Search-Space Reduction via Essential Vertices
| Autor: | Bumpus, Benjamin Merlin, Jansen, Bart M. P., de Kroon, Jari J. H. |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
Computational Complexity (cs.CC) 68W99 Theory of computation → Packing and covering problems essential vertices Theory of computation → Fixed parameter tractability Computer Science - Computational Complexity Theory of computation → Graph algorithms analysis fixed-parameter tractability TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY Computer Science - Data Structures and Algorithms Theory of computation → Linear programming Data Structures and Algorithms (cs.DS) covering versus packing F.2.0 MathematicsofComputing_DISCRETEMATHEMATICS |
| Popis: | We investigate preprocessing for vertex-subset problems on graphs. While the notion of kernelization, originating in parameterized complexity theory, is a formalization of provably effective preprocessing aimed at reducing the total instance size, our focus is on finding a non-empty vertex set that belongs to an optimal solution. This decreases the size of the remaining part of the solution which still has to be found, and therefore shrinks the search space of fixed-parameter tractable algorithms for parameterizations based on the solution size. We introduce the notion of a c-essential vertex as one that is contained in all c-approximate solutions. For several classic combinatorial problems such as Odd Cycle Transversal and Directed Feedback Vertex Set, we show that under mild conditions a polynomial-time preprocessing algorithm can find a subset of an optimal solution that contains all 2-essential vertices, by exploiting packing/covering duality. This leads to FPT algorithms to solve these problems where the exponential term in the running time depends only on the number of non-essential vertices in the solution. LIPIcs, Vol. 244, 30th Annual European Symposium on Algorithms (ESA 2022), pages 30:1-30:15 |
| Databáze: | OpenAIRE |
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