On Polynomial Kernels for Traveling Salesperson Problem and its Generalizations
| Autor: | Blažej, Václav, Choudhary, Pratibha, Knop, Dušan, Schierreich, Šimon, Suchý, Ondřej, Valla, Tomáš |
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| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
Subset TSP Discrete Mathematics (cs.DM) Theory of computation → Fixed parameter tractability Theory of computation → Graph algorithms analysis TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY Computer Science - Data Structures and Algorithms FOS: Mathematics Mathematics - Combinatorics Data Structures and Algorithms (cs.DS) Kernelization Combinatorics (math.CO) Traveling Salesperson Waypoint Routing MathematicsofComputing_DISCRETEMATHEMATICS Computer Science - Discrete Mathematics |
| Popis: | For many problems, the important instances from practice possess certain structure that one should reflect in the design of specific algorithms. As data reduction is an important and inextricable part of today’s computation, we employ one of the most successful models of such precomputation - the kernelization. Within this framework, we focus on Traveling Salesperson Problem (TSP) and some of its generalizations. We provide a kernel for TSP with size polynomial in either the feedback edge set number or the size of a modulator to constant-sized components. For its generalizations, we also consider other structural parameters such as the vertex cover number and the size of a modulator to constant-sized paths. We complement our results from the negative side by showing that the existence of a polynomial-sized kernel with respect to the fractioning number, the combined parameter maximum degree and treewidth, and, in the case of {Subset TSP}, modulator to disjoint cycles (i.e., the treewidth two graphs) is unlikely. LIPIcs, Vol. 244, 30th Annual European Symposium on Algorithms (ESA 2022), pages 22:1-22:16 |
| Databáze: | OpenAIRE |
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