Cuckoo Filter: Practically Better Than Bloom

Transcription

1 Cuckoo Filter: Practically Better Than Bloom Bin Fan (CMU/Google) David Andersen (CMU) Michael Kaminsky (Intel Labs) Michael Mitzenmacher (Harvard) 1

2 What is Bloom Filter? A Compact Data Structure Storing Set-membership Bloom Filters answer is item x in set Y by: definitely no, or probably yes with probability ε to be wrong false positive rate Benefit: not always precise but highly compact Typically a few bits per item Achieving lower ε (more accurate) requires spending more bits per 2 item

3 Example Use: Safe Browsing It is Good! Lookup( ) Probably Yes! No! Please verify Remote Server Known Malicious URLs Stored in Bloom Filter Scale to millions URLs 3

4 Bloom Filter Basics A Bloom Filter consists of m bits and k hash functions Example: m = 10, k = 3 Insert(x) Lookup(y) = not found hash 1 (x) hash 2 (x) hash 3 (x) hash 1 (y) hash 2 (y) hash 3 (y)

5 Succinct Data Structures for Approximate Set-membership Tests High Performance Low Space Cost Delete Support Bloom Filter Counting Bloom Filter Quotient Filter Can we achieve all three in practice? 5

6 Outline Background Cuckoo filter algorithm Performance evaluation Summary 6

7 Basic Idea: Store Fingerprints in Hash Table Fingerprint(x): A hash value of x Lower false positive rate ε, longer fingerprint 0: 1: 2: 3: 4: 5: 6: 7: FP(a) FP(c) FP(b) 7

8 Basic Idea: Store Fingerprints in Hash Table Fingerprint(x): A hash value of x Lower false positive rate ε, longer fingerprint Insert(x): add Fingerprint(x) to hash table 0: 1: 2: 3: 4: 5: 6: 7: FP(x) FP(a) FP(c) FP(b) 8

9 Basic Idea: Store Fingerprints in Hash Table Fingerprint(x): A hash value of x Lower false positive rate ε, longer fingerprint Insert(x): add Fingerprint(x) to hash table Lookup(x): search Fingerprint(x) in hashtable Lookup(x) = found 0: 1: 2: 3: 4: 5: 6: 7: FP(x) FP(a) FP(c) FP(b) 9

10 Basic Idea: Store Fingerprints in Hash Table Fingerprint(x): A hash value of x Lower false positive rate ε, longer fingerprint Insert(x): add Fingerprint(x) to hash table Lookup(x): search Fingerprint(x) in hashtable Delete(x): remove Fingerprint(x) from hashtable How to Construct Hashtable? Delete(x) 0: 1: 2: 3: 4: 5: 6: 7: FP(x) FP(a) FP(c) FP(b) 10

11 (Minimal) Perfect Hashing: No Collision but Update is Expensive Perfect hashing: maps all items with no collisions {a, b, c, d, e, f} f(x) FP(b) FP(e) FP(c) FP(d) FP(f) FP(a) 11

12 (Minimum) Perfect Hashing: No Collision but Update is Expensive Perfect hashing: maps all items with no collisions f(x) {a, b, c, d, e, f} {a, b, c, d, e, g} f(x) =? FP(b) FP(e) FP(c) FP(d) FP(f) FP(a) Changing set must recalculate f high cost/bad performance of update 12

13 Convention Hash Table: High Space Cost Chaining : Linear Probing bkt0 Lookup(x) FP(a) bkt1 FP(f) bkt2 FP(c) bkt3 FP(a) FP(c) FP(d) Lookup(x) Pointers low space utilization Making lookups O(1) requires large % table empty low space utilization Compare multiple fingerprints sequentially 13 more false positives

14 Cuckoo Hashing [Pagh2004] Good But.. High Space Utilization 4-way set-associative table: >95% entries occupied Fast Lookup: O(1) lookup(x) hash 1 (x) hash 2 (x) 0: 1: 2: 3: 4: 5: 6: 7: Standard cuckoo hashing doesn t work with fingerprints[pagh2004] Cuckoo hashing. 14

15 Standard Cuckoo Requires Storing Each Item 0: 1: Insert(x) h 1 (x) 2: 3: 4: b c h 2 (x) 5: 6: a 7: 15

16 Standard Cuckoo Requires Storing Each Item 0: 1: Insert(x) 2: 3: 4: b c h 2 (x) 5: 6: x Rehash a: alternate(a) = 4 Kick a to bucket 4 7: 16

17 Standard Cuckoo Requires Storing Each Item 0: 1: Insert(x) 2: 3: 4: b a Rehash c: alternate(c) = 1 Kick c to bucket 1 h 2 (x) 5: 6: x Rehash a: alternate(a) = 4 Kick a to bucket 4 7: 17

18 Standard Cuckoo Requires Storing Each Item Insert(x) 0: 1: 2: 3: 4: c b a Insert complete (or fail if MaxSteps reached) Rehash c: alternate(c) = 1 Kick c to bucket 1 h 2 (x) 5: 6: x Rehash a: alternate(a) = 4 Kick a to bucket 4 7: 18

19 Challenge: How to Perform Cuckoo? Cuckoo hashing requires rehashing and displacing existing items 0: 1: 2: 3: 4: 5: 6: 7: FP(b) FP(c) FP(a) Kick FP(c) to which bucket? Kick FP(a) to which bucket? With only fingerprint, how to calculate item s alternate bucket? 19

20 We Apply Partial-Key Cuckoo Standard Cuckoo Hashing: two independent hash functions for two buckets bucket1 = hash 1 (x) bucket2 = hash 2 (x) Partial-key Cuckoo Hashing: use one bucket and fingerprint to derive the other [Fan2013] bucket1 = hash(x) bucket2 = bucket1 hash(fp(x)) To displace existing fingerprint: alternate(x) = current(x) hash(fp(x)) [Fan2013] MemC3: Compact and Concurrent MemCache 20 with Dumber Caching and Smarter Hashing

21 Partial Key Cuckoo Hashing Perform cuckoo hashing on fingerprints 0: 1: 2: 3: 4: 5: 6: 7: FP(b) FP(c) FP(a) Kick FP(c) to 4 Kick FP(a) to 6 hash(fp(c)) hash(fp(a)) Can we still achieve high space utilization with partial-key cuckoo 21 hashing?

22 Fingerprints Must Be Long for Space Efficiency Table Space Utilization When fingerprint > 5 bits, high table space utilization Table size: n=128 million entries Fingerprint must be Ω(logn/b) bits in theory n: hash table size, b: bucket size see more analysis in paper 22

23 Space Efficiency More Space bits per item to achieve ε Lower bound More False Positive ε: target false positive rate 24

24 Space Efficiency More Space bits per item to achieve ε Bloom filter Lower bound More False Positive ε: target false positive rate 25

25 Space Efficiency More Space bits per item to achieve ε Bloom filter Lower bound Cuckoo filter More False Positive ε: target false positive rate 26

26 Space Efficiency More Space bits per item to achieve ε Bloom filter Lower bound Cuckoo filter Cuckoo filter + semisorting more compact than Bloom filter at 3% More False Positive ε: target false positive rate 27

27 Outline Background Cuckoo filter algorithm Performance evaluation Summary 28

28 Evaluation Compare cuckoo filter with Bloom filter (cannot delete) Blocked Bloom filter [Putze2007] (cannot delete) d-left counting Bloom filter [Bonomi2006] Cuckoo filter + semisorting More in the paper C++ implementation, single threaded [Putze2007] Cache-, hash- and space- efficient bloom filters. [Bonomi2006] Beyond Bloom filters: From approximate membership checks to approximate state machines. 29

29 Lookup Performance (MOPS) Hit Miss Cuckoo Cuckoo + semisort d-left counting Bloom blocked Bloom Bloom (no deletion) (no deletion) cf cfss dlbf bbf bf 30

30 Lookup Performance (MOPS) Hit Miss Cuckoo Cuckoo + semisort d-left counting Bloom blocked Bloom Bloom (no deletion) (no deletion) cf cfss dlbf bbf bf 31

31 Lookup Performance (MOPS) Hit Miss Cuckoo Cuckoo + semisort d-left counting Bloom blocked Bloom Bloom (no deletion) (no deletion) cf cfss dlbf bbf bf 32

32 Lookup Performance (MOPS) Hit Miss Cuckoo Cuckoo + semisort d-left counting Bloom blocked Bloom Bloom (no deletion) (no deletion) cf cfss dlbf bbf bf Cuckoo filter is among the fastest regardless 33 workloads.

33 Insert Performance (MOPS) Cuckoo Blocked Bloom d-left Bloom Standard Bloom Cuckoo + semisorting Cuckoo filter has decreasing insert rate, but overall is only slower than blocked Bloom 34 filter.

34 Summary Cuckoo filter, a Bloom filter replacement: Deletion support High performance Less Space than Bloom filters in practice Easy to implement Source code available in C++: 35

35 Othello Hashing and Its Applications for Network Processing Chen Qian Department of Computer Engineering Publications in ICNP 17, SIGMETRICS 17, MECOMM 17 and Bioinformatics

36 Background PhD in 2013 from UT Austin with Simon Lam Research: Computer networking SDN/NFV Internet of things Security 37

37 Motivation Network algorithms always prefer small memory and fast processing speed. Fast memory is precious resource on network devices Needs to reach the line rate to avoid being a bottleneck, under large traffic volume More important in networks with layer-two semantics 38

38 Othello Hashing Essentially a key-value lookup structure Keys can be any names, addresses, identifiers, etc. Values should not be too long. At most 64 bit. For example Key: network address; Value: link to forward a packet Key: virtual IP; Value: direct IP 39

39 Why Othello is special Minimal query time: only two memory read operations (cachelines) per query. Minimal memory cost: 10%-30% of existing hash tables (e.g., Cuckoo). Support dynamic updates: can be updated over a million times per second. 40

40 Idea of dynamic Othello lookups Controller Program Construct Update K-V Lookup Lookup Update via existing API of programmable networks 41 Optimize memory and query cost

41 How Othello works Basic version: Classifies keys to two sets XX and YY Equivalent to key lookups for a 1-bit value Query result ττ kk = 0 kk XX ττ kk = 1 kk YY Advance version: Classifies keys to 2 ll sets Equivalent to key lookups for a ll-bit value 42

42 Othello Query Structure nn is # of keys Two bitmaps aa, bb with size mm (mm in (1.33nn, 2nn)) h aa aa bb h bb Query is easy. Then how to construct it? mm bits ττ = is 0in set 1 = Y 1

43 Othello Control Structure: Construct GG: acyclic bipartite graph h aa aa uu 00 uu 11 uu 22 uu 33 uu 44 uu 55 uu 66 uu 77 kk h aa (kk) h bb (kk) 6 5 vv 00 vv 11 vv 22 vv 33 vv 44 vv 55 vv 66 vv 77 bb h bb 44

44 Othello Construct 45 h aa aa bb h bb If finding a cycle, use another pair kk <h a, h b > until an acyclic graph is built uu 00 vv 00 uu 11 uu 22 uu 33 uu 44 uu 55 uu 66 uu 77 h aa (kk) h bb (kk) For vv 11 vvn 22 names, vv 33 vv 44 vvthe 55 vvtime to find G is O(n)

45 Compute Bitmap aa uu 00 uu 11 uu 22 uu 33 uu 44 uu 55 1 uu 66 uu 77 kk h aa (kk) h bb (kk) set 6 5 Y vv 00 vv 11 vv 22 vv 33 vv 44 vv 55 vv 66 vv bb

46 Compute Bitmap aa uu 00 1 uu 11 uu 22 uu 33 0 uu 44 uu 55 1 uu 66 uu 77 kk h aa (kk) h bb (kk) set 6 5 Y 1 0 X 1 2 Y vv 00 vv 11 vv 22 vv 33 vv 44 vv 55 vv 66 vv X bb X If G is acyclic, easy to find a coloring plan 47

47 Name Addition color flip h aa aa uu 00 vv 00 1 uu 11 vv 11 uu 22 vv 22 uu 33 vv 33 0 uu 44 vv 44 uu 55 vv 55 uu 66 vv 66 uu 77 vv 77 bb h bb If G is acyclic, flipping is trivial 10 kk h aa (kk) h bb (kk) set 6 5 Y 1 0 X 1 2 Y 1 3 X 4 2 X 6 3 Y 48

48 L-Othello functionality Classifies names into 2 ll sets: ZZ 0, ZZ 1,, ZZ 2 ll 1 49 XX 1 YY1 ZZ 2 ZZ 0 ZZ 3 l < 8 for network devices ZZ 1 l Othellos can classify names to 2 l sets XX2 YY 2

49 Example Classify keys in 8 sets: ZZ 0, ZZ 1,, ZZ 7 Orthogonal separation of sets XX 3 = ZZ 0 ZZ 1 ZZ 2 ZZ 3 ; YY 3 = ZZ 4 ZZ 5 ZZ 6 ZZ 7. XX 2 = ZZ 0 ZZ 1 ZZ 4 ZZ 5 ; YY 2 = ZZ 2 ZZ 3 ZZ 6 ZZ 7. XX 1 = ZZ 0 ZZ 2 ZZ 4 ZZ 6 ; YY 1 = ZZ 1 ZZ 3 ZZ 5 ZZ 7. 6=(110) 2 kk YY 3 YY 2 XX 1 kk ZZ 6 ll Othellos : classify keys in 2 ll sets. 50

50 aa 1 uu uu 11 uu 22 uu 33 uu 44 uu 55 uu 66 uu 77 aa 2 uu 00 Same G, h a, h b uu 11 uu 22 uu 33 uu 44 uu 55 uu 66 Different coloring plan and bitmaps uu 77 bb 1 vv 00 vv 11 vv 22 vv 33 vv 44 vv 55 vv 66 vv bb 2 vv 00 vv 11 vv 22 vv 33 vv 44 Do we need 2l memory reads to query l Othellos? vv 55 vv 66 vv Othello 1 Same X UY Othello 2 51

51 aa 1 uu 00 h aa AA[0]AA[1] AA uu 11 uu 22 uu 33 uu 44 uu 55 uu 66 uu 77 aa 2 uu 00 uu 11 uu 22 uu 33 ττ kk = = 11 2 uu 44 uu 55 uu 66 uu 77 bb 1 vv vv 11 vv 22 vv 33 vv 44 vv 55 vv 66 vv 77 k is in set Z BB h bb bb 2 vv 00 vv 11 vv 22 vv 33 vv 44 vv 55 vv 66 vv CPUs can read l bits at one time Othello 1 Othello 2

52 Alien keys What is ττ kk = aa h aa kk not in SS? An arbitrary value bb[h bb kk ] when kk is ττ kk return 1 with when aa ii = 1 && bb jj = 0, or aa ii = 0&& bb jj = 1 53

53 Applications of Othello 1. Forwarding Information Base (FIB) 2. Software load balancer 3. Data placement and lookup 4. Private queries 5. Genomic sequencing search And more 54

54 A Concise FIB Resolving FIB explosion is crucial For layer-two interconnected data centers For OpenFlow-like fine-grained flow control Concise using l-othello is a portable solution In hardware devices Or software switches A Fast, Small, and Dynamic Forwarding Information Base, In ACM SIGMETRICS 2017 A 55 Concise Forwarding Information Base for Scalable and Fast Name Switching, in IEEE ICNP 2017.

55 Network-wide updating If all devices share a same set of network names/addresses Such as in layer-two Ethernet-based data centers All Othellos will share a same G. Hence network-wide updating is very efficient! Update consistency also provided 56

56 Implementation of three prototypes 1. Memory mode Query and control structures running on different threads. 2. CLICK modular router 3. Intel Data Plane Development Kit (DPDK) 57

57 Comparison: Buffalo Yu, Fabrikant, Rexford, in CoNEXT 09 Cuckoo hashing Zhou, Fan, Lim, Kaminsky, Andersen, in CoNEXT 13 and SIGCOMM 15 58

58 Comparison: Memory size FIB Example Memory Size Name Type # Names # Actions Concise Cuckoo Buffalo MAC (48 bits) 7* M 5.62M 2.64M MAC (48 bits) 5* M 40.15M 27.70M MAC (48 bits) 3* M M M IPv4 (32 bits) 1* M 4.27M 3.77M IPv6 (128 bits) 2* M 34.13M 11.08M OpenFlow (356 bits) 3* M 14.46M 1.67M OpenFlow (356 bits) 1.4* M 67.46M 18.21M File name (varied) K 19.32M 1.35M 59

59 Query speed 2x to 4x speed advantage 60

60 Update speed 61

61 For unknown network names 1. For data centers with most internal traffic Such situation is rare 2. For networks with much incoming traffic A filter can be installed at a firewall 3. Concise may include an r-bit checksum. A lookup still requires 2 memory accesses in total, as long as l + r <=

62 Thank You Chen Qian