In the paper we consider the problem of scheduling n identical jobs on 4
uniform machines with speeds s1​≥s2​≥s3​≥s4​, respectively.
Our aim is to find a schedule with a minimum possible length. We assume that
jobs are subject to some kind of mutual exclusion constraints modeled by a
bipartite incompatibility graph of degree Δ, where two incompatible jobs
cannot be processed on the same machine. We show that the problem is NP-hard
even if s1​=s2​=s3​. If, however, Δ≤4 and s1​≥12s2​,
s2​=s3​=s4​, then the problem can be solved to optimality in time
O(n1.5). The same algorithm returns a solution of value at most 2 times
optimal provided that s1​≥2s2​. Finally, we study the case s1​≥s2​≥s3​=s4​ and give an O(n1.5)-time 32/15-approximation algorithm in
all such situations