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Measurements of the coherence factors (R_Kpipi0 and R_K3pi) and the averagestrong-phase differences (delta^Kpipi0_D and delta^K3pi_D) for the decays D0->K-pi+pi0 and D0->K-pi+pi+pi- are presented. These parameters are importantinputs to the determination of the unitarity triangle angle gamma in B+/- ->DK+/- decays, where D designates a D0 or D0bar meson decaying to a common finalstate. The measurements are made using quantum correlated DDbar decayscollected by the CLEO-c experiment at the psi(3770) resonance, and augment apreviously published analysis by the inclusion of new events in which thesignal decay is tagged by the mode D-> K0Spi+pi-. The measurements also benefitfrom improved knowledge of external inputs, namely the D0D0bar mixingparameters, r_D^Kpi and several D-meson branching fractions. The measuredvalues are R_Kpipi0 = 0.82 +- 0.07, delta_D^Kpipi0 = (164+20-14) deg., R_K3pi =0.32+0.20-0.28 and delta^K3pi_D = (225+21_-78) deg. Consideration is given tohow these measurements can be improved further by using the largerquantum-correlated data set collected by BESIII.

New determination of the D0->K-pi+pi0 and D0->K-pi+pi+pi- coherence factors and average strong-phase differences