On the All-Pairs Shortest Path Algorithm of Moffat and Takaoka
نویسندگان
چکیده
We review how to solve the all-pairs shortest-path problem in a nonnegatively Ž 2 . weighted digraph with n vertices in expected time O n log n . This bound is shown to hold with high probability for a wide class of probability distributions on nonnegatively weighted Ž . digraphs. We also prove that, for a large class of probability distributions, V n log n time is necessary with high probability to compute shortest-path distances with respect to a single Ž . source. Q 1997 John Wiley & Sons, Inc. Random Struct. Alg., 10, 205]22
منابع مشابه
A note of an O(n3/logn) time algorithm for all pairs shortest paths
We improve the all pairs shortest path algorithm given by Takaoka to time complexity O(n3/ log n). Our improvement is achieved by using a smaller table and therefore saves time for the algorithm.
متن کاملالگوریتم مستطیل آبشاری و ماتریس انتقال در شبکه های کوتاه ترین مسیر بادور
Shortest path problem is among the most interesting problems in the field of graph and network theory. There are many efficient matrix based algorithms for detecting of shortest path and distance between all pairs of this problem in literature. In this paper, a new exact algorithm, named Cascade Rectangle Algorithm, is presented by using main structure of previous exact algorithms and developin...
متن کاملAn O(n 3 loglogn/log2 n) Time Algorithm for All Pairs Shortest Paths
We present an O(n log log n/ log n) time algorithm for all pairs shortest paths. This algorithm improves on the best previous result of O(n(log log n)/ log n) time.
متن کاملAn Efficient Parallel Algorithm for the All Pairs Shortest Path Problem
The all pairs shortest path problem is a class of the algebraic path problem. Many parallel algorithms for the solution of this problem appear in the literature. One of the efficient parallel algorithms on W-RAM model is given by Kucera[17]. Though efficient, algorithms written for the W-RAM model of parallel computation are too idealistic to be implemented on the current hardware. In this repo...
متن کاملAn O(n log log n/ log n) Time Algorithm for the All-Pairs Shortest Path Problem
We design a faster algorithm for the all-pairs shortest path problem under the conventional RAM model, based on distance matrix multiplication (DMM). Specifically we improve the best known time complexity of O(n(log log n)/ logn) to O(n log log n/ log n). As an application, we show the k-maximum subarray problem can be solved in O(kn log log n/ log n) time for small k.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Random Struct. Algorithms
دوره 10 شماره
صفحات -
تاریخ انتشار 1995