Abstract
This letter proposes two polynomial-time approximation algorithms for the distributed server allocation problem with preventive start-time optimization against a failure. Server allocation is decided in advance to minimize the largest maximum delay among all failure patterns. We analyze the approximation performances of proposed algorithm when only the delay between servers or all the delays including that between servers and users hold the triangle inequality. Numerical results reveal that the proposed algorithms are <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.0\times 10^{3}$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.9\times 10^{7}$ </tex-math></inline-formula> times faster than the integer linear programming approach while increasing the largest maximum delay by 1.033 times in average.
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