Abstract
Interactivity is a primary performance measure for distributed interactive applications (DIAs). In a network supporting a DIA, interactivity performance depends on both client-to-server network latencies and inter-server network latencies. An optimization problem, which we term FCSA, is to find an optimum way how clients are assigned to servers such that the largest latency on an interactivity path between two clients (client 1 to server 1, server 1 to server 2, then server 2 to client 2) is minimized. Previous work showed that it is NP-hard to approximate this problem with a ratio better than 4 / 3 and gave a 3-approximation algorithm. In this paper, we give a (3 / 2)-approximation algorithm for FCSA, and show that it is NP-hard to obtain a better ratio. We also give a (3 / 2)-approximation algorithm when server capacity constraints are considered.
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Notes
A function \(d\,{:}\,V\times V\rightarrow {\mathbb {R}}\) is a semimetric on V iff for every \(i_1,i_2,i_3\in V\), \(d(i_1,i_1) = 0\), \(d(i_1,i_2)\ge 0\), \(d(i_1,i_2) = d(i_2,i_1)\), and \(d(i_1,i_2)+d(i_2,i_3)\ge d(i_1,i_3)\). If, in addition, \(d(i_1,i_2) = 0\) implies \(i_1 = i_2\), then d is a metric.
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Acknowledgements
Gruia Calinescu thanks Niranjana Sompura Ramakrishna Reddy, a student in his Combinatorial Optimization class, for bringing this problem to his attention.
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Călinescu, G., Wang, X. Client assignment problems for latency minimization. J Comb Optim 37, 889–900 (2019). https://doi.org/10.1007/s10878-018-0326-2
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DOI: https://doi.org/10.1007/s10878-018-0326-2