TY - GEN
T1 - Algorithmic aspect on the minimum (weighted) doubly resolving set problem of graphs
AU - Lu, Changhong
AU - Ye, Qingjie
AU - Zhu, Chengru
N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2019.
PY - 2019
Y1 - 2019
N2 - Let G be a simple graph, where each vertex has a nonnegative weight. A vertex subset S of G is a doubly resolving set (DRS) of G if for every pair of vertices u, v in G, there exist x, y ∈ S such that d(x, u) − d(x, v) ≠ d(y, u) − d(y, v). The minimum weighted doubly resolving set (MWDRS) problem is finding a doubly resolving set with minimum total weight. We establish a linear time algorithm for the MWDRS problem of all graphs in which each block is complete graph or cycle. Hence, the MWDRS problems for block graphs and cactus graphs can be solved in linear time. We also prove that k-edge-augmented tree (a tree with additional k edges) with minimum degree δ(G) ≥ 2 admits a doubly resolving set of size at most 2k + 1. This implies that the DRS problem on k-edge-augmented tree can be solved in O(n2k+3) time.
AB - Let G be a simple graph, where each vertex has a nonnegative weight. A vertex subset S of G is a doubly resolving set (DRS) of G if for every pair of vertices u, v in G, there exist x, y ∈ S such that d(x, u) − d(x, v) ≠ d(y, u) − d(y, v). The minimum weighted doubly resolving set (MWDRS) problem is finding a doubly resolving set with minimum total weight. We establish a linear time algorithm for the MWDRS problem of all graphs in which each block is complete graph or cycle. Hence, the MWDRS problems for block graphs and cactus graphs can be solved in linear time. We also prove that k-edge-augmented tree (a tree with additional k edges) with minimum degree δ(G) ≥ 2 admits a doubly resolving set of size at most 2k + 1. This implies that the DRS problem on k-edge-augmented tree can be solved in O(n2k+3) time.
KW - Block graph
KW - Cactus graph
KW - Doubly resolving set
KW - k-edge-augmented trees
UR - https://www.scopus.com/pages/publications/85070624313
U2 - 10.1007/978-3-030-27195-4_20
DO - 10.1007/978-3-030-27195-4_20
M3 - 会议稿件
AN - SCOPUS:85070624313
SN - 9783030271947
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 212
EP - 222
BT - Algorithmic Aspects in Information and Management - 13th International Conference, AAIM 2019, Proceedings
A2 - Du, Ding-Zhu
A2 - Li, Lian
A2 - Sun, Xiaoming
A2 - Zhang, Jialin
PB - Springer Verlag
T2 - 13th International Conference on Algorithmic Aspects in Information and Management, AAIM 2019
Y2 - 6 August 2019 through 8 August 2019
ER -