 At: 03:52 27 Sep 2021; For: 9781315373485, chapter3, 10.1201/9781315373485-4 qain32[118]. 3.2 Equation rme by grammed rate false-positive the ements, zero, are bits DIR-24-8 of Implementation 3.18 FIGURE 68 lmnscnb acltda olw [118]: follows as calculated be can elements all If checked. functions, ot hspicpei sdb lo le oipoetepromnei a in the performance for the improve except to nodes, filter ancestor Bloom without a by exist used cannot is node principle Filter This a Bloom root. trie, a binary Using a Lookup In Address IP 3.9.0.4 for result negative a produces filter lo lesmyhv as oiie,btn as eaie.For negatives. false no but positives, false have may filters Bloom iue32 hw neapeo lo le.TeBomfitri pro- is filter Bloom The filter. Bloom a of example an shows 3.20 Figure an for functions hash of number optimal The input given a of membership the for Querying necnetosfrCmue omnctosadPce Networks Packet and Communications Computer for Interconnections h i 24 MSBs 24 Packet destination ( S y y k o 1 for ) = sdfiieyntamme of member a not definitely is isaeone, are bits f { x 1 0 = 1 x , " ≤ 2 1 24 2 TBL24 − x , i entries ≤ 8 LSBs  3 x , 1 k y − The . 4 } k f scniee ebrof member a considered is n ure yinputs by queried and , m opt 1 fan of  y = k kn 12 n as-oiiersl for result false-positive a and 8 20 isidctdb h ahidcsare indices hash the by indicated bits m # n k m n2(3.3) 2 ln ≈ btBomfitri acltdas calculated is filter Bloom -bit  S 1 . − 2 TBLlong 20 y e − entries loue h same the uses also kn/m m btBomfitrof filter Bloom -bit y  k and S fayo the of any If . z information h Bloom The . Next hop z . k n (3.2) hash el- n k Downloaded By: 10.3.98.104 At: 03:52 27 Sep 2021; For: 9781315373485, chapter3, 10.1201/9781315373485-4 h eaiersl en htteei ond eetdi h urn and current the in detected node produced. no is is result queried, there negative is that a filter means until Bloom result level, The negative access table. The the hash off-chip increasing an linearly in while stored address. the and destination filter reduce packet level Bloom given matching to a best used for the prefix is determining matching filter by longest the Bloom accesses holding memory The because off-chip memory requirements. on- off-chip of memory using in number implemented implemented larger be usually its may is filter of trie Bloom a The while [118]. memory, trie chip binary a on search filter. Bloom a of example An 3.20 FIGURE TBLong. on prefixes expanded with 123 interval of Example 3.19 FIGURE Lookup Address (IP) Protocol Internet nti prah oe fabnr reaeporme na on-chip an in programmed are trie binary a of nodes approach, this In 10.543 10.54 10.543 10.543 10.54 10.532 10.542 10.5 0 0 k=3 n=4 1 1 TBL24 0 2 0 3 0 4 0 0 1 0 0 0 0 5 X 1 6 1 0 7 123 A A A A A 0 8 0 y? 9 Key C B A 10 0 = = = 1 1 to 10.5492/6 10.543/2 10.56/ 12 0 table 13 X 0 2 14 1 15 entris 0 123x56+9 123x56+9 123x56+ 16 0 123x56 123x56+9 123x56+ 123x56+ 0 17 18 1 X 19 0 3 20 TBLlong 0 21 0 z? 2 1 23 0 24 0 X 25 0 4 B A C C C B B 26 0 27 1 28 0 29 0 (block alocted 256 30 1 10.543 31 0 prefix entris 123) to 69 Downloaded By: 10.3.98.104 At: 03:52 27 Sep 2021; For: 9781315373485, chapter3, 10.1201/9781315373485-4 xml fafradn table. forwarding a of Example 3.5 TABLE assumed is It node. 3.5. prefix prefix matching Table longest ancestor in the direct inherits table its 3.21 using forwarding Figure from algorithm in example node lookup gray-colored the easily address each for that can IP filter the prefix, node shows Bloom internal matching 3.21 each a best Figure for problem. the information this back- Precomputing solve corresponding the the encountered, place. because is storing takes level, node and the internal also on an is process If re- prefix exist. tracking positive matching may the best nodes occurs, the internal result that empty positive guarantee not a probability though does false-positive even sult the However, of level. product each the for is probability this because creases ec,tepoaiiyo h ubro aktakn rcse r calculated and are where processes 3.2, back-tracking of Equation number by the of probability the Hence, level levels at on occur positives outcome false negative if Similarly, place. takes process eutwe h lo le rdcsangtv rb aktakn process back-tracking a by or negative a produces filter Bloom the when result level on is prefix matching level best at called the the is that positive, Assuming process false tives. This If filter’s level. found. Bloom smaller is the a of prefix to because matching goes found the procedure not result. search after is the right node level, verify finish matching candidate to equal the may a probed from length process starts is a approach matching table this with the of hash prefix procedure off-chip search the the the Using Because level, candidate prefix. candidate the is matching the outcome to best positive the last the storing of level level the Therefore, levels. longer 70 h rbblt htmlil aktakn rcse cu ail de- rapidly occur processes back-tracking multiple that probability The oeta ahetyi cesdete o h ee ihtels positive last the with level the for either accessed is entry hash a that Note posi- false of rate the on depends processes back-tracking of number The f i necnetosfrCmue omnctosadPce Networks Packet and Communications Computer for Interconnections steflepstv aeo oei level in node a of rate false-positive the is L 1adangtv tlevel at negative a and +1 b j ersnsta aktakn a occurred has back-tracking that represents rob P L ( ,tobc-rcigpoesstk place. take processes back-tracking two 3, + b j L = ) 2aepoue,asnl back-tracking single a produced, are +2 11111* 111* 1101* 110101* 1* 010* 00* prefix IP i = L Y L + +1 j f i rfi ID prefix i . P6 P5 P4 P3 P2 P1 P0 L L and 1 + faflepositive false a if , back-tracking L n a and 2 + j times (3.4) . Downloaded By: 10.3.98.104 At: 03:52 27 Sep 2021; For: 9781315373485, chapter3, 10.1201/9781315373485-4 cesda ee sn h rfi f100 hc stelvlo h last the of level longest precomputed the the is returning which is by 11010, table over of hash is At prefix search the prefix results. matching the Hence the positive and result. using produces result, negative 5 it positive a level and produces at 5 filter Bloom through accessed The Bloom follows: 1 the as lengths 6, is 110100 for level of queried address is trie input a the filter for in procedure node search every the while table, filter. hash Bloom level Figure the the at in in in lines positive programmed stored dotted false is necessarily with a not (denoted nor children are both negative 3.21) with a nodes neither internal is Hence result the children, hnteBomfitrpoue as oiie fand tlevel at node a If positive. false a produces filter Bloom the when filter. Bloom a using search trie Improving 3.21 FIGURE Lookup Address (IP) Protocol Internet iaytes hs rprisaebsdo bevtosta fabnr tree binary of a properties if helicoidal that the observations on and based lengths are prefix search properties prefix different These parallel the lookup trees. 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