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TaCo: Semantic Equivalence of IP Prefix Tables

Author: Ahsan Tariq, Sana Jawad and Zartash Afzal Uzmi Publisher: IEEE ICCCN 2011Presenter: Li-Hsien, HsuData: 9/7/2011

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Outline

I. Introduction

II. Problem Statement

III. Tables with non-Overlapping Prefixes

IV. Tables with Overlapping Prefixes

V. TaCo Complexity and Real-World Routing Data

I. Introduction(1/4)

Routers in large service provider networks maintain the so-called default free zone (DFZ) tables.

the DFZ table in a service provider network enlists all the prefixes globally reachable, it has roughly the same number of prefixes for all service providers. This number has increased from fewer than 50,000 prefixes in 1998 to over 350,000 in 2011.

Increased number of prefixes in the DFZ table pose a threat to the scalability of global routing.

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I. Introduction(2/4)

To combat the increase in the DFZ table size is to aggregate the prefixes, resulting in a reduction in the number of prefixes.

the underlying intention behind aggregation is to substitute one table of prefixes with another with fewer prefixes.

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I. Introduction(3/4)

Brute force method

Randomly chosen IP addresses.

TaCo(Table Comparison)

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I. Introduction(4/4)

TaCo is not an aggregation algorithm; that is it does not reduce the size of FIB(forwarding information base) tables. Rather, TaCo is an algorithm to verify semantic equivalence of two given tables.

TaCo may be used to ascertain the correctness of an aggregation algorithm that claims to reduce the size of a given table.

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II. Problem Statement

We aim to verify if the two tables are semantically equivalent (i.e., T1 ≡ T2). That is, T1 and T2 can be used in place of each other by a router performing the lookup operation for forwarding purposes.

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III. Tables with non-Overlapping Prefixes

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III. Tables with non-Overlapping Prefixes

Non-overlapping, i.e., within each table, the prefixes cover disjoint IP address spaces.

Theorem 3.1 (Tables with non-overlapping prefixes):

Let T1 and T2 be two prefix tables, each of which contains non-overlapping prefixes. If any single IP address from the IP space covered by each prefix in T1 and T2 results in the same next hop information when looked up in either table, then T1 ≡ T2, i.e., the tables are semantically equivalent.

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A.Example

To determine the semantic equivalence of these two tables, we need to consider just eight IP addresses, one extended from each of these eight prefixes

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B. Number of LPM Lookups

IP addresses extended from prefixes 000, 001, 10, and 11 in the first table T1 need to be looked up (via LPM) in T2, and, similarly, IP addresses extended from prefixes 00 and 1 in T2 need to be looked up (via LPM) in T1. There is no need to extend the prefix 01 which is common between the two tables.

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IV. Tables with Overlapping Prefixes

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A. Example

a direct application of Theorem 3.1 will not be possible.

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B. Tree Normalizing and Leaf Pushing

Tree Normalizing

Normalizing a binary prefix tree transforms it into a strictly binary tree. In this process, new prefix nodes (without any next hop information) are added to the tree such that every prefix node has either two or no children.

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C. Number of Lookups (Overlapping Prefixes)

Theorem 4.3 (Number of LPM Lookups (Generic Case)): The number of LPM lookups needed by TaCo to establish the semantic equivalence of prefix tables T1 and T2 is bounded by (L + 1)(|T1| + |T2|), where L is the maximum length of a prefix (L = 32 for IPv4).

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V. TaCo Complexity and Real-World Routing Data

We obtained routing data from routeviews, and separately applied three existing aggregation algorithms (Level 1, Level 2, and ORTC proposed for local FIB reduction) to obtain the aggregated tables.

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V. TaCo Complexity and Real- World Routing Data

The number of such comparisons is a small fraction (between 5-7%) of the upper bound (also shown)

Consequently, TaCo is able to test the semantic equivalence of real-world prefix tables within a very short time

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