Department of Applied Mathematics, University of Twente
Abstract
We study the problem of minimizing the vector norm ∣∣⋅∣∣p​ of the workloads. We examine move-optimal assignments and prove a performance guarantee of
p2p−1​⋅(2p−2p−1​)pp−1​,
for any integer p>1 and moreover, we show that this guarantee is tight.
Additionally, we consider assignments obtained by applying the LPT-heuristic of Graham (1969). We prove that an LPT-assignment has a performance guarantee of
p3p−2p​⋅(2⋅3p−3⋅2pp−1​)pp−1​,
which reproves a result of Chandra and Wong (1975)