Brief announcement: on the complexity of the minimum latency scheduling problem on the euclidean plane

Authors:
Henry Lin;Frans Schalekamp
Affiliations:
University of Maryland, College Park, MD, USA;The College of William and Mary, Williamsburg, VA, USA
Venue:
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
Year:
2012

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Abstract

We announce 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 MLS 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 known to be 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 alpha = 3.