Optimal Reconstruction of the Velocity and Density Field: Potent and Max-Flow Algorithms

Although Potent purports to use only radial velocities in reconstructing the potential velocity field of galaxies, the derivation of transverse components is implicit in the smoothing procedures adopted. Thus the possibility arises of using nonradial line integrals to derive a smoothed velocity field. For an inhomogeneous galaxy distribution the optimal path for integration need not be radial, and can be obtained using max-flow algorithms. In this paper we describe how one may use Dijkstra's algorithm to obtain this optimal path and velocity field, and present the results of applying the algorithm to a realistic spatial distribution of galaxies. These results show that the method has limited effect due to the large smoothing scales employed in Potent. However, the viability of the technique is demonstrated and, finally, we discuss other possible methods involving averaging over an ensemble of non-radial paths for improving a potential velocity field derived from redshifts.