
More Effective Randomized Search Heuristics for Graph Coloring Through Dynamic Optimization
Dynamic optimization problems have gained significant attention in evolu...
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Dynamic coloring for Bipartite and General Graphs
We consider the dynamic coloring problem on bipartite and general graphs...
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Coloring in Graph Streams
In this paper, we initiate the study of the vertex coloring problem of a...
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Collecting Coupons with Random Initial Stake
Motivated by a problem in the theory of randomized search heuristics, we...
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Locality of notsoweak coloring
Many graph problems are locally checkable: a solution is globally feasib...
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Runtime Performances of Randomized Search Heuristics for the Dynamic Weighted Vertex Cover Problem
Randomized search heuristics such as evolutionary algorithms are frequen...
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Intuitive Analyses via Drift Theory
Humans are bad with probabilities, and the analysis of randomized algori...
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Time Complexity Analysis of Randomized Search Heuristics for the Dynamic Graph Coloring Problem
We contribute to the theoretical understanding of randomized search heuristics for dynamic problems. We consider the classical vertex coloring problem on graphs and investigate the dynamic setting where edges are added to the current graph. We then analyze the expected time for randomized search heuristics to recompute high quality solutions. The (1+1) Evolutionary Algorithm and RLS operate in a setting where the number of colors is bounded and we are minimizing the number of conflicts. Iterated local search algorithms use an unbounded color palette and aim to use the smallest colors and, consequently, the smallest number of colors. We identify classes of bipartite graphs where reoptimization is as hard as or even harder than optimization from scratch, i.e., starting with a random initialization. Even adding a single edge can lead to hard symmetry problems. However, graph classes that are hard for one algorithm turn out to be easy for others. In most cases our bounds show that reoptimization is faster than optimizing from scratch. We further show that tailoring mutation operators to parts of the graph where changes have occurred can significantly reduce the expected reoptimization time. In most settings the expected reoptimization time for such tailored algorithms is linear in the number of added edges. However, tailored algorithms cannot prevent exponential times in settings where the original algorithm is inefficient.
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