Optimal In-place Sorting of Vectors and Records
نویسندگان
چکیده
We study the problem of determining the complexity of optimal comparison-based in-place sorting when the key length, k, is not a constant. We present the first algorithm for lexicographically sorting n keys in O(nk+n log n) time using O(1) auxiliary data locations, which is simultaneously optimal in time and space.
منابع مشابه
Optimal Distribution System Reconfiguration Using Non-dominated Sorting Genetic Algorithm (NSGA-II)
In this paper, a Non-dominated Sorting Genetic Algorithm-II (NSGA-II) based approach is presented for distribution system reconfiguration. In contrast to the conventional GA based methods, the proposed approach does not require weighting factors for conversion of multi-objective function into an equivalent single objective function. In order to illustrate the performance of the proposed method,...
متن کاملOptimal Placement and Sizing of Distributed Generation Via an Improved Nondominated Sorting Genetic Algorithm II
The use of distributed generation units in distribution networks has attracted the attention of network managers due to its great benefits. In this research, the location and determination of the capacity of distributed generation (DG) units for different purposes has been studied simultaneously. The multi-objective functions in the optimization model are reducing system line losses; reducing v...
متن کاملSolving Multi-objective Optimal Control Problems of chemical processes using Hybrid Evolutionary Algorithm
Evolutionary algorithms have been recognized to be suitable for extracting approximate solutions of multi-objective problems because of their capability to evolve a set of non-dominated solutions distributed along the Pareto frontier. This paper applies an evolutionary optimization scheme, inspired by Multi-objective Invasive Weed Optimization (MOIWO) and Non-dominated Sorting (NS) strategi...
متن کاملOptimal Placement of Phasor Measurement Units to Maintain CompleteObservability Considering Maximum Reliability by Non-dominated Sorting Genetic Algorithm-II (NSGA-II)
Ever-increasing energy demand has led to geographic expansion of transmission lines and their complexity. In addition, higher reliability is expected in the transmission systemsdue to their vital role in power systems. It is very difficult to realize this goal by conventional monitoring and control methods. Thus, phasor measurement units (PMUs) are used to measure system parameters. Although in...
متن کاملAn In-Place Sorting Algorithm Performing O(n log n) Comparisons and O(n) Data Moves
In this paper we give a positive answer to the long-standing problem of finding an in-place sorting algorithm performing O(n log n) comparisons and O(n) data moves in the worst case. So far, the better in-place sorting algorithm with O(n) moves was proposed by Munro and V. Raman. Their algorithm requires O(n) comparisons in the worst case, for any ǫ > 0. Later, Katajainen and Pasanen discovered...
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 2005