Abstract. We give an overview of the LEDA platform for combinatorial and geometric computing and an account of its development. We discuss our motivation for building LEDA and to what extent we have reached our goals. We also discuss some recent theoretical developments. This paper contains no new technical material. It is intended as a guide to existing publications about the system. We refer the reader also to our web-pages for more information. What is LEDA?LEDA [MN95, MNU96] aims at being a comprehensive software platform for combinatorial and geometric computing. It provides a sizable collection of data types and algorithms. This collection includes most of the data types and algorithms described in the text books of the area ([AtHJ83, Meh84, Tar83, CLR90, 0'R94, Woo93, Sed91, Kin90, van88, NH93]). In particular, it includes stacks, queues, lists, sets, dictionaries, ordered sequences, partitions, priority queues, directed, undirected, and planar graphs, lines, points, planes, and polygons, and many algorithms in graph and network theory and computational geometry, e.g., shortest paths, matchings, maximum flow, rain cost flow, planarity testing, spanning trees, biconnected and strongly connected components, segment intersection, convex hulls, Delaunay triangulations, and Voronoi diagrams. LEDA supports applications in a broad range of areas. It has already been used in such diverse areas as code optimization, VLSI design, graph drawing, graphics, robot motion planning, traffic scheduling, machine learning and computational biology.We discuss different aspects of the LEDA system. Ease of Use:The library is easy to use. In fact, only a small fraction of our users are algorithms experts and many of our users are not even computer scientists. For these users the broad scope of the library, its ease of use, and the correctness and efficiency of the algorithms in the library are cruciM.

Abstract. We give an overview of the LEDA platform for combinatorial and geometric computing and an account of its development. We discuss our motivation for building LEDA and to what extent we have reached our goals. We also discuss some recent theoretical developments. This paper contains no new technical material. It is intended as a guide to existing publications about the system. We refer the reader also to our web-pages for more information. What is LEDA?LEDA [MN95, MNU96] aims at being a comprehensive software platform for combinatorial and geometric computing. It provides a sizable collection of data types and algorithms. This collection includes most of the data types and algorithms described in the text books of the area ([AtHJ83, Meh84, Tar83, CLR90, 0'R94, Woo93, Sed91, Kin90, van88, NH93]). In particular, it includes stacks, queues, lists, sets, dictionaries, ordered sequences, partitions, priority queues, directed, undirected, and planar graphs, lines, points, planes, and polygons, and many algorithms in graph and network theory and computational geometry, e.g., shortest paths, matchings, maximum flow, rain cost flow, planarity testing, spanning trees, biconnected and strongly connected components, segment intersection, convex hulls, Delaunay triangulations, and Voronoi diagrams. LEDA supports applications in a broad range of areas. It has already been used in such diverse areas as code optimization, VLSI design, graph drawing, graphics, robot motion planning, traffic scheduling, machine learning and computational biology.We discuss different aspects of the LEDA system. Ease of Use:The library is easy to use. In fact, only a small fraction of our users are algorithms experts and many of our users are not even computer scientists. For these users the broad scope of the library, its ease of use, and the correctness and efficiency of the algorithms in the library are cruciM.

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The problem of searching for a key in many ordered lists arises frequently in computational geometry. Chazelle and Guibas recently introduced fractional cascading as a general technique for solving this type of problem. In this paper we show that fractional cascading also supports insertions into and deletions from the lists efficiently. More specifically, we show that a search for a key in n lists takes time O(log N+ n log log N) and an insertion or deletion takes time O(log log N). Here N is the total size of all lists. If only insertions or deletions have to be supported the O(log log N) factor reduces to O(1). As an application we show that queries, insertions, and deletions into segment trees or range trees can be supported in time O(log n log log n), when n is the number of segments (points).

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