We compute the volumes of convex bodies that are given by inequalities of concave polynomials. These volumes are found to arbitrary precision thanks to the representation of periods by linear differential equations. Our approach rests on work of Lairez, Mezzarobba, and Safey El Din. We present a novel method to identify the relevant critical values. Convexity allows us to reduce the required number of creative telescoping steps by an exponential factor. We provide an implementation based on the ore_algebra package in SageMath. We present examples computed with our implementation in 2, 3 and 4 dimensions.

As data rates in the Internet increase, the Internet Protocol (IP) address lookup is required to be resolved in shorter resolution times. IP address lookup involves finding the longest matching prefix from a database of prefixes that better matches the destination address of a packet. The fastest IP-address lookup solutions are based on ternary content addressable memories (TCAMs), which can resolve the IP lookup in one memory-access time. However, TCAMs have a high power consumption and large complexity that may limit their scalability and storage capacity. An alternative is to use random access memory (RAM) that stores a forwarding table in a trie form. Proposed trie-based solutions for IP lookup require three or more memory-access times in the worst-case scenario. This makes them unattractive despite their reduced power consumption. In this paper, we propose a flexible and fast trie-based IP-lookup algorithm where parallel searching is performed. This algorithm performs lookup in two memory- access times whith a feasible amount of memory or three memory access times with reduced memory.