An Improved Approximation Bound for Minimum Weight Dominating Set on Graphs of Bounded Arboricity

We consider problems on intervals which can be solved by dynamic programming. Specifically, we give an efficient implementation of dynamic programming on intervals. As an application, an optimal sequential partition of a graph G=(V, E) can be obtained in O(m log n) time, where n=|V| and m=|E|. We also present an O(n log n) time algorithm for finding a minimum weight dominating set of an interval graph G=(V, E), and an O(m log n) time algorithm for finding a maximum weight clique of a circular-arc graph G=(V, E), provided their intersection models of n intervals (arcs) are given.

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Local Search for Minimum Weight Dominating Set with Two-Level Configuration Checking and Frequency Based Scoring Function (Extended Abstract)

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2017/728 ◽

2017 ◽

Cited By ~ 2

Author(s):

Yiyuan Wang ◽

Shaowei Cai ◽

Minghao Yin

Keyword(s):

Local Search ◽

Search Algorithm ◽

Dominating Set ◽

Minimum Weight ◽

Scoring Function ◽

Solution Quality ◽

Configuration Checking ◽

New Variant ◽

New Ideas ◽

Better Than

The Minimum Weight Dominating Set (MWDS) problem is an important generalization of the Minimum Dominating Set (MDS) problem with extensive applications. This paper proposes a new local search algorithm for the MWDS problem, which is based on two new ideas. The first idea is a heuristic called two-level configuration checking (CC2), which is a new variant of a recent powerful configuration checking strategy (CC) for effectively avoiding the recent search paths. The second idea is a novel scoring function based on the frequency of being uncovered of vertices. Our algorithm is called CC2FS, according to the names of the two ideas. The experimental results show that, CC2FS performs much better than some state-of-the-art algorithms in terms of solution quality on a broad range of MWDS benchmarks.

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Improved Memetic Algorithm for Solving the Minimum Weight Vertex Independent Dominating Set

Mathematics ◽

10.3390/math8071155 ◽

2020 ◽

Vol 8 (7) ◽

pp. 1155 ◽

Cited By ~ 1

Author(s):

Yupeng Zhou ◽

Jinshu Li ◽

Yang Liu ◽

Shuai Lv ◽

Yong Lai ◽

...

Keyword(s):

Dynamic Optimization ◽

Memetic Algorithm ◽

State Of The Art ◽

Dominating Set ◽

Minimum Weight ◽

High Quality ◽

Local Optima ◽

Configuration Checking ◽

Improved Memetic Algorithm ◽

Independent Dominating Set

The minimum weight vertex independent dominating set (MWVIDS) problem is an important version of the minimum independent dominating set. The MWVIDS problem has a number of applications in many fields. However, the MWVIDS problem is known to be NP-hard and thus computationally challenging. In this work, we present the improved memetic algorithm called MSSAS for solving the MWVIDS problem. The proposed MSSAS algorithm combines probability-based dynamic optimization (PDO) (to generate good and diverse offspring solutions by assembling elements of existing good solutions) as well as a local search phase named C_LS (to seek high-quality local optima by combining the idea of constrained-based two-level configuration checking strategy and tabu mechanism). The extensive results on popular DIMACS and BHOLIB benchmarks demonstrate that MSSAS competes favorably with the state-of-the-art algorithms. In addition, we analyze the benefits of the newly raised components including two above proposed ideas with our memetic framework. It is worth mentioning that the combination of both components has excellent effects for the MWVIDS problem.

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