STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Using the Pseudo-Dimension to Analyze Approximation Algorithms for Integer Programming
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Network file storage with graceful performance degradation
ACM Transactions on Storage (TOS)
Approximation algorithms for covering/packing integer programs
Journal of Computer and System Sciences
Approximation algorithms for stochastic and risk-averse optimization
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Content-access QoS in peer-to-peer networks using a fast MDS erasure code
Computer Communications
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Large matchings in uniform hypergraphs and the conjectures of Erdős and Samuels
Journal of Combinatorial Theory Series A
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The following file distribution problem is considered: Given a network of processors represented by an undirected graph $G=(V,E)$ and a file size $k$, an arbitrary file w of $k$ bits is to be distributed among all nodes of $G$. To this end, each node is assigned a memory device such that by accessing the memory of its own and of its adjacent nodes, the node can reconstruct the contents of w. The objective is to minimize the total size of memory in the network. This paper presents a file distribution scheme which realizes this objective for $k \gg \log \Delta_G$, where $\Delta_G$ stands for the maximum degree in $G$: For this range of $k$, the total memory size required by the suggested scheme approaches an integer programming lower bound on that size. The scheme is also constructive in the sense that given $G$ and $k$, the memory size at each node in $G$, as well as the mapping of any file w into the node memory devices, can be computed in time complexity which is polynomial in $k$ and $|V|$. Furthermore, each node can reconstruct the contents of such a file w in $O(k^2)$ bit operations. Finally, it is shown that the requirement of $k$ being much larger than $\log \Delta_G$ is necessary in order to have total memory size close to the integer programming lower bound.