Given an array X of n elements from a restricted domain of integers [1, n]. The integer sorting problem is the rearrangement of n integers in ascending order. We study the first optimal deterministic sublogarithmic algorithm for integer sorting on CRCW PRAM. We give two comments on the algorithm. The first comment is the algorithm not runs in sublogarithmic time for any distribution of input da...

New Result EREW PRAM: Compute gcd(x, y) with probability 1 − o(1) in O(n log log n/ log n) time using n6+ processors. [16] Reduction Our inputs are integers x, y with x ≥ y > 0. • Choose a prime bound B > 0, and assume p | x or p | y implies p > B. • Choose a at random, 1 ≤ a ≤ y − 1. • Compute r := ax mod y. • Remove all prime divisors ≤ B from r producing s. Thus P (r/s) ≤ B. We use (x, y) → ...

We investigate the relative computational power of parallel models with shared memory. Based on feasibility considerations present in the literature, we split these models into “lightweight” and “heavyweight,” and then find that the heavyweight class is strictly more powerful than the lightweight class, as expected. On the other hand, we contradict the long held belief that the heavyweight mode...

Thin irregularly-shaped surfaces such as clay drapes often have a major control on flow and transport in heterogeneous porous media. Clay drapes are often complex curvilinear 3dimensional surfaces and display a very complex spatial distribution. Variogram-based stochastic approaches are often also not able to describe the spatial distribution of clay drapes since complex, curvilinear, continuou...

We present a more efficient CREW PRAM algorithm for integer sorting. This algorithm sorts n integers in {0, 1, 2, ..., n} in O((log n)/ log log n) time and O(n(log n/ log log n)) operations. It also sorts n integers in {0, 1, 2, ..., n− 1} in O((log n)/ log log n) time and O(n(log n/ log log n) log log log n) operations. Previous best algorithm [13] on both cases has time complexity O(log n) bu...

We show that for all given n, t, w ∈ {1, 2, . . .} with n < 2, an array of n entries of w bits each can be represented on a word RAM with a word length of w bits in at most nw + dn(t/(2w))e bits of uninitialized memory to support constant-time initialization of the whole array and O(t)-time reading and writing of individual array entries. At one end of this tradeoff, we achieve initialization a...

Exercise 1 (page 378, line 5) Describe in your own words how the operations lookup, min, max, succ, pred are carried out, and what the time complexity is. Exercise 2 (page 379, line -8) Describe how the operations lookup, min, max, succ, pred, insert, delete are carried out using constant time and one operation in . Exercise 3 (page 381, line 13) Prove that multiplying X by 1 2 f 1 creates the ...

We describe a RAM algorithm computing all runs (=maximal repetitions) of a given string of length n over a general ordered alphabet in O(n log 2 3 n) time and linear space. Our algorithm outperforms all known solutions working in Θ(n log σ) time provided σ = n, where σ is the number of distinct letters in the input string. We conjecture that there exists a linear time RAM algorithm finding all ...

Analyzing the dynamic faulty behavior in DRAMs is a severely time consuming task, because of the exponential growth of the analysis time needed with each memory operation added to the sensitizing operation sequence of the fault. In this paper, a new fault analysis approach for DRAM cell defects is presented where the total infinite space of dynamic faulty behavior can be approximated within a l...