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).

No abstract

No abstract

There is a growing body of work on sorting and selection in models other than the unitcost comparison model. This work is the first treatment of a natural stochastic variant of the problem where the cost of comparing two elements is a random variable. Each cost is chosen independently and is known to the algorithm. In particular we consider the following three models: each cost is chosen uniformly in the range [0, 1], each cost is 0 with some probability p and 1 otherwise, or each cost is 1 with probability p and infinite otherwise. We present lower and upper bounds (optimal in most cases) for these problems. We obtain our upper bounds by carefully designing algorithms to ensure that the costs incurred at various stages are independent and using properties of random partial orders when appropriate.