LEDA: a platform for combinatorial and geometric computing

Abstract

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.

Minimal vertex covers on finite-connectivity random graphs: A hard-sphere lattice-gas picture

“…In this case only an approximation of the true minimum vertex cover is calculated, which is found to differ only by a few percent from the exact value. All methods have been implemented via the help of the LEDA library [32] which offers many useful data types and algorithms for linear algebra and graph problems.…”

A General Computational Framework and Simulations of Branching Programs of Boolean Circuits Using Higher Order Logic (HOL) Software - An Insight into ECAD Tool Design Paradigm

“…Though we highlighted an "Optical Circuit" for information processing and computation of even/odd parity circuit, we are not discussing in detail as such advanced topics like Photonics and Optical Computing, which deserve another research paper on an in-depth basis. Hence we are of the belief that our current research work is one of the pioneering efforts in this promising domain of Branching Programs which is interdisciplinary in nature (Mehlhorn & Nher, 1995;Moreinis, Morgenshtein, Wagner, & Kolodny, 2006;Morgenshtein, Fish, & Wagner, 2002;Morgenshtein, Friedman, Ginosar, & Kolodny, 2008;Nakano & Wada, 1998;Nishihara, Haruna, & Suhara, 1987;Okayama, Okabe, Kamijoh, & Sakamoto, 1999;Reed & Knights, 2004;Shi, Wa, Miller, Pamulapati, & Cooke, 1995;Isabelle, 2012;Anthony Fox, 2012; HOL: The Higher Order Logic Theorem Prover; Barrington's Theorem, 2009).…”

“…One can have similar branching programs for the parity function. It can be shown that every function on n bits can be computed by a branching program of width 3 and exponential length" (Hunsperger, 2002;Hussein, Nounou, Saada, Atef, & Khalil, 2006;Jang, Park, & Prasanna, 1992;Taki, 2000;Lattner, 2002;Mehlhorn & Nher, 1995;Moreinis, Morgenshtein, Wagner, & Kolodny, 2006;Morgenshtein, Fish, & Wagner, 2002;Morgenshtein, Friedman, Ginosar, & Kolodny, 2008;Nakano & Wada, 1998;Nishihara, Haruna, & Suhara, 1987;Okayama, Okabe, Kamijoh, & Sakamoto, 1999;Reed & Knights, 2004;Shi, Wa, Miller, Pamulapati, & Cooke, 1995;Isabelle, 2012;Anthony Fox, 2012; HOL: The Higher Order Logic Theorem Prover; Barrington's Theorem, 2009). Figure 1, we designed a simple boolean circuit and deduced its equivalent branching program, using the established mathematical and computational paradigms.…”

Dialogue patterns—A visual language for dynamic dialogue

“…1 be drawn as a planar graph? We used an implementation [20] of the Leda [21] algorithms to test the planarity of the graph in Fig. 1 and found that it is not planar, since there is a K3,3 sub-graph whose nodes are (H, J, M) and (H-1, H-3, H-5).…”