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Abstract-Peer-peer networking has recently emerged as a new paradigm for building distributed networked applications. In this paper we develop simple mathematical models to explore and illustrate fundamental performance issues of peer-peer file sharing systems. The modeling framework introduced and the corresponding solution method are flexible enough to accommodate different characteristics of such systems. Through the specification of model parameters, we apply our framework to three different peer-peer architectures: centralized indexing, distributed indexing with flooded queries, and distributed indexing with hashing directed queries. Using our model, we investigate the effects of system scaling, freeloaders, file popularity and availability on system performance. In particular, we observe that a system with distributed indexing and flooded queries cannot exploit the full capacity of peer-peer systems. We further show that peer-peer file sharing systems can tolerate a significant number of freeloaders without suffering much performance degradation. In many cases, freeloaders can benefit from the available spare capacity of peer-peer systems and increase overall system throughput. Our work shows that simple models coupled with efficient solution methods can be used to understand and answer questions related to the performance of peer-peer file sharing systems.

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Abstract-IEEE 802.11 WiFi equipment based wireless mesh networks have recently been proposed as an inexpensive approach to connect far-flung rural areas. Such networks are built using high-gain directional antennas that can establish long-distance wireless point-to-point links. Some nodes in the network (called gateway nodes) are directly connected to the wired internet, and the remaining nodes connect to the gateway(s) using one or more hops.The dominant cost of constructing such a mesh network is the cost of constructing antenna towers at nodes. The cost of a tower depends on its height, which in turn depends on the length of its links and the physical obstructions along those links. We investigate the problem of selecting which links should be established such that all nodes are connected, while the cost of constructing the antenna towers required to establish the selected links is minimized. We show that this problem is NPhard and that a better than O(log n) approximation cannot be expected, where n is the number of vertices in the graph. We then present the first algorithm in the literature, for this problem, with provable performance bounds. More precisely, we present a greedy algorithm that is an O(log n) approximation algorithm for this problem. Finally, through simulations, we compare our approximation algorithm with both the optimal solution, and a naive heuristic.