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.
In REF , the scheduling problem without power control in the SINR model, where nodes are arbitrarily distributed in Euclidean space, has been shown to be NP-complete.
Complexity in geometric SINR
MobiHoc '07
Computer Science