Given a rectangular m × n matrix stored as a two-dimensional array, we want to transpose it in place andmeasure the cost by the number of memory writes and the number of auxiliary cells used. We propose a transposition algorithm with optimal complexity O(mn) using only min(m, n) auxiliary memory cells. © 2009 Elsevier Inc. All rights reserved.

Every permutation of {1, 2, . . . , N} can be written as the product of two involutions. As a consequence, any permutation of the elements of an array can be performed in-place using simultaneous swaps in two rounds of swaps. In the case where the permutation is the k-way perfect shuffle we develop two methods for efficiently computing the pair of involutions that accomplishes these swaps. The ...

We examine the constrained via minimization problem with pin preassignments (CVMPP) which arises in connection with hierarchical physical synthesis. Let A be a circuit composed of subcircuits B, C, D,. . .. Assume that the placement and routing phase together with the 2-layer wiring of the subcircuits, and the placement and routing phase without the 2-layer wiring of A are completed. CVMPP is t...

Every permutation of {1, 2, . . . , N} can be written as the product of two involutions. As a consequence, any permutation of the elements of an array can be performed in-place using simultaneous swaps in two rounds of swaps. In the case where the permutation is the k-way perfect shuffle we develop two methods for efficiently computing the pair of involutions that accomplishes these swaps. The ...

Asano et al. [JoCG 2011] proposed an open problem of computing the minimum enclosing circle of a set of n points in R2 given in a read-only array in sub-quadratic time. We show that Megiddo’s prune and search algorithm for computing the minimum radius circle enclosing the given points can be tailored to work in a read-only environment in O(n1+ ) time using O(logn) extra space, where is a positi...

This paper investigates how to improve the worst case runtime of INSERTION SORT while keeping it in-place, incremental and adaptive. To sort an array of n elements with w bits for each element, classic INSERTION SORT runs in O(n) operations with wn bits space. GAPPED INSERTION SORT has a runtime of O(n lg n) with a high probability of only using (1+ )wn bits space. This paper shows that ROTATED...

the term globalization undoubtedly has affected all parts of humanity life in current century. globalization as a comprehensive phenomenon has influenced economical, political, social and cultural aspects of our societies. contemporary architecture as a multidimensional category is depended on various factors and needs to be pursued in different fields, in order to reach to a perfect comprehend...