We show that a unit-cost RAM with a word length of w bits can sort n integers in the range 0 : : 2 w \Gamma1 in O(n log log n) time, for arbitrary w log n, a significant improvement over the bound of O(n p log n) achieved by the fusion trees of Fredman and Willard. Provided that w (log n) 2+ffl for some fixed ffl ? 0, the sorting can even be accomplished in linear expected time with a randomized algorithm. Both of our algorithms parallelize without loss on a unit-cost PRAM with a word length of w bits. The first one yields an algorithm that uses O(logn) time and O(n log log n) operations on a deterministic CRCW PRAM. The second one yields an algorithm that uses O(log n) expected time and O(n) expected operations on a randomized EREW PRAM, provided that w (log n) 2+ffl for some fixed ffl ? 0. Our deterministic and randomized sequential and parallel algorithms generalize to the lexicographic sorting problem of sorting multiple-precision integers represented in several words. ...

We show that n integers in the range 1 : : n can be sorted stably on an EREW PRAM using O(t) time and O(n( p log n log log n + (log n) 2 =t)) operations, for arbitrary given t log n log log n, and on a CREW PRAM using O(t) time and O(n( p log n + log n=2 t=logn )) operations, for arbitrary given t log n. In addition, we are able to sort n arbitrary integers on a randomized CREW PRAM within the same resource bounds with high probability. In each case our algorithm is a factor of almost \Theta( p log n) closer to optimality than all previous algorithms for the stated problem in the stated model, and our third result matches the operation count of the best previous sequential algorithm. We also show that n integers in the range 1 : : m can be sorted in O((log n) 2 ) time with O(n) operations on an EREW PRAM using a nonstandard word length of O(log n log log n log m) bits, thereby greatly improving the upper bound on the word length necessary to sort integers with a linear t...

We present a simple and implementable algorithm that computes a minimum spanning tree of an undirected weighted graph G = (V, E) of n = |V| vertices and m = |E| edges on an EREW PRAM in O(log 3=2 n) time using n+m processors. This represents a substantial improvement in the running time over the previous results for this problem using at the same time the weakest of the PRAM models. It also implies the existence of algorithms having the same complexity bounds for the EREW PRAM, for connectivity, ear decomposition, biconnectivity, strong orientation, st-numbering and Euler tours problems.

Abstract We show that a unit-cost RAM with a word length of w bitscan sort n integers in the range 0: : 2w \Gamma 1 in O(n log log n)time, for arbitrary w * log n, a significant improvementover the bound of O(nplog n) achieved by the fusion treesof Fredman and Willard. Provided that w * (log n)2+ffl, forsome fixed ffl? 0, the sorting can even be accomplished inlinear expected time with a randomized algorithm. Both of our algorithms parallelize without loss on a unit-cost PRAM with a word length of w bits. The first one yieldsan algorithm that uses O(log n) time and O(n log log n) op-erations on a deterministic CRCW PRAM. The second one yields an algorithm that uses O(log n) expected time and O(n) expected operations on a randomized EREW PRAM,provided that w * (log n)2+ffl for some fixed ffl? 0.Our deterministic and randomized sequential and parallel algorithms generalize to the lexicographic sorting problemof sorting multiple-precision integers represented in several words. 1 Introduction Sorting is one of the most fundamental computational prob-lems, and n keys can be sorted in O(n log n) time by anyof a number of well-known sorting algorithms. These algorithms operate in the comparison-based setting, i.e., they ob-tain information about the relative order of keys exclusively through pairwise comparisons. It is easy to show that a run-ning time of

We show that a unit-cost RAM with a word length of w bits can sort n integers in the range 0 : : 2 w \Gamma 1 in O(n log log n) time, for arbitrary w log n, a significant improvement over the bound of O(n p log n) achieved by the fusion trees of Fredman and Willard. Provided that w (log n) 2+ffl for some fixed ffl ? 0, the sorting can even be accomplished in linear expected time with a randomized algorithm. Both of our algorithms parallelize without loss on a unit-cost PRAM with a word length of w bits. The first one yields an algorithm that uses O(log n) time and O(n log log n) operations on a deterministic CRCW PRAM. The second one yields an algorithm that uses O(log n) expected time and O(n) expected operations on a randomized EREW PRAM, provided that w (log n) 2+ffl for some fixed ffl ? 0. Our deterministic and randomized sequential and parallel algorithms generalize to the lexicographic sorting problem of sorting multiple-precision integers represented in several words...

The traditional algorithm for sorting gives a bound of expected time without randomization and with randomization. Recent researches have optimized lower bound for deterministic algorithms for integer sorting [1-3]. Andersson has given the idea of Exponential tree which can be used for sorting [4]. Andersson, Hagerup, Nilson and Raman have given an algorithm which sorts n integers in expected time but uses space [4, 5]. Andersson has given improved algorithm which sort integers in expected time and linear space but uses randomization [2, 4]. Yijie Han has improved further to sort integers in expected time and linear space but passes integers in a batch i.e. all integers at a time [6]. These algorithms are very complex to implement. In this paper we discussed a way to implement the exponential tree sorting and later compare results with traditional sorting technique.