In this paper, we propose a structured peer-to-peer (P2P) distribution scheme based on Fast Fourier Transform (FFT) graphs. We build a peer-to-peer network that reproduces the FFT graph initially designed for hardware FFT codecs. This topology allows content delivery with a maximum diversity level for a minimum global complexity. The resulting FFTbased network is a structured architecture with an adapted network coding that brings flexibility upon content distribution and robustness upon the dynamic nature of the network. This structure can achieve optimal capacity in terms of content recovery while solving the problem of last remaining blocks, even for large networks.
Structured and hierarchical topologies can also be designed for content delivery. The network can be built with a single tree-based approach @cite_11 or with a more sophisticated multi tree-based approach @cite_13 @cite_2 . In this case, in any branch of the tree, a node, usually the fastest one, is designated to be the head of the subset and represents the branch to interact with the upper layers. This node is also responsible for delivering the content from the upper layers to the other nodes of the subset. However, this scheme suffers from the same problem than the replication approach in a P2P scope as this node can leave at any time, leaving the other nodes and the lower layers orphans. In order to have more reliable connections, multi-head schemes have also been investigated @cite_9 , with delivery and representation to upper layers separated. Nevertheless, this solution remains more complex to build.
@cite_2 @cite_9 @cite_13 @cite_11
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This paper studies a multi-facility network synthesis problem, called the Two-level Network Design (TLND) problem, that arises in the topological design of hierarchical communication, transportation, and electric power distribution networks. We are given an undirected network containing two types of nodes---primary and secondary---and fixed costs for installing either a primary or a secondary facility on each edge. Primary nodes require higher grade interconnections than secondary nodes, using the more expensive primary facilities. The TLND problem seeks a minimum cost connected design that spans all the nodes, and connects primary nodes via edges containing primary facilities; the design can use either primary or secondary edges to connect the secondary nodes. The TLND problem generalizes the well-known Steiner network problem and the hierarchical network design problem. In this paper, we study the relationship between alternative model formulations for this problem (e.g., directed and undirected models), and analyze the worst-case performance for a composite TLND heuristic based upon solving embedded subproblems (e.g., minimum spanning tree and either Steiner tree or shortest path subproblems). When the ratio of primary to secondary costs is the same for all edges and when we solve the embedded subproblems optimally, the worst-case performance ratio of the composite TLND heuristic is 4 3. This result applies to the hierarchical network design problem with constant primary-to-secondary cost ratio since its subproblems are shortest path and minimum spanning tree problems. For more general situations, we express the TLND heuristic worst-case ratio in terms of the performance of any heuristic used to solve the embedded Steiner tree subproblem. A companion paper develops and tests a dual ascent procedure that generates tight upper and lower bounds on the optimal value of a multi-level extension of this problem. Structured peer-to-peer overlay networks such as CAN, Chord, Pastry, and Tapestry can be used to implement Internet-scale application-level multicast. There are two general approaches to accomplishing this: tree building and flooding. This paper evaluates these two approaches using two different types of structured overlay: 1) overlays which use a form of generalized hypercube routing, e.g., Chord, Pastry and Tapestry, and 2) overlays which use a numerical distance metric to route through a Cartesian hyperspace, e.g., CAN. Pastry and CAN are chosen as the representatives of each type of overlay. To the best of our knowledge, this paper reports the first head-to-head comparison of CAN-style versus Pastry-style overlay networks, using multicast communication workloads running on an identical simulation infrastructure. The two approaches to multicast are independent of overlay network choice, and we provide a comparison of flooding versus tree-based multicast on both overlays. Results show that the tree-based approach consistently outperforms the flooding approach. Finally, for tree-based multicast, we show that Pastry provides better performance than CAN. We propose localized, self organizing, robust, and energy-efficient data aggregation tree approaches for sensor networks, which we call Localized Power-Efficient Data Aggregation Protocols (L-PEDAPs). They are based on topologies, such as LMST and RNG, that can approximate minimum spanning tree and can be efficiently computed using only position or distance information of one-hop neighbors. The actual routing tree is constructed over these topologies. We also consider different parent selection strategies while constructing a routing tree. We compare each topology and parent selection strategy and conclude that the best among them is the shortest path strategy over LMST structure. Our solution also involves route maintenance procedures that will be executed when a sensor node fails or a new node is added to the network. The proposed solution is also adapted to consider the remaining power levels of nodes in order to increase the network lifetime. Our simulation results show that by using our power-aware localized approach, we can almost have the same performance of a centralized solution in terms of network lifetime, and close to 90 percent of an upper bound derived here. In practical military or first responder deployment scenarios, information flows need to adhere to specified policies regardless of the physical connectivity of nodes. Nodes in such networks are associated with various levels in a command-and-control hierarchy, and therefore typically form a logical hierarchical tree network that is used to route both command and data traffic. Associated with this logical hierarchical network is a communication network that represents the connectivity of these nodes in the deployed scenario. Such composite networks introduce constraints that can result in information flows having to traverse much longer paths in the underlying communication network. In this paper, we look at the problem of adding edges to a logical hierarchical network (or any other social network) so as to minimize the number of hops required to route data traffic in the underlying communication network from a node to other specified nodes. The edges added are a subset of all possible edges in the complementary logical hierarchical graph and have to satisfy specified hierarchical constraints. First, we consider the general problem of minimizing the eccentricity of a source node 's' (where eccentricity of 's' is the maximum of the shortest paths from 's' to all other nodes) in a metric graph on adding upto 'B' unequal cost metric edges from the set of all edges in the complementary graph. We develop an efficient constant factor approximation algorithm for this case that outperforms existing constant factor algorithms for eccentricity minimization. Here the added edge metric cost as well as the graph edge metric cost correspond to the number of hops in the shortest path required to route traffic in the actual deployed topology (i.e., underlying communication network). Next, we consider the case where the set of possible added edges is a specified subset of the edges in the complementary graph and the set of destinations is a subset of the graph nodes. For this case, we develop heuristic algorithms based on the previous eccentricity minimizing algorithm that show good performance. We validate our algorithms using two realistic military deployment scenarios. We find that adding even a low number of hierarchically constrained edges (of the order of 10) can cause a significant decrease (around 50 ) in the eccentricity of a node in the logical hierarchical network and thus can reduce the number of hops required for data traffic traversal.