Lower bounds for constrained task allocation problem in distributed computing environment

In this paper, we propose three lower bounds to the constrained task allocation problem (CTAP). These three lower bounds are: a heuristic lower bound (HLB), a linear programming relaxation (LPR) lower bound and a lagrangean relaxation with subgradient optimization (LRSO) based lower bound. We empirically compare the performance of these three bounds under different task executing times. Our experiments with real-world CTAPs indicate that the LPR provides efficient and tight lower bounds for the CTAP.