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Reoptimization of Path Vertex Cover ProblemOpen Access

Published in Springer Verlag

2019

Volume: 11653 LNCS

Pages: 363 - 374

Most optimization problems are notoriously hard. Considerable efforts must be spent in obtaining an optimal solution to certain instances that we encounter in the real world scenarios. Often it turns out that input instances get modified locally in some small ways due to changes in the application world. The natural question here is, given an optimal solution for an old instance IN, can we construct an optimal solution for the new instance IN, where IN is the instance IO with some local modifications. Reoptimization of NP-hard optimization problem precisely addresses this concern. It turns out that for some reoptimization versions of the NP-hard problems, we may only hope to obtain an approximate solution to a new instance. In this paper, we specifically study the reoptimization of path vertex cover problem. The objective in k-path vertex cover problem is to compute a minimum subset S of the vertices in a graph G such that after removal of S from G there is no path with k vertices in the graph. We show that when a constant number of vertices are inserted, reoptimizing unweighted k-path vertex cover problem admits a PTAS. For weighted 3-path vertex cover problem, we show that when a constant number of vertices are inserted, the reoptimization algorithm achieves an approximation factor of 1.5, hence an improvement from known 2-approximation algorithm for the optimization version. We provide reoptimization algorithm for weighted k-path vertex cover problem (k ≥ 4) on bounded degree graphs, which is also an NP-hard problem. Given a p -approximation algorithm for k-path vertex cover problem on bounded degree graphs, we show that it can be reoptimized within an approximation factor of (2) under constant number of vertex insertions. © Springer Nature Switzerland AG 2019.

Topics: Vertex cover (66)%66% related to the paper, Approximation algorithm (59)%59% related to the paper, Vertex (geometry) (58)%58% related to the paper and Optimization problem (51)%51% related to the paper

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About the journal

Journal | Data powered by TypesetLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Publisher | Data powered by TypesetSpringer Verlag |

ISSN | 03029743 |

Open Access | Yes |

Concepts (13)

- Approximation algorithms
- Computational complexity
- Optimal systems
- Optimization
- Approximate solution
- APPROXIMATION FACTOR
- BOUNDED DEGREE GRAPHS
- Optimization problems
- RE-OPTIMIZATION ALGORITHMS
- REOPTIMIZATION
- Vertex cover
- Vertex cover problems
- Graph theory