We study dynamic routing in store-and-forward packet networks where each network link has bounded buffer capacity for receiving incoming packets and is capable of transmitting a fixed number of packets per unit of time. At any moment in time, packets are injected at various network nodes with each packet specifying its destination node. The goal is to maximize the throughput, defined as the number of packets delivered to their destinations.In this paper, we make some progress on throughput maximization in various network topologies. Let n and m denote the number of nodes and links in the network, respectively. For line networks, we show that Nearest-to-Go (NTG), a natural distributed greedy algorithm, isÕ( √ n)-competitive, essentially matching a known ( √ n) lower bound on the performance of any greedy algorithm. We also show that if we allow the online routing algorithm to make centralized decisions, there is a randomized polylog(n)-competitive algorithm for line networks as well as for rooted tree An extended abstract appeared in the 72 Algorithmica (2009) 55: 71-94 networks, where each packet is destined for the root of the tree. For grid graphs, we show that NTG has a competitive ratio of˜ (n 2/3 ) while no greedy algorithm can achieve a ratio better than ( √ n). Finally, for arbitrary network topologies, we show that NTG is˜ (m)-competitive, improving upon an earlier bound of O(mn).

Abstract. The diff3 algorithm is widely considered the gold standard for merging uncoordinated changes to list-structured data such as text files. Surprisingly, its fundamental properties have never been studied in depth.We offer a simple, abstract presentation of the diff3 algorithm and investigate its behavior. Despite abundant anecdotal evidence that people find diff3's behavior intuitive and predictable in practice, characterizing its good properties turns out to be rather delicate: a number of seemingly natural intuitions are incorrect in general. Our main result is a careful analysis of the intuition that edits to "well-separated" regions of the same document are guaranteed never to conflict.

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