The combination of the buffer sizes of routers deployed in the Internet, and the Internet traffic itself, leads routinely to the dropping of packets. Motivated by this, we are interested in the problem of maximizing the throughput of protocols that control packet networks. Moreover, we are interested in a setting where different packets have different priorities (or weights), thus taking into account Quality-of-Service considerations. We first extend the Competitive Network Throughput (CNT) model introduced by Aiello et al. [2003] to the weighted packets case. We analyze the performance of online, local-control protocols by their competitive ratio, in the face of arbitrary traffic, using as a measure the total weight of the packets that arrive to their destinations, rather than being dropped en-route. We prove that on Directed Acyclic Graphs (DAGs), any greedy protocol is competitive, with competitive ratio independent of the weights of the packets. Here we mean by a “greedy protocol” a protocol that not only does not leave a resource idle unnecessarily, but also prefers packets with higher weight over those with lower weight. We give two independent upper bounds on the competitive ratio of general greedy protocols on DAGs. We further give lower bounds that show that our upper bounds cannot be improved (other than constant factors) in the general case. Both our upper and lower bounds apply also to the unweighted case, and they improve the results given in Aiello et al. [2003] for that case. We thus give tight (up to constant factors) upper and lower bounds for both the unweighted and weighted cases. In the course of proving our upper bounds we prove a lemma that gives upper bounds on the delivery times of packets by any greedy protocol on general DAGs (without buffer size considerations). We believe that this lemma may be of independent interest and may find additional applications.

The combination of the buffer sizes of routers deployed in the Internet, and the Internet traffic itself, leads routinely to the dropping of packets. Motivated by this, we are interested in the problem of maximizing the throughput of protocols that control packet networks. Moreover, we are interested in a setting where different packets have different priorities (or weights), thus taking into account Quality-of-Service considerations.We first extend the Competitive Network Throughput (CNT) model introduced by Aiello et al. [2] to the weighted packets case. We analyze the performance of online, local-control protocols by their competitive ratio, in the face of arbitrary traffic, using as a measure the total weight of the packets that arrive to their destinations, rather than being dropped en-route. We prove that on directed acyclic graphs (DAGs), any greedy protocol is competitive, with competitive ratio independent of the weights of the packets. We give two independent upper bounds on the competitive ratio of general greedy protocols on DAGs. We further give lower bounds that show that our upper bounds cannot be improved (other than constant factors) in the general case. Both our upper and lower bounds apply also to the unweighted case, and they improve the results given in [2] for that case. We thus give tight (up to constant factors) upper and lower bounds for both the unweighted and weighted cases.In the course of proving our upper bounds we prove a lemma that gives upper bounds on the delivery times of packets by any greedy protocol on general DAGs (without buffer size considerations). We believe that this lemma may be of independent interest and may find additional applications.

We discuss the synthesis between the 3D and the 2D data in three-dimensional face recognition. We show how to compensate for the illumination and racial expressions using the 3D facial geometry and present the approach of canonical images, which allows us to incorporate geometric information into standard face recognition approaches.