A fast approximation algorithm for the maximum 2-packing set problem on planar graphs

被引:0
|
作者
Trejo-Sanchez, Joel Antonio [1 ]
Madera-Ramirez, Francisco A. [2 ]
Alberto Fernandez-Zepeda, Jose [3 ]
Luis Lopez-Martinez, Jose [2 ]
Flores-Lamas, Alejandro [4 ]
机构
[1] CONACYT Ctr Res Math, Dept Comp Sci, Merida, Yucatan, Mexico
[2] Univ Autonoma Yucatan, Dept Comp Sci, Merida, Yucatan, Mexico
[3] Ctr Sci Res & Higher Educ Ensenada CICESE, Dept Comp Sci, Ensenada, Baja California, Mexico
[4] Royal Holloway Univ London, Dept Comp Sci, Egham Hill, Egham, Surrey, England
基金
英国工程与自然科学研究理事会; 芬兰科学院;
关键词
Approximation algorithms; Maximum 2-packing set; Linear programming; Planar graphs; SELF-STABILIZING ALGORITHM; DISTRIBUTED ALGORITHM; INDEPENDENT SETS; DOMINATION;
D O I
10.1007/s11590-022-01939-w
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
Given an undirected graph G = (V, E), a subset S subset of V is a 2-packing set if, for any pair of vertices u, v is an element of S, the shortest path between them is at least three-edge long. Finding a 2-packing set of maximum cardinality is an NP-hard problem for arbitrary graphs. This paper proposes an approximation algorithm for the maximum 2-packing set problem for planar graphs. We show that our algorithm is at least lambda-2/lambda of the optimal (i.e. the approximation ratio is lambda/lambda-2), where lambda is a constant related to how the proposed algorithm decomposes the input graph into smaller subgraphs. Then, we improve the solution given by our approximation algorithm by adding some vertices to the solution. Experimentally, we show that our improved algorithm computes a near-optimal 2-packing set. This algorithm is the first approximation algorithm for the maximum 2-packing set to the best of our knowledge.
引用
收藏
页码:1435 / 1454
页数:20
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