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Covering of Graphs of Bounded Cycolomatic Number with Preselected Paths

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  • Christoph Geis

    (Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau)

  • Sven O. Krumke

    (Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau)

Abstract

We consider a special case of the set cover problem which we call the Preselected Path Multi-Cover problem. Given a graph G with demands on the vertices as well as a family of paths on G with capacities and cost, our goal is to find a minimum-cost multisubset of these paths that cover the demands of all vertices. This problem has applications for example in software testing, where graphs of bounded cyclomatic number appear in a natural way in order to bound the software module complexity. We give a 3-approximation for this problem restricted to graphs with minimum-degree at least 2 and bounded cyclomatic number, and a 5-approximation for graphs with bounded cyclomatic number (with no restriction on the minimum degree).

Suggested Citation

  • Christoph Geis & Sven O. Krumke, 2025. "Covering of Graphs of Bounded Cycolomatic Number with Preselected Paths," Lecture Notes in Operations Research,, Springer.
    • Handle: RePEc:spr:lnopch:978-3-031-92575-7_25
    DOI: 10.1007/978-3-031-92575-7_25
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