scholarly journals Partial Quicksort and Quickpartitionsort

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Conrado Martínez ◽  
Uwe Rösler
Keyword(s):  
Lower Bound ◽  
Time Analysis ◽  
Information Theoretic ◽  
Running Time ◽  
Running Time Analysis ◽  
International Audience

International audience Partial Quicksort sorts the $l$ smallest elements in a list of length $n$. We provide a complete running time analysis for this combination of Find and Quicksort. Further we give some optimal adapted versions, called Partition Quicksort, with an asymptotic running time $c_1l\ln l+c_2l+n+o(n)$. The constant $c_1$ can be as small as the information theoretic lower bound $\log_2 e$.

scholarly journals The analysis of find and versions of it

2012 ◽  
Vol Vol. 14 no. 2 (Analysis of Algorithms) ◽  
Author(s):  
Diether Knof ◽  
Uwe Roesler
Keyword(s):  
Branching Process ◽  
Analysis Of Algorithms ◽  
Time Analysis ◽  
Running Time ◽  
Random Time Change ◽  
Running Time Analysis ◽  
Finite Dimensional ◽  
Exponential Moments ◽  
International Audience ◽  
Point Measure

Analysis of Algorithms International audience In the running time analysis of the algorithm Find and versions of it appear as limiting distributions solutions of stochastic fixed points equation of the form X D = Sigma(i) AiXi o Bi + C on the space D of cadlag functions. The distribution of the D-valued process X is invariant by some random linear affine transformation of space and random time change. We show the existence of solutions in some generality via the Weighted Branching Process. Finite exponential moments are connected to stochastic fixed point of supremum type X D = sup(i) (A(i)X(i) + C-i) on the positive reals. Specifically we present a running time analysis of m-median and adapted versions of Find. The finite dimensional distributions converge in L-1 and are continuous in the cylinder coordinates. We present the optimal adapted version in the sense of low asymptotic average number of comparisons. The limit distribution of the optimal adapted version of Find is a point measure on the function [0, 1] there exists t -> 1 + mint, 1 - t.

Running-time Analysis of Ant System Algorithms with Upper-bound Comparison

2017 ◽  
Vol 8 (4) ◽  
pp. 1-17
Author(s):  
Han Huang ◽  
Hongyue Wu ◽  
Yushan Zhang ◽  
Zhiyong Lin ◽  
Zhifeng Hao
Keyword(s):  
Optimal Solution ◽  
Numerical Results ◽  
Ant System ◽  
Time Analysis ◽  
Traveling Salesman Problems ◽  
Running Time ◽  
Cycle System ◽  
Running Time Analysis ◽  
Global Optimal

Running-time analysis of ant colony optimization (ACO) is crucial for understanding the power of the algorithm in computation. This paper conducts a running-time analysis of ant system algorithms (AS) as a kind of ACO for traveling salesman problems (TSP). The authors model the AS algorithm as an absorbing Markov chain through jointly representing the best-so-far solutions and pheromone matrix as a discrete stochastic status per iteration. The running-time of AS can be evaluated by the expected first-hitting time (FHT), the least number of iterations needed to attain the global optimal solution on average. The authors derive upper bounds of the expected FHT of two classical AS algorithms (i.e., ant quantity system and ant-cycle system) for TSP. They further take regular-polygon TSP (RTSP) as a case study and obtain numerical results by calculating six RTSP instances. The RTSP is a special but real-world TSP where the constraint of triangle inequality is stringently imposed. The numerical results derived from the comparison of the running time of the two AS algorithms verify our theoretical findings.

scholarly journals Running Time Analysis of the ( $$1+1$$ 1 + 1 )-EA for OneMax and LeadingOnes Under Bit-Wise Noise

Algorithmica ◽  
2018 ◽  
Vol 81 (2) ◽  
pp. 749-795 ◽  
Author(s):  
Chao Qian ◽  
Chao Bian ◽  
Wu Jiang ◽  
Ke Tang
Keyword(s):  
Time Analysis ◽  
Running Time ◽  
Running Time Analysis

scholarly journals A General Approach to Running Time Analysis of Multi-objective Evolutionary Algorithms

2018 ◽  
Author(s):  
Chao Bian ◽  
Chao Qian ◽  
Ke Tang
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Theoretical Aspect ◽  
Combinatorial Problems ◽  
Time Analysis ◽  
Running Time ◽  
Asymptotic Bounds ◽  
Multi Objective ◽  
Running Time Analysis ◽  
Empirical Performance

Evolutionary algorithms (EAs) have been widely applied to solve multi-objective optimization problems. In contrast to great practical successes, their theoretical foundations are much less developed, even for the essential theoretical aspect, i.e., running time analysis. In this paper, we propose a general approach to estimating upper bounds on the expected running time of multi-objective EAs (MOEAs), and then apply it to diverse situations, including bi-objective and many-objective optimization as well as exact and approximate analysis. For some known asymptotic bounds, our analysis not only provides their leading constants, but also improves them asymptotically. Moreover, our results provide some theoretical justification for the good empirical performance of MOEAs in solving multi-objective combinatorial problems.

scholarly journals On Compact Encoding of Pagenumber $k$ Graphs

2008 ◽  
Vol Vol. 10 no. 3 ◽  
Author(s):  
Cyril Gavoille ◽  
Nicolas Hanusse
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Constant Time ◽  
Worst Case ◽  
Encoding Scheme ◽  
Information Theoretic ◽  
Auxiliary Table ◽  
Minimum Number ◽  
International Audience

International audience In this paper we show an information-theoretic lower bound of kn - o(kn) on the minimum number of bits to represent an unlabeled simple connected n-node graph of pagenumber k. This has to be compared with the efficient encoding scheme of Munro and Raman of 2kn + 2m + o(kn+m) bits (m the number of edges), that is 4kn + 2n + o(kn) bits in the worst-case. For m-edge graphs of pagenumber k (with multi-edges and loops), we propose a 2mlog2k + O(m) bits encoding improving the best previous upper bound of Munro and Raman whenever m ≤ 1 / 2kn/log2 k. Actually our scheme applies to k-page embedding containing multi-edge and loops. Moreover, with an auxiliary table of o(m log k) bits, our coding supports (1) the computation of the degree of a node in constant time, (2) adjacency queries with O(logk) queries of type rank, select and match, that is in O(logk *minlogk / loglogm, loglogk) time and (3) the access to δ neighbors in O(δ) runs of select, rank or match;.

scholarly journals Running time analysis of the (1+1)-EA for robust linear optimization

2020 ◽  
Vol 843 ◽  
pp. 57-72
Author(s):  
Chao Bian ◽  
Chao Qian ◽  
Ke Tang ◽  
Yang Yu
Keyword(s):  
Linear Optimization ◽  
Time Analysis ◽  
Running Time ◽  
Running Time Analysis
Sign in / Sign up

Export Citation Format

Share Document