Bloomier filter
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1 Chisel: A Storage-efficient, Collision-free Hash-based Network Processing Architecture Author: Jahangir Hasan, Srihari Cadambi, Venkatta Jakkula Srimat Chakradhar Publisher: ISCA 2006 Presenter: Yuen-Shuo Li Date: 2012/10/03 Outline Introduction Bloomier Filter Issue – False Positive Issue - Wildcard Issue - Update Performance 2 Introduction(1/2) There are three major families of techniques for performing LPM TCAM Trie-Based Large cost and power dissipation Large memory requirements and long lookup latencies Hash-Based lower power, small memory requirement, and short lookup latencies can’t handle wildcard and have collision problem 3 Introduction(2/2) Chisel(Collision-free Hashing-Scheme for LPM) use collision-free hashing scheme called Bloomier filter solve two key problem false positive wildcard support incremental updates 4 Bloomier Filter(1/5) recall Bloom Filter a bit vector multiple hash function false-positive problem 5 Bloomier Filter(2/5) an extension of Bloom filter collision-free hashing scheme support storage and retrieval of arbitrary per-key information support static sets of keys and not dynamic update inherit Bloom filter’s false-positive problem 6 Bloomier Filter(3/5) Idea 7 HN: The set of k hash values of a key find a T(t) among HN(t) such that there is a one-to-one mapping between all t and T(t) setup the Index Table, so that a lookup for t return location T(t) and store value in a separate Result Table at address T(t) Bloomier Filter(4/5) It is possible that this setup process can fail • use more hash function or expand the table • and use a little TCAM 8 Bloomier Filter(5/5) 9 In order to retrieve T(t), the solution is to store some value in T(t) use XOR 𝐻𝑖 𝑡 ∶ the value of the i’th hash function D[𝐻𝑖 𝑡 ] ∶ the data value in the 𝐻𝑖 𝑡 ‘th location Issue – False Positive(1/2) can occur when lookup involves some key t which was not in the set of original keys used for setup two way add a checksum field to each hash bucket still has false positives use chisel architecture eliminating false positives 10 Issue – False Positive(2/2) encode a pointer p(t) for each t instead of 𝐻𝑖 𝑡 use two separate tables to store f(t) and t 11 Issue – Wildcard(1/3) Because hash functions cannot operate on wildcard bits the way to support wildcard bits large number of tables CPE results in considerable hardware complexity and cost resulting in huge amounts of memory prefix collapsing 12 Issue – Wildcard(2/3) 13 Issue – Wildcard(3/3) 14 Issue - Update update for existing prefix is easy just change the entry in the Result Table remove: temporarily mark the prefix dirty 15 a large fraction of updates are actually route-flaps maintain shadow copy of the date structures in software first incrementally update the shadow copy then transfer the data structure to the hardware engine route-flaps: a prefix is added back after being recently removed Performance(1/3) 16 Performance(2/3) 17 Performance(3/3) 18
