Cost-sensitive analysis of communication protocols
PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
The rectilinear Steiner arborescence problem is NP-complete
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Generalized self-approaching curves
Discrete Applied Mathematics - Special issue 14th European workshop on computational geometry CG'98 Selected papers
Gradient-constrained minimum networks. I. Fundamentals
Journal of Global Optimization
INFOVIS '05 Proceedings of the Proceedings of the 2005 IEEE Symposium on Information Visualization
The Rectilinear Steiner Arborescence Problem Is NP-Complete
SIAM Journal on Computing
Network optimization for the design of underground mines
Networks - Special Issue on Multicommodity Flows and Network Design
Flow Map Layout via Spiral Trees
IEEE Transactions on Visualization and Computer Graphics
New approximations for the rectilinear Steiner arborescence problem [VLSI layout]
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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We introduce a new variant of the geometric Steiner arborescence problem, motivated by the layout of flow maps. Flow maps show the movement of objects between places. They reduce visual clutter by bundling lines smoothly and avoiding self-intersections. To capture these properties, our angle-restricted Steiner arborescences, or flux trees, connect several targets to a source with a tree of minimal length whose arcs obey a certain restriction on the angle they form with the source. We study the properties of optimal flux trees and show that they are planar and consist of logarithmic spirals and straight lines. Flux trees have the shallow-light property. Computing optimal flux trees is NP-hard. Hence we consider a variant of flux trees which uses only logarithmic spirals. Spiral trees approximate flux trees within a factor depending on the angle restriction. Computing optimal spiral trees remains NP-hard, but we present an efficient 2-approximation, which can be extended to avoid "positive monotone" obstacles.