Scheduling wireless links under the SINR model has attracted increasing attention in the past few years [1–6, 8–15, 18–20, 23–25, 27, 28, 33–36, 39, 41, 42, 45, 46]. However, most of previous work did not account for the precedence constraint that might exist among the wireless links. Precedence constraints are common in data aggregation problems where a sensor can not send data to its parent node before it has received data from all of its children. Existing solutions to the so-called minimum latency aggregation scheduling problem [7, 16, 21, 26, 29, 30, 32, 40, 43, 44] mainly focus on specific tree topologies rooted at the sink node. In this paper, we study the minimum latency link scheduling problem for arbitrary directed acyclic networks under both precedence and SINR constraints. Our formulation allows multiple sinks, and each sensor may transmit data to more than one parent node. We first show that the problem is NP-hard, and then propose a linear power assignment based polynomial time approximation algorithm and a dynamic labeling based heuristic algorithm. We have carried out extensive simulations for both dense and sparse arbitrary directed acyclic networks. The simulation results show that: (1) compared with both uniform and linear power assignments based algorithms, we can achieve much shorter scheduling lengths using our proposed labeling algorithm, and (2) the dynamic labeling based heuristic algorithm can lead to significantly shorter scheduling lengths than the heuristic algorithm which does not use labeling.
Multicommodity Flow Modeling for the Data Transmission Scheduling Problem in Navigation Satellite Systems
