On Sorting an Intransitive Total Ordered Set Using Semi-Heap
نویسنده
چکیده
1 The problem of sorting an intransitive total ordered set, a generalization of regular sorting, is considered. This generalized sorting is based on the fact that there exists a special linear ordering for any intransitive total ordered set. A new data structure called semi-heap is proposed to construct an optimal (n logn) sorting algorithm. Finally, we propose a cost-optimal parallel algorithm using semi-heap. The run time of this algorithm is (n) with (logn) processors under the EREW PRAM model.
منابع مشابه
On Finding a Hamiltonian Path in a Tournament Using Semi-Heap
In [8] a new data structure called semi-heap is proposed to construct an optimal (n logn) sorting algorithm to sort an intransitive total ordered set, a generalization of regular sorting. In this part, we provide a cost-optimal parallel algorithm using semi-heap. The run time of this algorithm is (n) with (logn) processors under the EREW PRAM model. The use of a Hamiltonian path (generalized so...
متن کاملFinal Course Paper on Parallel Sorting of Intransitive Total Ordered Sets
For the problem of sorting an Intransitive Total Ordered Set, a combination of two parallel algorithms already known by literature is proposed and implemented. The benchmarks show significant speedup on a shared-memory multi-processor system.
متن کاملLiterature Review on Parallel Sorting of Intransitive Total Ordered Sets
Sorting of transitive total ordered sets is one of the best investigated topics in Computer Science. A generalization of this is sorting an intransitive total ordered set which is more complex. While a transitive total ordered set (e. g. a subset of the real numbers) holds a ≥ b∧b ≥ a⇒ a ≥ c, this does not have to be true for a intransitive total ordered set. Only a → b ∨̇ b → a is claimed. Neve...
متن کاملTwo New Methods for Simulating Photolithography Development in 3D
I. L. Z I{ Two methods are presented for simulating the development of photolithographic profiles during the resist dissolution phase. These algorithms are the volume-of-fluid I algorithm. and the steady level-set algorithm. These methods are compared with the ray-trace, cell and level-set techniques employed in SAMPLE-3D2. The volume-of-fluid algorithm employs an Euclidean Grid with volume fra...
متن کاملOrdered Dags: HypercubeSort
We generalise the insertion into a binary heap to any directed acyclic graph (DAG) with one source vertex. This lets us formulate a general method for converting any such DAG into a data structure with priority queue interface. We apply our method to a hypercube DAG to obtain a sorting algorithm of complexity $\mathcal{O}(n\log^2 (n))$. As another curious application, we derive a relationship b...
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:
دوره شماره
صفحات -
تاریخ انتشار 2000