Scheduling of unit-length jobs with bipartite incompatibility graphs on four uniform machines
The problem of scheduling n identical jobs on 4 uniform machines with speeds s1>=s2>=s3>=s4 is considered.The aim is to find a schedule with minimum possible length. We assume that jobs are subject to mutual exclusion constraints modeled by a bipartite incompatibility graph of degree delta. We show that the general problem is NP-hard even if s1=s2=s3. If, however, delta<5 and s1>12s2 s2=s3=s4, then the problem can be solved to optimality in polynomial time. The same algorithm returns a solution of value at most 2 times optimal provided that s1>2s2.
Hanna Furmańczyk, Marek Kubale. (2017). Scheduling of unit-length jobs with bipartite incompatibility graphs on four uniform machines, 65(1), 29-34. https://doi.org/10.1515/bpasts-2017-0004
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