On the Complexity of the Minimum Latency Scheduling Problem on the Euclidean Plane
This resolves a long-standing open problem for the wireless networking community by establishing computational hardness for a fundamental scheduling problem.
The paper proves NP-hardness of the minimum latency scheduling problem under the SINR model for nodes in the Euclidean plane with arbitrary power levels, resolving an open question for path loss exponent α ≥ 3.
We show NP-hardness of the minimum latency scheduling (MLS) problem under the physical model of wireless networking. In this model a transmission is received successfully if the Signal to Interference-plus-Noise Ratio (SINR), is above a given threshold. In the minimum latency scheduling problem, the goal is to assign a time slot and power level to each transmission, so that all the messages are received successfully, and the number of distinct times slots is minimized. Despite its seeming simplicity and several previous hardness results for various settings of the minimum latency scheduling problem, it has remained an open question whether or not the minimum latency scheduling problem is NP-hard, when the nodes are placed in the Euclidean plane and arbitrary power levels can be chosen for the transmissions. We resolve this open question for all path loss exponent values $α\geq 3$.