Exploiting Order Independence for Scalable and Expressive Packet - PowerPoint PPT Presentation

Exploiting Order Independence for Scalable and Expressive Packet Classification Author: Kirill Kogan, Sergey I. Nikolenko, Ori Rottenstreich, William Culhane, and Patrick Eugster Presenter: Qing Lyu 2017/04/12 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 24, NO. 2, APRIL 2016

Outline l Introduction l Order-independence l Problem formulation and theorem l Solutions l Simulations l Conclusions 2 Outline

Outline l Introduction l Order-independence l Problem formulation and theorem l Solutions l Simulations l Conclusions 3 Outline

Packet Classification 4 l Introduction

Packet Classification TCAM l NFV, power consumption and heat l cannot efficiently represent range rules, especially multiple fields l exponential space growth Software (SW) l tradeoffs between (memory) space and (lookup) time. 5 Introduction

TCAM Advantages: efficiently represent multi-field classification with prefixes Disadvantages: suffers an exponential blowup from range expansion each range-based field in a rule introduces an additional multiplicative factor 6 Introduction

SW-Complexity bounds Software-based packet classifier with rules and fields K ≥ 3 O(𝑂 ( ) space, 𝑃(log𝑂) time 𝑃 𝑂 𝑡𝑞𝑏𝑑𝑓 , 𝑃(𝑚𝑝𝑕 (67 𝑂) time E.g. 100 rules and 4 fields, O(𝑂 ( ) is about 100MB, 𝑃(𝑚𝑝𝑕 (67 𝑂) time is about 350 memory accesses 7 Introduction

Ranges Standard five-tuples with two fields which include ranges Desired implementations for classifiers on ranges: IP or MAC addresses dates packet lengths etc 8 Introduction

Outline l Introduction l Order-independence l Problem formulation and theorem l Solutions l Simulations l Conclusions 9 Outline

Contributions Exploit the order-independenceof classifiers Reduce the number of classification fields represented by prefixes or ranges Implemented in linear space and with worst-case guaranteed logarithmic time Allows the addition of more fields including range constraints without impacting space and time complexities 10 Introduction

Model Description A packet header contains 𝑙 fields A field 𝑗, 1 ≤ i ≤ 𝑙 is a string of 𝑋 ? bits A classifier K is an ordered set of rules , 𝑆 7 , … , 𝑆 B A rule 𝑆 C is a is an ordered set of 𝑙 fields and an associated action 𝐵 C A field 𝐺 ? is represented by a range of values on 𝑋 ? bits each rule contains 𝑙 ranges 𝑆 = (𝐽 7 , … , 𝐽 ( ) , 𝐽 ? = [𝑚 ? , 𝑣 ? ] 11 Order-independence

Denotation K 6K the classifier obtained from by K by removing a set of fields 𝐺 from each rule K LK the classifier obtained from K by extending its rules with 𝐺 (with values defined separately for every rule) 12 Order-independence

Denotation 𝑗𝑜𝑢𝑓𝑠𝑡𝑓𝑑𝑢 at least one header that matches both rules 𝑆 7 , 𝑆 P 𝑒𝑗𝑡𝑘𝑝𝑗𝑜𝑢 𝑆 7 , 𝑆 S 𝑆 7 = 100 ∗ 𝑝𝑠𝑒𝑓𝑠 − 𝑗𝑜𝑒𝑓𝑞𝑓𝑜𝑒𝑓𝑜𝑢 𝑆 S = 01 ∗∗ 𝑆 7 , 𝑆 S are order-independent if the 𝑆 P = 1 ∗∗∗ corresponding sets of matching headers are disjoint, every header matches at most one of them. 13 Order-independence

Denotation A classifier K is called order-independent if any two of its rules are filter-order-independent K ( S ) denotes a classifier that uses only a subset 𝑇 of fields in classification 14 Order-independence

Order-independence K X : with the same rules as K sorted in a different order Then, any packet header 𝑞 is matched by the same rule in K X and K The condition is satisfied when rules do not intersect i.e., for each pair of rules there is at least one field in which the corresponding ranges (or prefixes) are disjoint. Transitively order- dependent 𝑆 7 , 𝑆 S 𝑆 S , 𝑆 P 15 Order-independence

Cont. K 𝑆 7 =([1,3],[4,5]) 𝑆 S =([5,6],[4,5]) order-independent K X 𝑆 P =([1,3],[4,5]) 𝑆 Z =([2,4],[4,5]) order-dependent as (3,4) matches both rules 16 Order-independence

Two Encoding Schemes Binary Encoding Worst case 2(𝑋 − 1) TCAM entries SRGE Encoding Worst case 2(𝑋 − 2) TCAM entries Multi-field ( 𝑙 -field) range, upper bound entries # Binary: (𝑋 − 2) ( , SRGE: (𝑋 − 4) ( 17 Order-independence

Binary Encoding Binary Encoding 𝑋 − 𝑐𝑗𝑢 range is encoded as a union of disjoint subtrees in the binary tree of 2 ^ leaves Each subtree is represented by a single prefix TCAM entry the maximal number of entries to encode a range (worst-case expansion) is 2(𝑋 − 1) 18 Order-independence

Binary Encoding 𝑋 = 5 Range [16,23] A single entry (01 ∗∗∗) Range 1,30 2𝑋 − 2 entries (00001),(0001*),(001**),(01***),(10***),(110**),(1 110*),(11110) 19 Order-independence

SRGE Improve the worst-case bound to 2(𝑋 − 2) entries by representing values in Gray code. Entries are not necessarily prefixes and do not necessarily represent disjoint subsets of the range Range 1,30 2𝑋 − 4 entries 20 Order-independence

Example1 K = 𝑆 7 , 𝑆 S ,𝑆 P with two fields of 5 bits each 𝑆 7 = ( 1,3 , [4,31]) Binary encoding 1 st field:(00001,0001*) 6 entries 2 nd field:(00100,01***,1****) 𝑆 S = ( 4,4 ,[2,30]) 7 entries 1 st field:(00100) 2 nd field:(00010,001**,01***,10***,110**,1110*,11110) 𝑆 P = ( 7,9 ,[5,21]) 10 entries 1 st field:(00111,0100*) 2 nd field:(00101,0011*,01***,100**,1010*) 21 Order-independence

Example1 K L7 = 𝑆 7 L7 with one additional fields L7 ,𝑆 S L7 , 𝑆 P of 5 bits L7 = ( 1,3 , 4,31 , [1,28]) 𝑆 7 L7 = ( 4,4 , 2,30 , [4,27]) 𝑆 S L7 = ( 7,9 , 5,21 , [3,18]) 𝑆 P 42+28+50=120 entries 22 Order-independence

Outline l Introduction l Order-independence l Problem formulation and theorem l Solutions l Simulations l Conclusions 23 Outline

Tested Classifiers 12 classifiers from Classbench generated with real parameters Each with 50K rule on 6 fields 5 real-life classifiers from Cisco Systems 24 Problem formulation and theorem

Tested Classifiers 12 25 Problem formulation and theorem

Fields Expansion Theorem ---Theorem 1 let K Ld be a classifier that results from an order- independent classifier K by adding new fields 𝑛 of any width Then, K with a false-positive check of a single matched rule is a semantically equivalent representation of K Ld 26 Problem formulation and theorem

Theorem 1 Introducing additional fields based on prefixes or ranges to an order−dependent classifier 1. affects only the encoding size of its order−dependent part 2. new fields in the order-independent part can be ignored without affecting the classification outcome 3. The space and lookup time complexity of classification in the order-independent do not increase 27 Problem formulation and theorem

Theorem 1 Previous new fields based on prefixes or ranges significant increase the software solution 𝑃(𝑚𝑝𝑕 (67 𝑂) look up time in linear memory Likewise, TCAM-based solution, range converted to prefixes, new field based on ranges adds an additional multiplicative factor for the required TCAM space 28 Problem formulation and theorem

Theorem 1 Support for additional fields amenable to range rules would greatly improve classification expressiveness e.g., ranges on dates, packet length, etc 29 Problem formulation and theorem

Theorem 1 fsadf 30 Problem formulation and theorem

Theorem 1 fsadf 31 Problem formulation and theorem

Example2 K = 𝑆 7 , 𝑆 S ,𝑆 P with three fields of 5 bits 𝑆 7 = ( 1,3 , 4,31 , [1,28]) 𝑆 S = ( 4,4 , 2,30 , [4,27]) 42+28+50=120 entries 𝑆 P = ( 7,9 , 5,21 , [3,18]) K 6{S,P} = (𝑆 7 6{S,P} ,𝑆 S 6{S,P} , 𝑆 P 6{S,P} ) 6{S,P} = ( 1,3 ) 𝑆 7 6{S,P} = 2+1+2=5 entries 𝑆 S 4,4 6{S,P} = ( 7,9 ) 𝑆 P 32 Problem formulation and theorem

Fields Reduction Theorem ---Theorem 2 let K 6d be a classifier that results from an order- independent classifier K by removing 𝑛 fields If K 6d is order-independent,then, K 6d with a false-positive check of a single matched rule is a semantically equivalent representation of K 33 Problem formulation and theorem

Theorem 2 If the reduced classifier K 6d contains at most two fields Then, we can efficiently implement lookup in time logarithmic 𝑂 in with (near-) linear memory For TCAM based solutions, reduces the required TCAM space proportionally 34 Problem formulation and theorem

Theorem 2 asfd 35 Problem formulation and theorem

Fields Subset Minimization (FSM) Find a maximal subset of fields M of an order- independent classifier K such that K 6d is order-independent ， if there are several such subsets, choose M with maximal total width (to minimize lookup word width) multi-group representation 𝛾 groups 36 Problem formulation and theorem

FSM+multi-group representation 𝛾 groups: 1. each rule belongs to a single group 2. the rules of each group are order-independent on a subset of 𝑙 fields of K 3. different groups can reuse the same fields to keep order-independence 𝑚 − 𝑁𝐻𝑆: find the minimal number of disjoint groups that each group is order-independent on 𝑚 fields 37 Problem formulation and theorem

FSM+multi-group representation dfs 38 Problem formulation and theorem