In this paper, we study a set of combinatorial optimization problems on weighted graphs: the shortest path problem with negative weights, the weighted perfect bipartite matching problem, the unit-capacity minimum-cost maximum flow problem and the weighted perfect bipartite b-matching problem under the assumption that ‖b‖1 = O(m). We show that each one of these four problems can be solved in Õ(m...

1. Problem Description The problem of optical flow estimation focuses on generating the pattern of (apparent) motion of objects, surfaces, and edges in a visual scene caused by the relative motion between the camera and the scene. Sequences of ordered images allow the estimation of motion as either instantaneous image velocities or discrete image displacements. The optical flow estimation metho...

We introduce two throughput metrics referred to as flowand time-sampled throughputs. The former gives the throughput statistics of an arbitrary flow while the latter weights these throughput statistics by the flow durations. Under fair sharing assumptions, the latter is shown to coincide with the steady-state instantaneous throughput weighted by the number of flows, which provides a useful mean...

Following work of Ecker (Comm Anal Geom 15:1025–1061, 2007), we consider a weighted Gibbons-Hawking-York functional on a Riemannian manifold-withboundary. We compute its variational properties and its time derivative under Perelman’s modified Ricci flow. The answer has a boundary term which involves an extension of Hamilton’s differential Harnack expression for the mean curvature flow in Euclid...