A new approach to the maximum flow problem
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Proc. of the sixth conference on Foundations of software technology and theoretical computer science
SIAM Journal on Computing
SCG '87 Proceedings of the third annual symposium on Computational geometry
Rectilinear shortest paths through polygonal obstacles in O(n(logn)2) time
SCG '87 Proceedings of the third annual symposium on Computational geometry
An algorithmic approach to some problems in terrain navigation
Artificial Intelligence - Special issue on geometric reasoning
Path planning in 0/1/ weighted regions with applications
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Path planning in 0/1/ weighted regions with applications
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Globally Minimal Surfaces by Continuous Maximal Flows
IEEE Transactions on Pattern Analysis and Machine Intelligence
Maximum flows and minimum cuts in the plane
Journal of Global Optimization
Identification of Robust Terminal-Area Routes in Convective Weather
Transportation Science
| Hi-index | 0.00 |
We introduce a new class of problems concerned with the computation of maximum flows through two-dimensional polyhedral domains. Given a polyhedral space (e.g., a simple polygon with holes), we want to find the maximum “flow” from a source edge to a sink edge. Flow is defined to be a divergence-free vector field on the interior of the domain, and capacity constraints are specified by giving the maximum magnitude of the flow vector at any point. Strang proved that max flow equals min cut; we address the problem of constructing min cuts and max flows. We give polynomial-time algorithms for maximum flow from a source edge to a sink edge through a simple polygon with uniform capacity constraint (with or without holes), maximum flow through a simple polygon from many sources to many sinks, and maximum flow through weighted polygonal regions. Central to our methodology is the intimate connection between the max-flow problem and its dual, the min-cut problem. We show how the continuous Dijkstra paradigm of solving shortest paths problems corresponds to a continuous version of Berge's algorithm for computation of maximum flow in a planar network.