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.

We present a randomized and a deterministic data structure for maintaining a dynamic family of sequences under equality tests of pairs of sequences and creations of new sequences by joining or splitting existing sequences. Both data structures support equality tests in O (1) time. The randomized version supports new sequence creations in O(log 2 n) expected time where n is the length of the sequence created. The deterministic solution supports sequence creations in O (log n (log m log* m +log n)) time for the mth operation.

Abstract. We study rigid motions of a rectangle amidst polygonal obstacles. The best known algorithms for this problem have a running time of f~(n2), where n is the number of obstacle corners. We introduce the tightness of a motion-planning problem as a measure of the difficulty of a planning problem in an intuitive sense and describe an algorithm with a running time of O((a/b. 1/eorlt + 1)n(log n)2), where a > b are the lengths of the sides of a rectangle and ecrit is the tightness of the problem. We show further that the complexity ( = number of vertices) of the boundary of n bow ties (see Figure 1) is O(n). Similar results for the union of other simple geometric figures such as triangles and wedges are also presented.

A program checker verifies that a particular program execution is correct.

No abstract