An empirical analysis of algorithms for constructing a minimum spanning tree

Moret, Bernard M. E.; Shapiro, Herbert

doi:10.1007/bfb0028279

Cited by 49 publications

(51 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our implementation is much faster than any other Kruskal's implementation we could program or find for any graph density. As a matter of fact, our Kruskal's version is faster than Prim's algorithm [20], even as optimized by B. Moret and H. Shapiro [18], and also competitive with the best alternative implementations we could find [14,15].…”

Section: Introductionmentioning

confidence: 87%

Optimal Incremental Sorting

Paredes

Navarro

2006

2006 Proceedings of the Eighth Workshop on Algorithm Engineering and Experiments (ALENEX)

View full text Add to dashboard Cite

Let A be a set of size m. Obtaining the first k ≤ m elements of A in ascending order can be done in optimal O(m+k log k) time. We present an algorithm (online on k) which incrementally gives the next smallest element of the set, so that the first k elements are obtained in optimal time for any k. We also give a practical version of the algorithm, with the same complexity on average, which performs better in practice than the best existing online algorithm. As a direct application, we use our technique to implement Kruskal's Minimum Spanning Tree algorithm, where our solution is competitive with the best current implementations. We finally show that our technique can be applied to several other problems, such as obtaining an interval of the sorted sequence and implementing heaps.

show abstract

Section: Introductionmentioning

confidence: 87%

Optimal Incremental Sorting

Paredes

Navarro

2006

2006 Proceedings of the Eighth Workshop on Algorithm Engineering and Experiments (ALENEX)

View full text Add to dashboard Cite

show abstract

“…The pairing heap [10] is the most efficient among other Fibonacci-like heaps from the practical point of view [17,21]. Still, it is theoretically inefficient according to the following fact [9].…”

Section: Drawbacks Of Other Structuresmentioning

confidence: 99%

“…They also conducted experiments showing that pairing heaps are more efficient in practice than Fibonacci heaps and than other known heap structures, even for applications requiring many decrease-key operations! More experiments were also conducted [17] illustrating the practical efficiency of pairing heaps. The bounds for the standard implementation were later improved by Iacono [14] to: O(1) per insert, and zero cost per meld.…”

Section: Introductionmentioning

confidence: 99%

The Violation Heap: A Relaxed Fibonacci-Like Heap

Elmasry

2010

Discrete Math. Algorithm. Appl.

View full text Add to dashboard Cite

Abstract. We give a priority queue that achieves the same amortized bounds as Fibonacci heaps. Namely, find-min requires O(1) worst-case time, insert, meld and decrease-key require O(1) amortized time, and delete-min requires O(log n) amortized time. Our structure is simple and promises an efficient practical behavior when compared to other known Fibonacci-like heaps. The main idea behind our construction is to propagate rank updates instead of performing cascaded cuts following a decrease-key operation, allowing for a relaxed structure.

show abstract

“…Despite the inability to prove better bounds for decrease-key, several experiments [8,9,13] were conducted illustrating that the pairing heaps are practically superior to other heaps, including the Fibonacci heaps, especially for applications that involve decrease-key operations! Other experiments [3] were also conducted with an attempt to construct a worst-case scenario for the decrease-key operation, but the outcome was that decrease-key takes a constant time in practice!…”

Section: Introductionmentioning

confidence: 99%

Pairing Heaps with O(log log n) decrease Cost

Elmasry¹

2009

Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

We give a variation of the pairing heaps for which the time bounds for all the operations match the lower bound proved by Fredman for a family of similar self-adjusting heaps. Namely, our heap structure requires O(1) for insert and findmin, O(log n) for delete-min, and O(log log n) for decreasekey and meld (all the bounds are in the amortized sense except for find-min).1 Introduction A self-adjusting data structure is a structure that does not maintain structural information (like size or height) within its nodes, still can adjust itself to perform efficiently and theoretically compete with other structures. Avoiding the restrictions governing other structures and the necessity of maintaining structural information, selfadjusting structures showed practical superiority over their counterparts.Following splay trees [12], a self-adjusting alternative to balanced trees with many other interesting properties, the next move was a self-adjusting heap. Fredman et al. [6] introduced the pairing heaps as a selfadjusting alternative to Fibonacci heaps. Despite the ingenuity of their structure and proofs, they were able to illustrate an amortized O(log n) bound for various heap operations. Lagging behind the Fibonacci heaps, the asymptotic time bounds for various heap operations except for delete-min were to be improved.The pairing heap [6] is a heap-ordered general tree. The values in the heap are stored one value per node. The basic operation on a pairing heap is the linking operation in which two trees are combined by linking the root with the larger key value to the other as its leftmost child. The following operations are defined for the standard implementation of the pairing heaps:

show abstract

An empirical analysis of algorithms for constructing a minimum spanning tree

Cited by 49 publications

References 11 publications

Optimal Incremental Sorting

Optimal Incremental Sorting

The Violation Heap: A Relaxed Fibonacci-Like Heap

Pairing Heaps with O(log log n) decrease Cost

Contact Info

Product

Resources

About