The LEDA platform for combinatorial and geometric computing

Mehlhorn, Kurt; Näher, Stefan; Uhrig, Christian

doi:10.1007/3-540-63165-8_161

Cited by 369 publications

(439 citation statements)

References 9 publications

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“…All graphs were constructed using the G(n; p) model, for p = 4/n, 0.3, 0.5 and 0.9. Our implementation uses LEDA [9]. All experiments were performed on a Pentium 1.7Ghz machine with 1 GB of memory, running GNU/Linux.…”

Section: Methodsmentioning

confidence: 99%

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Implementing Minimum Cycle Basis Algorithms

Mehlhorn

Michail

2005

Experimental and Efficient Algorithms

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Abstract. In this paper we consider the problem of computing a minimum cycle basis of an undirected graph G = (V, E) with n vertices and m edges. We describe an efficient implementation of an O(m 3 + mn 2 log n) algorithm presented in [1]. For sparse graphs this is the currently best known algorithm. This algorithm's running time can be partitioned into two parts with time O(m 3 ) and O(m 2 n + mn 2 log n) respectively. Our experimental findings imply that the true bottleneck of a sophisticated implementation is the O(m 2 n + mn 2 log n) part. A straightforward implementation would require Ω(nm) shortest path computations, thus we develop several heuristics in order to get a practical algorithm. Our experiments show that in random graphs our techniques result in a significant speedup. Based on our experimental observations, we combine the two fundamentally different approaches to compute a minimum cycle basis used in [1,2] and [3,4], to obtain a new hybrid algorithm with running time O(m 2 n 2 ). The hybrid algorithm is very efficient in practice for random dense unweighted graphs. Finally, we compare these two algorithms with a number of previous implementations for finding a minimum cycle basis in an undirected graph.

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Section: Methodsmentioning

confidence: 99%

“…Our implementation uses LEDA [9]. We develop a set of heuristics which improve the best-case performance of the algorithm while maintaining its asymptotics.…”

Section: Introductionmentioning

confidence: 99%

Implementing Minimum Cycle Basis Algorithms

Mehlhorn

Michail

2005

Experimental and Efficient Algorithms

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“…The work on the TPIE project is in progress. LEDA-SM [11] external memory library was designed as an extension to the LEDA library [25] for handling large data sets. The library offers implementations of I/O-efficient sorting, external memory stack, queue, radix heap, array heap, buffer tree, array, B + -tree, string, suffix array, matrices, static graph, and some simple graph algorithms.…”

Section: Related Workmentioning

confidence: 99%

Stxxl: Standard Template Library for XXL Data Sets

Dementiev¹,

Kettner

Sanders³

2005

Algorithms – ESA 2005

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We present a software library Stxxl, that enables practice-oriented experimentation with huge data sets. Stxxl is an implementation of the C++ standard template library STL for external memory computations. It supports parallel disks, overlapping between I/O and computation and is the first external memory algorithm library that supports the pipelining technique that can save more than half of the I/Os. Stxxl has already been used for the following applications: implementations of external memory algorithms for computing minimum spanning trees, connected components, breadth-first search decompositions, constructing suffix arrays, and computing social network analysis metrics for huge graphs.

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“…A brief description of the algorithm follows. More details can be found in [13]. Let S be a set of n points in the plane, let x 1 , x 2 , .…”

Section: Clarkson Et Al Algorithmmentioning

confidence: 99%

Speculative Parallelization of a Randomized Incremental Convex Hull Algorithm

Cintra

Llanos

Palop

2004

Computational Science and Its Applications – ICCSA 2004

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Abstract. Finding the fastest algorithm to solve a problem is one of the main issues in Computational Geometry. Focusing only on worst case analysis or asymptotic computations leads to the development of complex data structures or hard to implement algorithms. Randomized algorithms appear in this scenario as a very useful tool in order to obtain easier implementations within a good expected time bound. However, parallel implementations of these algorithms are hard to develop and require an in-depth understanding of the language, the compiler and the underlying parallel computer architecture. In this paper we show how we can use speculative parallelization techniques to execute in parallel iterative algorithms such as randomized incremental constructions. In this paper we focus on the convex hull problem, and show that, using our speculative parallelization engine, the sequential algorithm can be automatically executed in parallel, obtaining speedups with as little as four processors, and reaching 5.15x speedup with 28 processors.

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The LEDA platform for combinatorial and geometric computing

Cited by 369 publications

References 9 publications

Implementing Minimum Cycle Basis Algorithms

Implementing Minimum Cycle Basis Algorithms

Stxxl: Standard Template Library for XXL Data Sets

Speculative Parallelization of a Randomized Incremental Convex Hull Algorithm

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