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A parameterized runtime analysis of randomized local search and evolutionary algorithm for max l-uncut

Published: 06 July 2018 Publication History

Abstract

In the last few years, parameterized complexity has emerged as a new tool to analyze the running time of randomized local search algorithm. However, such analysis are few and far between. In this paper, we do a parameterized running time analysis of a randomized local search algorithm and a (1 + 1) EA for a classical graph partitioning problem, namely, Max l-Uncut, and its balanced counterpart Max Balanced l-Uncut. In Max l-Uncut, given an undirected graph G = (V, E), the objective is to find a partition of V(G) into l parts such that the number of uncut edges - edges within the parts - is maximized. In the last few years, Max l-Uncut and Max Balanced l-Uncut are studied extensively from the approximation point of view. In this paper, we analyze the parameterized running time of a randomized local search algorithm (RLS) for Max Balanced l-Uncut where the parameter is the number of uncut edges. RLS generates a solution of specific fitness in polynomial time for this problem. Furthermore, we design a fixed parameter tractable randomized local search and a (1 + 1) EA for Max l-Uncut and prove that they perform equally well.

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References

[1]
M. R. Garey and David S. Johnson. 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman.
[2]
Olivier Goldschmidt and Dorit S. Hochbaum. 1988. Polynomial Algorithm for the k-Cut Problem. In 29th Annual Symposium on Foundations of Computer Science, White Plains, New York, USA, 24--26 October 1988. 444--451.
[3]
Lov K Grover. 1992. Local search and the local structure of NP-complete problems. Operations Research Letters 12, 4 (1992), 235--243.
[4]
Stefan Kratsch, Per Kristian Lehre, Frank Neumann, and Pietro Simone Oliveto. 2010. Fixed Parameter Evolutionary Algorithms and Maximum Leaf Spanning Trees: A Matter of Mutation. In Parallel Problem Solving from Nature - PPSN XI, 11th International Conference, Kraków, Poland, September 11--15, 2010, Proceedings, Part I. 204--213.
[5]
Stefan Kratsch and Frank Neumann. 2013. Fixed-Parameter Evolutionary Algorithms and the Vertex Cover Problem. Algorithmica 65, 4 (2013), 754--771.
[6]
Frank Neumann and Carsten Witt. 2015. On the Runtime of Randomized Local Search and Simple Evolutionary Algorithms for Dynamic Makespan Scheduling. In Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, July 25--31, 2015. 3742--3748.
[7]
Mojgan Pourhassan, Feng Shi, and Frank Neumann. 2016. Parameterized Analysis of Multi-objective Evolutionary Algorithms and the Weighted Vertex Cover Problem. In Parallel Problem Solving from Nature - PPSN XIV - 14th International Conference, Edinburgh, UK, September 17--21, 2016, Proceedings. 729--739.
[8]
Andrew M. Sutton, Frank Neumann, and Samadhi Nallaperuma. 2014. Parameterized Runtime Analyses of Evolutionary Algorithms for the Planar Euclidean Traveling Salesperson Problem. Evolutionary Computation 22, 4 (2014), 595--628.
[9]
Chenchen Wu, Dachuan Xu, Donglei Du, and Wenqing Xu. 2016. An approximation algorithm for the balanced Max-3-Uncut problem using complex semidefinite programming rounding. Journal of Combinatorial Optimization 32, 4 (2016), 1017--1035.
[10]
Yinyu Ye and jiawei Zhang. 2003. Approximation of dense-n/2-subgraph and the complement of min-bisection. Journal of Global Optimization 25, 1 (2003), 55--73.
[11]
Peng Zhang, Chenchen Wu, Dachuan Xu, and Xinghe Zhang. 2016. Approximation and Hardness Results for the Max k-Uncut Problem. In Combinatorial Optimization and Applications - 10th International Conference, COCOA 2016, Hong Kong, China, December 16--18, 2016, Proceedings. 49--61.

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    cover image ACM Conferences
    GECCO '18: Proceedings of the Genetic and Evolutionary Computation Conference Companion
    July 2018
    1968 pages
    ISBN:9781450357647
    DOI:10.1145/3205651
    Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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    Publication History

    Published: 06 July 2018

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    Author Tags

    1. (1 + 1) EA
    2. max l-Uncut
    3. max balanced l-Uncut
    4. randomized local search
    5. running time analysis

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