This paper proposes two algorithms, namely Server-User Matching (SUM) algorithm and
Extended Server-User Matching (ESUM) algorithm, for the distributed server allocation
problem. The server allocation problem is to determine the matching between servers
and users to minimize the maximum delay, which is the maximum time to complete user
synchronization. We analyze the computational time complexity. We prove that the SUM
algorithm obtains the optimal solutions in polynomial time for the special case that
all server-server delay values are the same and constant. We provide the upper and
lower bounds when the SUM algorithm is applied to the general server allocation problem.
We show that the ES UM algorithm is a fixed-parameter tractable algorithm that can
attain the optimal solution for the server allocation problem parameterized by the
number of servers. Numerical results show that the computation time of ESUM follows
the analyzed complexity while the ESUM algorithm outperforms the approach of integer
linear programming solved by our examined solver.