Time usingO Research Articles

Parallel algorithms for minimum cuts and maximum flows in planar networks

Algorithms are given that compute maximum flows in planar directed networks either in O ((log n ) 3 ) parallel time using O ( n 4 ) processors or O ((log n ) 2 ) parallel time using O ( n 6 ) processors. The resource consumption of these algorithms is dominated by the cost of finding the value of a maximum flow. When such a value is given, or when the computation is on an undirected network, the bound is O ((log n ) 2 ) time using O ( n 3 ) processors. No efficient parallel algorithm is known for the maximum flow problem in general networks.

Ordered priority queues

A new data structure called ordered priority queue is introduced in this paper. Elements stored in the data structure have a primary order (key) and a secondary order (priority) associated with them. An ordered min-priority queue allows users to find the minimum priority element in any range (according to key order) inO(logn) time. Such a data structure withn elements can be created inO(n logn) time usingO(n) storage. A specific implementation based on median split trees is presented. Sequential access of the elements can be done inO(n log logn) time andO(logn) extra storage.

An optimal speed-up parallel algorithm for triangulating simplicial point sets in space

Previous research on developing parallel triangulation algorithms concentrated on triangulating planar point sets.O(log3n) running time algorithms usingO(n) processors have been developed in Refs. 1 and 2. Atallah and Goodrich(3) presented a data structure that can be viewed as a parallel analogue of the sequential plane-sweeping paradigm, which can be used to triangulate a planar point set inO(logn loglogn) time usingO(n) processors. Recently Merks(4) described an algorithm for triangulating point sets which runs inO(logn) time usingO(n) processors, and is thus optimal. In this paper we develop a parallel algorithm for triangulating simplicial point sets in arbitrary dimensions based on the idea of the sequential algorithm presented in Ref. 5. The algorithm runs inO(log2n) time usingO(n/logn) processors. The algorithm hasO(n logn) as the product of the running time and the number of processors; i.e., an optimal speed-up.

An optimal parallel algorithm for triangulating a set of points in the plane

This paper presents an optimal parallel algorithm for triangulating an arbitrary set ofn points in the plane. The algorithm runs inO(logn) time usingO(n) space andO(n) processors on a Concurrent-Read, Exclusive-Write Parallel RAM model (CREW PRAM). The parallel lower bound on triangulation is Ω(logn) time so the best possible linear speedup has been achieved. A parallel divide-and-conquer technique of subdividing a problem into\(\sqrt n \) subproblems is employed.