560 research outputs found
Semidefinite approximation for mixed binary quadratically constrained quadratic programs
Motivated by applications in wireless communications, this paper develops
semidefinite programming (SDP) relaxation techniques for some mixed binary
quadratically constrained quadratic programs (MBQCQP) and analyzes their
approximation performance. We consider both a minimization and a maximization
model of this problem. For the minimization model, the objective is to find a
minimum norm vector in -dimensional real or complex Euclidean space, such
that concave quadratic constraints and a cardinality constraint are
satisfied with both binary and continuous variables. {\color{blue}By employing
a special randomized rounding procedure, we show that the ratio between the
norm of the optimal solution of the minimization model and its SDP relaxation
is upper bounded by \cO(Q^2(M-Q+1)+M^2) in the real case and by
\cO(M(M-Q+1)) in the complex case.} For the maximization model, the goal is
to find a maximum norm vector subject to a set of quadratic constraints and a
cardinality constraint with both binary and continuous variables. We show that
in this case the approximation ratio is bounded from below by
\cO(\epsilon/\ln(M)) for both the real and the complex cases. Moreover, this
ratio is tight up to a constant factor
Joint Downlink Base Station Association and Power Control for Max-Min Fairness: Computation and Complexity
In a heterogeneous network (HetNet) with a large number of low power base
stations (BSs), proper user-BS association and power control is crucial to
achieving desirable system performance. In this paper, we systematically study
the joint BS association and power allocation problem for a downlink cellular
network under the max-min fairness criterion. First, we show that this problem
is NP-hard. Second, we show that the upper bound of the optimal value can be
easily computed, and propose a two-stage algorithm to find a high-quality
suboptimal solution. Simulation results show that the proposed algorithm is
near-optimal in the high-SNR regime. Third, we show that the problem under some
additional mild assumptions can be solved to global optima in polynomial time
by a semi-distributed algorithm. This result is based on a transformation of
the original problem to an assignment problem with gains , where
are the channel gains.Comment: 24 pages, 7 figures, a shorter version submitted to IEEE JSA
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