We consider a set of transmitter-receiver pairs, or links, that share a wireless medium and address the problem of emptying backlogged queues with given initial size at the transmitters in minimum time. The problem amounts to determining activation subsets of links, and their time durations, to form a minimum-time schedule. Scheduling in wireless networks has been studied under various formulations before. In this paper, we present fundamental insights and solution characterizations that include: 1) showing that the complexity of the problem remains high for any continuous and increasing rate function; 2) formulating and proving sufficient and necessary optimality conditions of two baseline scheduling strategies that correspond to emptying the queues using one-at-a-time or all-at-once strategies; and 3) presenting and proving the tractability of the special case in which the transmission rates are functions only of the cardinality of the link activation sets. These results are independent of physical-layer system specifications and are valid for any form of rate function. We then develop an algorithmic framework for the solution to this problem. The framework encompasses exact as well as sub-optimal, but fast, scheduling algorithms, all under a unified principle design. Through computational experiments, we finally investigate the performance of several specific algorithms from this framework.

We consider a wireless network with a set of transmitter-receiver pairs, or links, that share a common channel, and address the problem of emptying finite traffic volume from the transmitters in minimum time. This, so called, minimum-time scheduling problem has been proved to be NP-hard in general. In this paper, we study a class of minimum-time scheduling problems in which the link rates have a particular structure. We show that global optimality can be reached in polynomial time and derive optimality conditions. Then we consider a more general case in which we apply the same approach and obtain an approximation as well as lower and upper bounds to the optimal solution. Simulation results confirm and validate our approach.

We address the maximum link activation problem in wireless networks with new features, namely when the transmitters can perform cooperative transmission, and the receivers are able to perform successive interference cancellation. In this new problem setting, which transmitters should transmit and to whom, as well as the optimal cancellation patterns at the receivers, are strongly intertwined. We present contributions along three lines. First, we provide a thorough tractability analysis, proving the NP-hardness as well as identifying tractable cases. Second, for benchmarking purposes, we deploy integer linear programming for achieving global optimum using off-theshelf optimization methods. Third, to overcome the scalability issue of integer programming, we design a sub-optimal but efficient optimization algorithm for the problem in its general form, by embedding maximum-weighted bipartite matching into local search. Numerical results are presented for performance evaluation, to validate the benefit of cooperative transmission and interference cancellation for maximum link activation and to demonstrate the effectiveness of the proposed algorithm.