Kun Suk Kim

Data Structures for One-Dimensional Packet Classification Using Most-Specific-Rule Matching

We review the data structures that have been proposed for one-dimensional packet classification. Our review is limited to data structures for the case when ties among the rules that match an incoming packet are broken by selecting the matching rule that is most specific. For the case when the rule filters are destination-address prefixes or are nonintersecting ranges, this tie breaker corresponds to longest-prefix or shortest-range matching, respectively. When the rule filters are arbitrary ranges, this tie breaker resolves the tie only when the rule set is conflict free. Data structures for both static and dynamic rule tables are discussed.

Efficient Construction of Pipelined Multibit-Trie Router-Tables

Efficient algorithms to construct multibit tries suitable for pipelined router-table applications are developed. We first enhance the 1-phase algorithm of Basu and Narlikar, obtaining a 1-phase algorithm that is 2.5 to 3 times as fast. Next, we develop 2-phase algorithms that not only guarantee to minimize the maximum per-stage memory but also guarantee to use the least total memory subject to the former constraint. Our 2-phase algorithms not only generate better pipelined trees than those generated by the 1-phase algorithm, but they also take much less time. A node pull-up scheme that guarantees no increase in maximum per-stage memory as well as a partitioning heuristic that generates pipelined multibit tries requiring less maximum per-stage memory than required by the tries obtained using the 1-phase and 2-phase algorithms are also proposed

Efficient construction of fixed-stride multibit tries for IP lookup

Srinivasan and Varghese (1999) have proposed the use of multibit tries to represent routing tables used for Internet (IP) address lookups. They propose an O(k*W/sup 2/) time dynamic programming algorithm to determine the strides of an optimal k-level multibit fixed-stride trie when the longest prefix in the routing table has length W. The authors improve on this algorithm by providing an alternative dynamic programming formulation. While the asymptotic complexity of the resulting algorithm for fixed-stride tries is the same as that of the algorithm of Srinivasan and Varghese, experiments using real IPv4 routing table data indicate that their algorithm runs 2 to 4 times as fast.

An O(logn) dynamic router-table design

Internet (IP) packet forwarding is typically done by finding the longest prefix in a router table that matches the packets destination address. For W-bit destination addresses, the use of binary tries enables us to determine the longest matching prefix in O(W) time, independent of the number n of prefixes in the router table. New prefixes may be inserted and old ones deleted in O(W) time also. Since n/spl Lt/2/sup W/ in real router tables, it is desirable to develop a data structure that permits longest prefix matching as well as the insertion and deletion of prefixes in O(logn). These three operations can be done with O(logn) cache misses using a B-tree data structure [S. Suri et al., (2001)]. However, the runtime (including operation cost and cost of cache misses) is not O(logn). In this paper, we develop a data structure in which prefix matching, prefix insertion, and deletion can each be done in O(logn) time. Experiments using real IPv4 routing databases indicate that, although the proposed data structure is slower than optimized variable-stride tries for longest prefix matching, the proposed data structure is considerably faster for the insert and delete operations.

Efficient construction of variable-stride multibit tries for IP lookup

Srinivasan and Varghese (1999) have proposed the use of multibit tries to represent routing tables used for Internet (IP) address lookups. They propose an O(n /sub */W/sup 2//sub */ k) dynamic programming algorithm to determine the strides for an optimal variable-stride trie that has at most k levels. Here, n is the number of prefixes in the routing table and W is the length of the longest prefix. We improve on this algorithm by providing an alternative dynamic programming formulation. The complexity of our algorithm is O(n/sub */W/sub */k), on real router data sets. This is an improvement by a factor of W over the corresponding algorithm of Srinivasan. Experiments conducted by us indicate that our variable-stride algorithm is between 2 and 17 times as fast for IPv4 routing table data.

O(log n) dynamic packet routing

A data structure is developed that permits one to find longest matching prefixes as well as to insert and delete a prefix in O(log n) time, where n is the number of prefixes in the router table. Experimental results using a real IPv4 routing database are also presented.

Data structures for one-dimensional packet classification using most-specific-rule matching

We review the data structures that have been proposed for one-dimensional packet classification. Our review is limited to data structures for the case when ties among the rules that match an incoming packet are broken by selecting the matching rule that is most specific. For the case when the rule filters are destination-address prefixes or are nonintersecting ranges, this tie breaker corresponds to longest-prefix or shortest-range matching, respectively. When the rule filters are arbitrary ranges, this tie breaker resolves the tie only when the rule set is conflict free. Data structures for both static and dynamic rule tables are discussed.

Prefix and interval-partitioned dynamic IP router-tables

Two schemes - prefix partitioning and interval partitioning - are proposed to improve the performance of dynamic IP router-table designs. While prefix partitioning applies to all known dynamic router-table designs, interval partitioning applies to the alternative collection of binary search tree designs of Sahni and Kim [S. Sahni et al., (2004)]. Experiments using public-domain IPv4 router databases indicate that one of the proposed prefix partitioning schemes - TLDP - results in router tables that require less memory than when prefix partitioning is not used. Further significant reduction in the time to find the longest matching-prefix, insert a prefix, and delete a prefix is achieved.

EFFICIENT DYNAMIC LOOKUP FOR BURSTY ACCESS PATTERNS

Internet (IP) packet forwarding is typically done by finding the longest prefix in a router table that matches the packets destination address. Although significant effort has been devoted to the development of data structures for static and dynamic router-tables for random packet-access-patterns, considerably less effort has been expended in the development of such structures for bursty access-patterns (i.e., streams of packets in which destination addresses repeat frequently within localized windows of packets). In this paper, we first formulate a variant, ACRBT (alternative collection of red-black trees), of the CRBT (collection of red-black trees) data structure proposed earlier for dynamic router-tables. By replacing the red-black trees used in the ACRBT with splay trees, we obtain the CST (collection of splay trees) structure in which search, insert, and delete take O(log n) amortized time per operation, where n is the number of prefixes in the router table. By replacing the front end of the CST with biased skip lists, we obtain the BSLPT (biased skip lists with prefix trees) structure in which search, insert, and delete take O(log n) expected time. The CST and BSLPT structures are designed so as to perform much better when the access pattern is bursty than when it is not. Experimental results using real IPv4 routing databases and synthetically generated search sequences as well as trace sequences are presented. For extremely bursty access patterns, the CST structure is best. Otherwise, the ACRBT is recommended. Our experiments also indicate that a supernode implementation of the ACRBT usually has better search performance than does the traditional one-element-per-node implementation.

IP lookup by binary search on prefix length

Waldvogel et al. [ACM SIGCOMM, 1997, 25-36] have proposed a collection of hash tables (CHT) organization for an IP router table. IP lookup can be done with O(log l/sub dist/) hash-table searches, where l/sub dist/ is the number of distinct prefix-lengths (also equal to the number of hash tables in the CHT). Srinivasan and Varghese [ACM transactions on Computer Systems, Feb:1-40, 1999] have proposed the use of controlled prefix-expansion to reduce the value of l/sub dist/. The algorithm of [V. Srinivasan, 1999] does not minimize the storage required by the prefixes and markers for the resulting set of prefixes. We develop an algorithm that minimizes storage requirement but takes O(nW/sup 3/ + kW/sup 4/) time, where k is the desired number of distinct lengths, n is the number of prefixes, and W is the length of the longest prefix. Also, we propose improvements to the heuristic of [V. Srinivasan, 1999].