Fixed-Parameter Tractability of the (1 + 1) Evolutionary Algorithm on Random Planted Vertex Covers
Pages 96 - 104
Abstract
We present the first parameterized analysis of a standard (1+1) Evolutionary Algorithm on a distribution of vertex cover problems. We show that if the planted cover is at most logarithmic, restarting the (1+1) EA every O(n log n) steps will find a cover at least as small as the planted cover in polynomial time for sufficiently dense random graphs p > 0.71. For superlogarithmic planted covers, we prove that the (1+1) EA finds a solution in fixed-parameter tractable time in expectation.
We complement these theoretical investigations with a number of computational experiments that highlight the interplay between planted cover size, graph density and runtime.
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Index Terms
- Fixed-Parameter Tractability of the (1 + 1) Evolutionary Algorithm on Random Planted Vertex Covers
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August 2023
169 pages
ISBN:9798400702020
DOI:10.1145/3594805
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Published: 30 August 2023
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