Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Capacitated vertex covering with applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
A Hybrid Genetic Algorithm for the Maximum Clique Problem
Proceedings of the 6th International Conference on Genetic Algorithms
Evolutionary Algorithms and the Maximum Matching Problem
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Evolutionary Algorithms for Vertex Cover
EP '98 Proceedings of the 7th International Conference on Evolutionary Programming VII
Representations for Genetic and Evolutionary Algorithms
Representations for Genetic and Evolutionary Algorithms
Adjacency list matchings: an ideal genotype for cycle covers
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Speeding up evolutionary algorithms through asymmetric mutation operators
Evolutionary Computation
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Expected runtimes of evolutionary algorithms for the Eulerian cycle problem
Computers and Operations Research
Comparing global and local mutations on bit strings
Proceedings of the 10th annual conference on Genetic and evolutionary computation
A better approximation ratio for the vertex cover problem
ACM Transactions on Algorithms (TALG)
Analysis of diversity-preserving mechanisms for global exploration*
Evolutionary Computation
Analysis of the (1 + 1)-EA for finding approximate solutions to vertex cover problems
IEEE Transactions on Evolutionary Computation
Edge-based representation beats vertex-based representation in shortest path problems
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Inapproximability of hypergraph vertex cover and applications to scheduling problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Bioinspired Computation in Combinatorial Optimization: Algorithms and Their Computational Complexity
Bioinspired Computation in Combinatorial Optimization: Algorithms and Their Computational Complexity
Approximating covering problems by randomized search heuristics using multi-objective models*
Evolutionary Computation
On the analysis of the immune-inspired B-cell algorithm for the vertex cover problem
ICARIS'11 Proceedings of the 10th international conference on Artificial immune systems
Evolutionary algorithms and dynamic programming
Theoretical Computer Science
Worst-case and average-case approximations by simple randomized search heuristics
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Analysis of an iterated local search algorithm for vertex cover in sparse random graphs
Theoretical Computer Science
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In the literature only lower bounds are available on the approximation ratio of randomised search heuristics for vertex cover in the single-objective problem setting. These analyses are based on the natural vertex-based representation. Inspired by a well-known problem-specific approximation algorithm, we present an analysis of randomised search heuristics using edge-based representations. For the canonical objective function we prove that the performance can still be arbitrarily bad for the (1+1) EA and also RLS, even when using large search neighbourhoods. Adding slightly more information to the objective function turns RLS and the (1+1) EA into efficient 2-approximation algorithms requiring O(m log m) steps where m is the number of edges. Although equivalent in the worst case, such an upper bound on the runtime is at least a linear factor better than that of the multi-objective case for sparse graphs and for graphs with large optimal vertex covers. Furthermore RLS algorithms, that after an improvement do not flip tested bits before trying previously untested ones, guarantee 2-approximations in O(m) steps.