On non-linear lower bounds in computational complexity
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
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The problem of minimizing the number of service ports of a central facility which serves a number of users subject to some constraints is addressed. At any time, a set of at most s users may want to use the facility, and one user can be connected to each port at a given time. It is assumed that there are direct communication links from users to service ports, with at most d links incident at a single service port. This problem maps to the graph-theoretic problem of minimizing the number of outputs of a bipartite graph with n inputs, such the degree of each output node is at most d and every set of kor=s inputs is joined collectively to at least k different outputs. This minimum is denoted by f(n, s, d). A linear programming formulation is also given.