Optimized Network Data Storage and Topology Control

This thesis addresses two key challenges for network data-storage systems: optimizing data placement for highly efficient and robust data access, and constructing network topologies that facilitate data transmission scalable to both network sizes and network dynamics. It focuses on two new topics — data placement using erasure-correcting codes, and topology control for nodes in normed spaces. The first topic generalizes traditional file-assignment problems, and has the distinct feature of interleavingly placing data in networks. The second topic emphasizes the construction of network topologies that achieve excellent global performance in comprehensive measurements, through purely local decisions on connectivity. The results of the thesis deepen the current understanding on these important and intriguing topics, and follow a mathematically rigorous approach.