Fault tolerant networks with small degree

Li Zhang
<span title="">2000</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tewj77cuufbzbgbk265bb462ga" style="color: black;">Proceedings of the twelfth annual ACM symposium on Parallel algorithms and architectures - SPAA &#39;00</a> </i> &nbsp;
In this paper, we study the design of fault tolerant networks for arrays and meshes by adding redundant nodes and edges. For a target graph G (linear array or mesh in this paper), a graph G is called a k-fault-tolerant graph of G if when we remove any k nodes from G , it still contains a subgraph isomorphic to G. The major quality measures for a faulttolerant graph are the number of spare nodes it uses and the maximum degree it has. The degree is particularly important in practice as it poses
more &raquo; ... nstraints on the scalability of the system. In this paper, we aim at designing fault-tolerant graphs with both small degree and small number of spare nodes. The graphs we obtain have degree O(1) for arrays and O(log 3 k) for meshes. The number of spare nodes used are O(k log 2 k) and O(k 2 / log k), respectively. Compared to the previous results, the number of spare nodes used in our construction has one fewer linear factor in k.
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