Computing earliest arrival flows with multiple sources

Earliest arrival flows are motivated by applications related to evacuation. Given a network with capacities and transit times on the arcs, a subset of source nodes with supplies and a sink node, the task is to send the given supplies from the sources to the sink "as quickly as possible". The latter requirement is made more precise by the earliest arrival property which requires that the total amount of flow that has arrived at the sink is maximal for all points in time simultaneously. It is a classical result from the 1970s that, for the special case of a single source node, earliest arrival flows do exist and can be computed by essentially applying the Successive Shortest Path Algorithm for min-cost flow computations. While it has previously been observed that an earliest arrival flow still exists for multiple sources, the problem of computing one efficiently has been open. We present an exact algorithm for this problem whose running time is strongly polynomial in the input plus output size of the problem

New distance-directed algorithms for maximum flow and parametric maximum flow problems

"July 1987."Bibliography: p. 34-36.Supported, in part, by the Presidential Young Investigator Grant of the National Science Foundation. 8451517-ECS Supported, in part, by a grant from Analog Devices, Apple Computer,Inc., and Prime Computer.J. B. Orlin and Ravindra K. Ahuja

Parametric shortest-path algorithms via tropical geometry

We study parameterized versions of classical algorithms for computing shortest-path trees. This is most easily expressed in terms of tropical geometry. Applications include shortest paths in traffic networks with variable link travel times.Comment: 24 pages and 8 figure

Implementation and complexity of the watershed-from-markers algorithm computed as a minimal cost forest

The watershed algorithm belongs to classical algorithms in mathematical morphology. Lotufo et al. published a principle of the watershed computation by means of an Image Foresting Transform (IFT), which computes a shortest path forest from given markers. The algorithm itself was described for a 2D case (image) without a detailed discussion of its computation and memory demands for real datasets. As IFT cleverly solves the problem of plateaus and as it gives precise results when thin objects have to be segmented, it is obvious to use this algorithm for 3D datasets taking in mind the minimizing of a higher memory consumption for the 3D case without loosing low asymptotical time complexity of O(m+C) (and also the real computation speed). The main goal of this paper is an implementation of the IFT algorithm with a priority queue with buckets and careful tuning of this implementation to reach as minimal memory consumption as possible. The paper presents five possible modifications and methods of implementation of the IFT algorithm. All presented implementations keep the time complexity of the standard priority queue with buckets but the best one minimizes the costly memory allocation and needs only 19-45% of memory for typical 3D medical imaging datasets. Memory saving was reached by an IFT algorithm simplification, which stores more elements in temporary structures but these elements are simpler and thus need less memory. The best presented modification allows segmentation of large 3D medical datasets (up to 512x512x680 voxels) with 12-or 16-bits per voxel on currently available PC based workstations.Comment: v1: 10 pages, 6 figures, 7 tables EUROGRAPHICS conference, Manchester, UK, 2001. v2: 12 pages, reformated for letter, corrected IFT to "Image Foresting Tranform