Priyank Ramesh Warkhede

Fast packet classification for two-dimensional conflict-free filters

Routers can use packet classification to support advanced functions. Routers with packet classification capability can forward packets based on multiple header fields, such as source address, protocol type, or application port numbers. The destination-based forwarding can be thought of as one-dimensional packet classification. While several efficient solutions are known for the one-dimensional IP lookup problem, the multi-dimensional packet classification has proved to be far more difficult. While an O(log w) time scheme is known for the IP lookup, Srinivisan et al. (1999) show a lower bound of /spl Omega/(/spl omega//sup k-1/) for k-dimensional filter lookup, where /spl omega/ is the number of bits in a header field. In particular, this lower bound precludes the possibility of a binary search like scheme even for 2-dimensional filters. In this paper, we examine this lower bound more closely, and discover that the lower bound depends crucially on conflicts in the filter database. We then show that for two-dimensional conflict-free filters, a binary search scheme does work! Our lookup scheme requires O(log/sup 2/ /spl omega/) hashes in the worst-case, and uses O(n log/sup 2/ /spl omega/) memory. Alternatively, our algorithm can be viewed as making O (log /spl omega/) calls to a prefix lookup scheme. It has been observed in practice that filter databases have very few conflicts, and these conflicts can be removed by adding additional filters (one per conflict). Thus, our scheme may also be quite practical. Our simulation and experimental results show that the proposed scheme also performs as good as or better than existing schemes.

Compressing Two-Dimensional Routing Tables

We consider an algorithmic problem that arises in the context of routing tables used by Internet routers. The Internet addressing scheme is hierarchical, where a group of hosts are identified by a prefix that is common to all the hosts in that group. Each host machine has a unique 32-bit address. Thus, all traffic between a source group s and a destination group d can be routed along a particular route c by maintaining a routing entry (s, d, c) at all intermediate routers, where s and d are binary bit strings. Many different routing tables can achieve the same routing behavior. In this paper we show how to compute the most compact routing table. In particular, we consider the following optimization problem: given a routing table D with N entries of the form (s, d, c) , determine a conflict-free routing table with fewest entries that has the same routing behavior as D. If the source and destination fields have up to w bits, and there are at most K different route values, then our algorithm runs in worst-case time O( NK w2) .

Multiway range trees: scalable IP lookup with fast updates

Internet routers forward packets based on the destination address of a packet. A packets address is matched against the destination prefixes stored in the routers forwarding table, and the packet is sent to the output interface determined by the longest matching prefix. While some existing schemes work well for IPv4 addresses, we believe that none of the current schemes scales well to IPv6, especially when fast updates are required. As the Internet evolves into a global communication medium, requiring multiple addresses per user, the switch to longer addresses (e.g. IPv6) seems inevitable despite temporary measures such as network address translation boxes. Since IPv6 uses 128 bit addresses, schemes whose lookup time grows with address length (such as patricia or multibit tries) become less attractive. Because of backbone protocol instabilities, it is also important that lookup schemes be able to accommodate fast updates.In this paper, we introduce a new IP lookup scheme with worst-case search and update time of O(log n), where n is the number of prefixes in the forwarding table. Our scheme is based on a new data structure, a multiway range tree, which achieves the optimal lookup time of binary search, but can also be updated in logarithmic time when a prefix is added or deleted; by contrast, plain binary search relies on precomputation, and a single update can require O(n) time. Our performance analysis shows that, even for IPv4, multiway range trees are competitive with the best lookup schemes currently known. In fact, among existing schemes, only multibit tries have update performance comparable to our scheme and such schemes have patent restrictions. Further, when considering IPv6 or any future routing protocol that uses longer addresses, our scheme outperforms all existing schemes, including multibit tries.

Optimal Flow Aggregation

Current IP routers are stateless: they forward individual packets based on the destination address contained in the packet header, but maintain no information about the application or flow to which a packet belongs. This stateless service model works well for best effort datagram delivery, but is grossly inadequate for applications that require quality of service guarantees, such as audio, video, or multimedia. Maintaining state for each flow is expensive because the number of concurrent flows at a router can be in the hundreds of thousands. Thus, stateful solutions such as Intserv (integrated services) have not been adopted for their lack of scalability. Motivated by this dilemma, we formulate and solve the flow aggregation problem, where we give an efficient algorithm for computing the smallest set of aggregated flows that encode the forwarding state of individual flows. Such aggregation of state information might increase the viability of Intserv-type protocols.