A primal-dual approximation algorithm for the k-prize-collecting minimum vertex cover problem with submodular penalties

In this paper, we consider the k -prize-collecting minimum vertex cover problem with submodular penalties, which generalizes the well-known minimum vertex cover problem, minimum partial vertex cover problem and minimum vertex cover problem with submodular penalties. We are given a cost graph G = ( V...

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Bibliographic Details
Published in:Frontiers of Computer Science Vol. 17; no. 3; p. 173404
Main Authors: LIU, Xiaofei, LI, Weidong, YANG, Jinhua
Format: Journal Article
Language:English
Published: Beijing Higher Education Press 01.06.2023
Springer Nature B.V
Subjects:
Algorithms
Apexes
Approximation
approximation algorithm
Combinatorial analysis
Computer Science
Cost function
Graph theory
k-prize-collecting
Mathematical analysis
primal-dual
Research Article
vertex cover
Vertex sets
approximation algorithm
vertex cover
prize-collecting
primal-dual
ISSN:2095-2228, 2095-2236
Online Access:Get full text
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Summary:In this paper, we consider the k -prize-collecting minimum vertex cover problem with submodular penalties, which generalizes the well-known minimum vertex cover problem, minimum partial vertex cover problem and minimum vertex cover problem with submodular penalties. We are given a cost graph G = ( V , E ; c ) and an integer k . This problem determines a vertex set S ⊆ V such that S covers at least k edges. The objective is to minimize the total cost of the vertices in S plus the penalty of the uncovered edge set, where the penalty is determined by a submodular function. We design a two-phase combinatorial algorithm based on the guessing technique and the primal-dual framework to address the problem. When the submodular penalty cost function is normalized and nondecreasing, the proposed algorithm has an approximation factor of 3 . When the submodular penalty cost function is linear, the approximation factor of the proposed algorithm is reduced to 2 , which is the best factor if the unique game conjecture holds.
Bibliography:approximation algorithm
k-prize-collecting
Document accepted on :2022-04-15
vertex cover
Document received on :2021-11-23
primal-dual
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2095-2228
2095-2236
DOI:10.1007/s11704-022-1665-9