scholarly journals Efficient Local Search based on Dynamic Connectivity Maintenance for Minimum Connected Dominating Set

2021 ◽  
Vol 71 ◽  
pp. 89-119
Author(s):  
Xindi Zhang ◽  
Bohan Li ◽  
Shaowei Cai ◽  
Yiyuan Wang
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Dominating Set ◽  
Practical Importance ◽  
Scoring Function ◽  
Connected Dominating Set ◽  
Minimum Connected Dominating Set ◽  
Important Extension ◽  
Connectivity Maintenance ◽  
Dynamic Connectivity

The minimum connected dominating set (MCDS) problem is an important extension of the minimum dominating set problem, with wide applications, especially in wireless networks. Most previous works focused on solving MCDS problem in graphs with relatively small size, mainly due to the complexity of maintaining connectivity. This paper explores techniques for solving MCDS problem in massive real-world graphs with wide practical importance. Firstly, we propose a local greedy construction method with reasoning rule called 1hopReason. Secondly and most importantly, a hybrid dynamic connectivity maintenance method (HDC+) is designed to switch alternately between a novel fast connectivity maintenance method based on spanning tree and its previous counterpart. Thirdly, we adopt a two-level vertex selection heuristic with a newly proposed scoring function called chronosafety to make the algorithm more considerate when selecting vertices. We design a new local search algorithm called FastCDS based on the three ideas. Experiments show that FastCDS significantly outperforms five state-of-the-art MCDS algorithms on both massive graphs and classic benchmarks.

scholarly journals NuCDS: An Efficient Local Search Algorithm for Minimum Connected Dominating Set

2020 ◽  
Author(s):  
Bohan Li ◽  
Xindi Zhang ◽  
Shaowei Cai ◽  
Jinkun Lin ◽  
Yiyuan Wang ◽  
...  
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Dominating Set ◽  
Practical Importance ◽  
Connected Dominating Set ◽  
Local Search Algorithm ◽  
Massive Graphs ◽  
Minimum Connected Dominating Set ◽  
Important Extension ◽  
Connectivity Maintenance

The minimum connected dominating set (MCDS) problem is an important extension of the minimum dominating set problem, with wide applications, especially in wireless networks. Despite its practical importance, there are few works on solving MCDS for massive graphs, mainly due to the complexity of maintaining connectivity. In this paper, we propose two novel ideas, and develop a new local search algorithm for MCDS called NuCDS. First, a hybrid dynamic connectivity maintenance method is designed to switch alternately between a novel fast connectivity maintenance method based on spanning tree and its previous counterpart. Second, we define a new vertex property called \emph{safety} to make the algorithm more considerate when selecting vertices. Experiments show that NuCDS significantly outperforms the state-of-the-art MCDS algorithms on both massive graphs and classic benchmarks.

scholarly journals Multi-Start Local Search Algorithm for the Minimum Connected Dominating Set Problems

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1173 ◽  
Author(s):  
Ruizhi Li ◽  
Shuli Hu ◽  
Huan Liu ◽  
Ruiting Li ◽  
Dantong Ouyang ◽  
...  
Keyword(s):  
Local Search ◽  
Ad Hoc ◽  
Search Algorithm ◽  
Dominating Set ◽  
Connected Dominating Set ◽  
Local Optimum ◽  
Local Search Algorithm ◽  
Solution Quality ◽  
Minimum Connected Dominating Set ◽  
Hoc Networks

The minimum connected dominating set (MCDS) problem is a very significant NP-hard combinatorial optimization problem, and it has been used in many fields such as wireless sensor networks and ad hoc networks. In this paper, we propose a novel multi-start local search algorithm (MSLS) to tackle the minimum connected dominating set problem. Firstly, we present the fitness mechanism to design the vertex score mechanism so that our algorithm can jump out of the local optimum. Secondly, we use the configuration checking (CC) mechanism to avoid the cycling problem. Then, we propose the vertex flipping mechanism to change the vertex state by combing the CC mechanism with the vertex score mechanism. Finally, we propose a multi-start local search framework based on these mechanisms. We compare the algorithm MSLS with other compared algorithms on extensive instances. The results of experiment show that MSLS is superior to other algorithms in solution quality and time efficiency on most instances.

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

2017 ◽  
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.

scholarly journals Local Search for Minimum Weight Dominating Set with Two-Level Configuration Checking and Frequency Based Scoring Function

2017 ◽  
Vol 58 ◽  
pp. 267-295 ◽  
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.

A Fast Vertex Weighting-Based Local Search for Finding Minimum Connected Dominating Sets

2021 ◽  
Author(s):  
Xinyun Wu ◽  
Zhipeng Lü ◽  
Fred Glover
Keyword(s):  
Local Search ◽  
Dominating Set ◽  
Connected Dominating Set ◽  
Computational Experiments ◽  
Hard Problem ◽  
Np Hard ◽  
Dominating Sets ◽  
Minimum Connected Dominating Set ◽  
Benchmark Instances ◽  
Np Hard Problem

The minimum connected dominating set (MCDS) problem consists of selecting a minimum set of vertices from an undirected graph, such that each vertex not in this set is adjacent to at least one of the vertices in it, and the subgraph induced by this vertex set is connected. This paper presents a fast vertex weighting (FVW) algorithm for solving the MCDS problem, which integrates several distinguishing features, such as a vertex weighting-based local search with tabu and perturbation strategies to help the search to jump out of the local optima, as well as a search space reduction strategy to improve the search efficiency. Computational experiments on four sets of 112 commonly used public benchmark instances, as well as 15 newly introduced sparse instances, show that FVW is highly competitive compared with the state-of-the-art algorithms in the literature despite its simplicity. FVW improves the previous best-known results for 20 large public benchmark instances while matching the best-known results for all but 2 of the remaining ones. Several ingredients of FVW are investigated to demonstrate the importance of the proposed ideas and techniques. Summary of Contribution: As a challenging classical NP-hard problem, the minimum connected dominating set (MCDS) problem has been studied for decades in the areas of both operations research and computer science, although there does not exist an exact polynomial algorithm for solving it. Thus, the new breakthrough on this classical NP-hard problem in terms of the computational results on classical benchmark instances is significant. This paper presents a new fast vertex weighting local search for solving the MCDS problem. Computational experiments on four sets of 112 commonly used public benchmark instances show that fast vertex weighting (FVW) is able to improve the previous best-known results for 20 large instances while matching the best-known results for all but 2 of the remaining instances. Several ingredients of FVW are also investigated to demonstrate the importance of the proposed ideas and techniques.

A Binary Search Algorithm to Determine the Minimum Transmission Range for Minimum Connected Dominating Set of a Threshold Size in Ad Hoc Networks

2020 ◽  
Vol 9 (2) ◽  
pp. 1-16
Author(s):  
Natarajan Meghanathan
Keyword(s):  
Ad Hoc ◽  
Search Algorithm ◽  
Dominating Set ◽  
Binary Search ◽  
Connected Dominating Set ◽  
Point Of View ◽  
Transmission Range ◽  
Threshold Size ◽  
Minimum Connected Dominating Set ◽  
Binary Search Algorithm

The set of nodes constituting a minimum connected dominating set (MCDS) in a wireless ad hoc network (WANET) could be considered as the minimum number of nodes that are required to forward a broadcast message so that the message reaches all the nodes in the network. With regards to MCDS construction, we notice that smaller the transmission range for the nodes, the larger the size of the MCDS and vice-versa. Hence, from an energy efficiency point of view, it is imperative to determine the minimum transmission range (we assume uniform transmission range for all the nodes) that would be needed to construct a MCDS of a certain threshold size in WANETs. In this pursuit, we propose a binary search algorithm of logarithmic time complexity to determine the minimum uniform transmission range that would be sufficient to obtain a connected network and construct a MCDS whose size is within a threshold.

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