In this paper we study the problem of scheduling wireless links in the geometric SIN R model, which explicitly uses the fact that nodes are distributed in the Euclidean plane. We present the first NP-completeness proofs in such a model. In particular, we prove two problems to be NP-complete: Scheduling and One-Shot Scheduling. The first problem consists in finding a minimum-length schedule for a given set of links. The second problem receives a weighted set of links as input and consists in finding a maximum-weight subset of links to be scheduled simultaneously in one shot. In addition to the complexity proofs, we devise an approximation algorithm for each problem.
Goussevskaia et al. REF considered a weighted version of the LS problem, whose objective is to find a maximumweight subset of links to be scheduled in one time-slot.
Complexity in geometric SINR
MobiHoc '07
Computer Science