Space-Efficient TCAM-Based Classification Using Gray Coding

• Published in: IEEE transactions on computers Vol. 61; no. 1; pp. 18 - 30
• Main Authors: Bremler-Barr, A., Hendler, D.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2012; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Classification; Comparative analysis; Encoding; Gray code; packet classification; Pattern matching; range encoding; Redundancy; Reflective binary codes; TCAM; Throughput
• ISSN: 0018-9340; 1557-9956
• DOI: 10.1109/TC.2010.267

Ternary content-addressable memories (TCAMs) are increasingly used for high-speed packet classification. TCAMs compare packet headers against all rules in a classification database in parallel and thus provide high throughput unparalleled by software-based solutions. TCAMs are not well-suited, however, for representing rules that contain range fields. Such rules typically have to be represented (or encoded) by multiple TCAM entries. The resulting range expansion can dramatically reduce TCAM utilization. A TCAM range-encoding algorithm A is database-independent if, for all ranges r, it encodes r independently of the database in which it appears; otherwise, we say that A is database-dependent. Typically, when storing a classification database in TCAM, a few dozens of so-called extra bits in each TCAM entry remain unused. These extra bits are used by some (both database-dependent and database-independent) prior algorithms to reduce range expansion. The majority of real-life database ranges are short. We present a novel database-independent algorithm called Short Range Gray Encoding (SRGE) for the efficient representation of short range rules. SRGE encodes range endpoints as binary-reflected Gray codes and then represents the resulting range by a minimal set of ternary strings. To the best of our knowledge, SRGE is the first algorithm that achieves a reduction in range expansion in general, and a significant expansion reduction for short ranges in particular, without resorting to the use of extra bits. The "traditional" database-independent technique for representing range entries in TCAM is prefix expansion. As we show, SRGE significantly reduces the expansion of short ranges in comparison with prefix expansion. We also prove that the SRGE algorithm's range expansion is at least as good as that of prefix expansion for any range. Real-world classification databases contain a small number of unique long ranges, some of which appear in numerous rules. These long ranges cause high expansion which is not significantly reduced by any database-independent range encoding scheme that we are aware of, including SRGE. We introduce hybrid SRGE, a database-dependent encoding scheme that uses SRGE for reducing the expansion of short ranges and uses extra bits for reducing the expansion caused by long ones. Our comparative analysis establishes that hybrid SRGE utilizes TCAM more efficiently than previously published range-encoding algorithms. This work also makes a more theoretic contribution. Prefix expansion for ranges defined by W-bit endpoints has worst-case expansion ratio of 2W-2. It follows from the work of Schieber et al. [1] that the SRGE algorithm has a slightly better worst-case expansion ratio of 2W-4. We prove that any independent TCAM encoding scheme has worst-case expansion ratio of at least W.