## Algorithm Design and Software Libraries: Recent Developments in the LEDA Project (1992)

Venue: | IN PROC. IFIP 12TH WORLD COMPUTER CONGRESS |

Citations: | 11 - 0 self |

### BibTeX

@INPROCEEDINGS{Mehlhorn92algorithmdesign,

author = {Kurt Mehlhorn and Stefan Näher},

title = {Algorithm Design and Software Libraries: Recent Developments in the LEDA Project},

booktitle = {IN PROC. IFIP 12TH WORLD COMPUTER CONGRESS},

year = {1992},

pages = {493--505},

publisher = {Elsevier}

}

### Years of Citing Articles

### OpenURL

### Abstract

LEDA (Library of Efficient Data Types and Algorithms) is an ongoing project which aims to build a library of the efficient data structures and algorithms used in combinatorial computing [12]. We discuss three recent aspects of the project: The cost of flexibility, implementation parameters, and augmented trees.

### Citations

8543 |
Introduction to Algorithms
- Cormen, Leiserson, et al.
- 1990
(Show Context)
Citation Context ...ection of data types and algorithms in a form which allows them to be used by non-experts. This collection includes most of the data types and algorithms described in the text books of the area (e.g. =-=[1, 11, 6]-=-), i.e., stacks, queues, lists, sets, dictionaries, ordered sequences, partitions, priority queues, directed, undirected, and planar graphs, lines, points, planes and basic algorithms in graph and net... |

707 |
Data structures and algorithms
- Aho, Hopcroft, et al.
- 1983
(Show Context)
Citation Context ...ection of data types and algorithms in a form which allows them to be used by non-experts. This collection includes most of the data types and algorithms described in the text books of the area (e.g. =-=[1, 11, 6]-=-), i.e., stacks, queues, lists, sets, dictionaries, ordered sequences, partitions, priority queues, directed, undirected, and planar graphs, lines, points, planes and basic algorithms in graph and net... |

372 |
Self-adjusting binary search trees
- Sleator, Tarjan
- 1985
(Show Context)
Citation Context ... have recently shown that a variant of pseudo-balanced trees [9] has strong bounds, too. For randomized search trees [2] the question is open and other weighted tree schemes, most notably splay trees =-=[20]-=- don't have it. However, D-trees a difficult to implement. 9 5.2 Skip Lists as a Basis for Augmented Trees Skip lists [18] are a probabilistic alternative to balanced trees. In a skip list, each eleme... |

322 | lists: A probabilistic alternative to balanced trees
- Pugh
- 1989
(Show Context)
Citation Context ...17]. Asymptotically efficient realizations of augmented trees are usually based on weight-balanced trees [16]; in the case of range and segment trees implementations are available in LEDA. Skip lists =-=[18, 19]-=- were recently proposed as an alternative to balanced trees for one dimensional dictionaries. We argue in section 5 that skip lists can also serve as the basis for augmented tree schemes. They lead to... |

137 | Randomized Search Trees
- Aragon, Seidel
- 1989
(Show Context)
Citation Context ... :. For many functions C, this sums to O(C(n)). The geometric size decrease property holds for weight-balanced trees [16] [11, section III.5.1.] and their derivatives, and for randomized search trees =-=[2]-=-; it does not hold for any kind of height balanced tree scheme. (Consider for example a (2; 3)-tree of height 3h where a subtree T of height 2h consists solely for nodes of degree 3 and all 8 nodes ou... |

80 |
Binary search trees of bounded balance
- Nievergelt, Reingold
- 1973
(Show Context)
Citation Context ...ment trees [4], interval trees [8], and dynamization of order decomposable searching problems [17]. Asymptotically efficient realizations of augmented trees are usually based on weight-balanced trees =-=[16]-=-; in the case of range and segment trees implementations are available in LEDA. Skip lists [18, 19] were recently proposed as an alternative to balanced trees for one dimensional dictionaries. We argu... |

51 |
Adding range restriction capability to dynamic data structures
- Willard, Lueker
- 1985
(Show Context)
Citation Context ...e such a mechanism based on multiple inheritance. It will be available in the next version of LEDA. Augmented trees are abundant in computational geometry. Examples of augmented trees are range trees =-=[3, 21]-=-, segment trees [4], interval trees [8], and dynamization of order decomposable searching problems [17]. Asymptotically efficient realizations of augmented trees are usually based on weight-balanced t... |

39 | LEDA: A Library of Efficient Data Types and Algorithms
- Mehlhorn, Näher
- 1989
(Show Context)
Citation Context ...aher Abstract LEDA (Library of Efficient Data Types and Algorithms) is an ongoing project which aims to build a library of the efficient data structures and algorithms used in combinatorial computing =-=[12]-=-. We discuss three recent aspects of the project: The cost of flexibility, implementation parameters, and augmented trees. Keyword Codes: D.2.0; D.1.5; F.2.2 Keywords: Software Engineering, General; o... |

28 | A skip list cookbook
- Pugh
- 1990
(Show Context)
Citation Context ...17]. Asymptotically efficient realizations of augmented trees are usually based on weight-balanced trees [16]; in the case of range and segment trees implementations are available in LEDA. Skip lists =-=[18, 19]-=- were recently proposed as an alternative to balanced trees for one dimensional dictionaries. We argue in section 5 that skip lists can also serve as the basis for augmented tree schemes. They lead to... |

21 | The interval skip list: A data structure for finding all intervals that overlap a point
- Hanson, Johnson
- 1991
(Show Context)
Citation Context ...aries. We argue in section 5 that skip lists can also serve as the basis for augmented tree schemes. They lead to simpler and more efficient programs. Related but weaker results were also obtained by =-=[10]-=-. 2 LEDA, a Brief Review LEDA is a growing library of efficient data types and algorithms used in combinatorial computing. The main features are: ffl LEDA provides a sizable collection of data types a... |

16 |
Data structures and algorithms, vol. 1: Sorting and searching
- Mehlhorn
- 1984
(Show Context)
Citation Context ...ection of data types and algorithms in a form which allows them to be used by non-experts. This collection includes most of the data types and algorithms described in the text books of the area (e.g. =-=[1, 11, 6]-=-), i.e., stacks, queues, lists, sets, dictionaries, ordered sequences, partitions, priority queues, directed, undirected, and planar graphs, lines, points, planes and basic algorithms in graph and net... |

11 |
Two new kinds of biased search trees
- Feigenbaum, Tarjan
- 1983
(Show Context)
Citation Context ...ound on amortized update cost. D-trees [11, section III.6.2.] are a weighted tree scheme with a strong bound on the rebalancing cost and we have recently shown that a variant of pseudo-balanced trees =-=[9]-=- has strong bounds, too. For randomized search trees [2] the question is open and other weighted tree schemes, most notably splay trees [20] don't have it. However, D-trees a difficult to implement. 9... |

4 |
On the Average Number of Rebalancing Operations
- Blum, Mehlhorn
- 1980
(Show Context)
Citation Context ...ong bound for the rebalancing frequency if the amortized rebalancing cost is logarithmic even if the cost of a local change is proportional to the size of the subtrees involved. Weight-balanced trees =-=[21, 5]-=- and randomized search trees [2] have strong bounds but no height-balanced scheme has. Also, at least for weight-balanced trees the known bounds involve large constant factors. For example, [21] state... |

3 |
Dynamic rectangle intersection searching
- Edelsbrunner
- 1980
(Show Context)
Citation Context ...tance. It will be available in the next version of LEDA. Augmented trees are abundant in computational geometry. Examples of augmented trees are range trees [3, 21], segment trees [4], interval trees =-=[8]-=-, and dynamization of order decomposable searching problems [17]. Asymptotically efficient realizations of augmented trees are usually based on weight-balanced trees [16]; in the case of range and seg... |

2 |
Decomposable Searching
- Bentley
- 1979
(Show Context)
Citation Context ...e such a mechanism based on multiple inheritance. It will be available in the next version of LEDA. Augmented trees are abundant in computational geometry. Examples of augmented trees are range trees =-=[3, 21]-=-, segment trees [4], interval trees [8], and dynamization of order decomposable searching problems [17]. Asymptotically efficient realizations of augmented trees are usually based on weight-balanced t... |

2 |
Leeuwen, Two General Methods for Dynamization of Decomposable Searching Problems
- Overmars, van
- 1981
(Show Context)
Citation Context ...ted trees are abundant in computational geometry. Examples of augmented trees are range trees [3, 21], segment trees [4], interval trees [8], and dynamization of order decomposable searching problems =-=[17]-=-. Asymptotically efficient realizations of augmented trees are usually based on weight-balanced trees [16]; in the case of range and segment trees implementations are available in LEDA. Skip lists [18... |

1 |
Solutions to Klee's Rectangle Problems, typescript
- Bentley
- 1977
(Show Context)
Citation Context ...d on multiple inheritance. It will be available in the next version of LEDA. Augmented trees are abundant in computational geometry. Examples of augmented trees are range trees [3, 21], segment trees =-=[4]-=-, interval trees [8], and dynamization of order decomposable searching problems [17]. Asymptotically efficient realizations of augmented trees are usually based on weight-balanced trees [16]; in the c... |

1 |
Efficient Algorithms for Enumerating Intersecting Intervals and Rectangles, Xerox Parc Report CSL-80-09
- Creight
- 1980
(Show Context)
Citation Context ...gant and efficient way to satisfy them. 5.1 Requirements Augmented trees are abundant in computational geometry. Examples of augmented trees are range trees [3, 21], segment trees [4], interval trees =-=[8, 7]-=-, and dynamization of order decomposable searching problems [17]. An account of these data structures can also be found in sections VII.2.2, VIII.5.1.3., VIII.5.1.1., and VII.1.3 of [11]. We will use ... |

1 |
Skip Lists as a Basis for Augmented Trees
- Mehlhorn, Naher, et al.
(Show Context)
Citation Context ... merging, joining, and splitting. We will now sketch that skip lists are also an alternative to weight-balanced and randomized search trees as a basis for augmented trees; the details can be found in =-=[13]-=-. For the sequel it will be convenient to associate a tree with a skip list. This tree can be obtained as follows: 1. Delete the tower stop. 2. Replace every tower v of height h by a linear list v h ;... |

1 |
Parameterized Data Types
- Naher
(Show Context)
Citation Context ...d redefines the cmp inf function according to the linear order of I. Similar virtual functions are used to copy or destroy objects of types unknown to the implementation. More details can be found in =-=[15]-=-. As a consequence of the above described method every compare operation performed by the implementation results in a C++ function call. This can slow down computation if I is a simple type like int w... |