Given arbitrarily distributed single-hop wireless links, using the physical interference model, the objective is to minimize the scheduling length. This is an open problem (Problem 1) proposed by Locher et al. [21] . In this paper, we solve this open problem at the cost of moderately exponential time. Specifically, this paper gives two classes of exact and approximate link scheduling algorithms, one based on the somewhat straightforward link independent set covering, and the other on counting the number of set covers. Let denote the time of checking whether the spectral radius of an irreducible non-negative matrix is smaller than 1 or not, then the time complexity for the set covering based exact algorithm is , whereas the proposed counting based exact scheduling algorithm called ESA_MLSAT needs only time with polynomial space. If exponential space is allowed, the time complexity can be further reduced to . The time complexity for the set covering based approximate algorithm is
In addition to heuristic and approximation algorithms, an exponential time exact algorithm has been proposed by Hua and Lau in REF .
Exact and approximate link scheduling algorithms under the physical interference model
DIALM-POMC '08
Mathematics Computer Science