LEDA, a Platform for Combinatorial and Geometric Computing:Algorithms

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Algorithms

The Leda project had never the goal to provide a complete collection of all algorithms. Leda was designed and implemented to establish a platform for combinatorial and geometric computing enabling programmers to implement these algorithms themselves more easily and customized to their particular needs. But of course the library already contains a considerable number of standard algorithms.

Here we give a brief overview and refer the reader to the user manual for precise specifications and to chapter 10 of the Leda-book ([27]) for a detailed description and analysis of the corresponding implementations. In the current version Leda offers different implementation of algorithms for the following problems:

• sorting and searching

• basic graph properties

• graph traversals

• different kinds of connected components

• planarity test and embeddings

• minimum spanning trees

• shortest paths

• network flows

• maximum weight and cardinality matchings

• graph drawing

• convex hulls (also three-dimensional)

• half-plane intersections

• (constraint) triangulations

• closest and farthest Delaunay and Voronoi diagrams

• Euclidean minimum spanning trees

• closest pairs

• boolean operations on generalized polygons

• segment intersection and construction of line arrangements

• Minkowski sums and differences

• nearest neighbors and closest points

• minimum enclosing circles and annuli

• curve reconstruction

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