Partial fillup and search time in LC tries

Andersson and Nilsson introduced in 1993 a level-compressed trie (in short: LC trie) in which a full subtree of a node is compressed to a single node of degree being the size of the subtree. Recent experimental results indicated a 'dramatic improvement' when full subtrees are replaced by partially filled subtrees. In this paper, we provide a theoretical justification of these experimental results showing, among others, a rather moderate improvement of the search time over the original LC tries. For such an analysis, we assume that n strings are generated independently by a binary memoryless source with p denoting the probability of emitting a 1. We first prove that the so called alpha-fillup level (i.e., the largest level in a trie with alpha fraction of nodes present at this level) is concentrated on two values with high probability. We give these values explicitly up to O(1), and observe that the value of alpha (strictly between 0 and 1) does not affect the leading term. This result directly yields the typical depth (search time) in the alpha-LC tries with p not equal to 1/2, which turns out to be C loglog n for an explicitly given constant C (depending on p but not on alpha). This should be compared with recently found typical depth in the original LC tries which is C' loglog n for a larger constant C'. The search time in alpha-LC tries is thus smaller but of the same order as in the original LC tries.Comment: 13 page

An algorithm for fast route lookup and update

Increase in routing table sizes, number of updates, traffic, speed of links and migration to IPv6 have made IP address lookup, based on longest prefix matching, a major bottleneck for high performance routers. Several schemes are evaluated and compared based on complexity analysis and simulation results. A trie based scheme, called Linked List Cascade Addressable Trie (LLCAT) is presented. The strength of LLCAT comes from the fact that it is easy to be implemented in hardware, and also routing table update operations are performed incrementally requiring very few memory operations guaranteed for worst case to satisfy requirements of dynamic routing tables in high speed routers. Application of compression schemes to this algorithm is also considered to improve memory consumption and search time. The algorithm is implemented in C language and simulation results with real-life data is presented along with detailed description of the algorithm

IP routing lookup: hardware and software approach

The work presented in this thesis is motivated by the dual goal of developing a scalable and efficient approach for IP lookup using both hardware and software approach. The work involved designing algorithms and techniques to increase the capacity and flexibility of the Internet. The Internet is comprised of routers that forward the Internet packets to the destination address and the physical links that transfer data from one router to another. The optical technologies have improved significantly over the years and hence the data link capacities have increased. However, the packet forwarding rates at the router have failed to keep up with the link capacities. Every router performs a packet-forwarding decision on the incoming packet to determine the packet??s next-hop router. This is achieved by looking up the destination address of the incoming packet in the forwarding table. Besides increased inter-packet arrival rates, the increasing routing table sizes and complexity of forwarding algorithms have made routers a bottleneck in the packet transmission across the Internet. A number of solutions have been proposed that have addressed this problem. The solutions have been categorized into hardware and software solutions. Various lookup algorithms have been proposed to tackle this problem using software approaches. These approaches have proved more scalable and practicable. However, they don??t seem to be able to catch up with the link rates. The first part of my thesis discusses one such software solution for routing lookup. The hardware approaches today have been able to match up with the link speeds. However, these solutions are unable to keep up with the increasing number of routing table entries and the power consumed. The second part of my thesis describes a hardware-based solution that provides a bound on the power consumption and reduces the number of entries required to be stored in the routing table

A Content Caching Strategy for Named Data Networking

Ph.DDOCTOR OF PHILOSOPH