Abstract
The minimum orientation problem is a classical graph theoretical problem in which we aim at finding an orientation of a graph G that minimizes the maximum out-degree \(D^+(G)\). Graph orientation is motivated by load balancing problems in which a set of tasks have to be allocated to a set of processes in order to minimize the completion time. If we consider load balancing in networks, the decisions for the allocation have to be made by the nodes without a global knowledge of the graph. In this paper, we propose a distributed algorithm that computes a graph orientation that provides a \(2(2+\epsilon )\)-approximation of the optimal. The algorithm is asynchronous and runs in \(O((\log n +diam(G))\log D^+(OPT(G))\) rounds, where n is the number of nodes, diam is the diameter of the graph and \(D^+(OPT(G))\) is the maximum out-degree with an optimal orientation. The algorithm does not need any global knowledge on G and tolerates initial faults.
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Notes
- 1.
This result was initially stated for undirected graph but it is immediately adaptable for bi-directed graphs since the both are equivalent representations.
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Gillet, N., Hanusse, N. (2017). A Fully Asynchronous and Fault Tolerant Distributed Algorithm to Compute a Minimum Graph Orientation. In: Spirakis, P., Tsigas, P. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2017. Lecture Notes in Computer Science(), vol 10616. Springer, Cham. https://doi.org/10.1007/978-3-319-69084-1_22
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