LEDA, a Platform for Combinatorial and Geometric Computing:Algorithms

By -

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

Comments

Post a Comment

Popular posts from this blog

Data Structure Visualization:Introduction and Value of Data Structure Rendering

By -
Introduction Important advances in programming languages have occurred since the early days of assembly languages and op codes, and modern programming languages have significantly simplified the task of writing computer programs. Unfortunately, tools for un d e rstanding programs have not achieved the accompanying levels of improvement. Software developers still face difficulties in understanding, analyzing, debugging, and improving code. As an example of the difficulties still evident, consider a developer who has just implemented a new algorithm and is now ready to examine the program’s behavior. After issuing a command to begin program execution, the developer examines output data and/or inter- active behavior, attempting to ascertain if the program functioned correctly, and if not, the reasons for the program’s failure. This task can be laborious and usually requires the use of a debugger or perhaps even the addition of explicit checking code, usually through output statements. Furt
Read more

Collision Detection:Penetration Depth Computation

By -
Image
Penetration Depth Computation In this section, we give a brief overview of penetration depth (PD) computation algorithms between convex polytopes and general polyhedral models. The PD of two inter-penetrating objects A and B is defined as the minimum translation distance that one object undergoes to make the interiors of A and B disjoint. It can be also defined in terms of the TCSO. When two objects are overlapping, the origin of the Minkowski sum of A and − B is contained inside the TCSO. The penetration depth corresponds to the minimum distance from the origin to the surface of TCSO [18]. PD computation is often used in motion planning [37], contact resolution for dynamic simulation [38, 39] and force computation in haptic rendering [40]. For example, computation of dynamic response in penalty-based methods often needs to perform PD queries for imposing the non-penetration constraint for rigid body simulation. In addition, many applications, such as motion planning and dynamic simula
Read more

Concurrent Data Structures:Linked Lists

By -
Linked Lists Consider implementations of concurrent search structures supporting insert, delete, and search operations. If these operations deal only with a key value, then the resulting data structure is a se t ; if a data value is associated with each key, we have a dic tionary [24]. These are closely related data structures, and a concurrent set implementation can often be adapted to implement a dictionary. In the next three sections, we concentrate on implementing sets using different structures: linked lists, hash tables, and trees. Suppose we use a linked list to implement a set. Apart from globally locking the linked list to prevent concurrent manipulation, the most popular approach to concurrent lock- based linked lists is ha nd-over-hand locking (sometimes called l o c k coupling ) [14, 89]. In this approach, each node has an associated lock. A thread traversing the linked list releases a node’s lock only after acquiring the lock of the next node in the list, thus preventin
Read more