Abstract
In this paper we propose a new problem of finding the maximal bi-connected partitioning of a graph with a size constraint (MBCPG-SC). With the goal of finding approximate solutions for the MBCPG-SC, a heuristic method is developed based on the open ear decomposition of graphs. Its essential part is an adaptation of the breadth first search which makes it possible to grow bi-connected subgraphs. The proposed randomized algorithm consists of growing several subgraphs in parallel. The quality of solutions generated in this way is further improved using a local search which exploits neighboring relations between the subgraphs. In order to evaluate the performance of the method, an algorithm for generating pseudo-random unit disc graphs with known optimal solutions is created. Computational experiments have also been conducted on graphs representing electrical distribution systems for the real-world problem of dividing them into a system of fault tolerant interconnected microgrids. The experiments show that the proposed method frequently manages to find optimal solutions and has an average error of only a few percent to known optimal solutions. Further, it manages to find high quality approximate solutions for graphs having up to 10,000 nodes in reasonable time.
| Original language | English |
|---|---|
| Pages (from-to) | 1-26 |
| Number of pages | 26 |
| Journal | Journal of Heuristics |
| Volume | 23 |
| Issue number | 2-3 |
| DOIs | |
| Publication status | Published - 1 Jun 2017 |
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Keywords
- 2-Connected
- Bi-connected graphs
- Breadth first search
- Graph partitioning
- Growth algorithm
- Heuristic
ASJC Scopus subject areas
- Software
- Information Systems
- Computer Networks and Communications
- Control and Optimization
- Management Science and Operations Research
- Artificial Intelligence
Cite this
A heuristic approach for dividing graphs into bi-connected components with a size constraint. / Jovanovic, Raka; Nishi, Tatsushi; Voß, Stefan.
In: Journal of Heuristics, Vol. 23, No. 2-3, 01.06.2017, p. 1-26.Research output: Contribution to journal › Article
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TY - JOUR
T1 - A heuristic approach for dividing graphs into bi-connected components with a size constraint
AU - Jovanovic, Raka
AU - Nishi, Tatsushi
AU - Voß, Stefan
PY - 2017/6/1
Y1 - 2017/6/1
N2 - In this paper we propose a new problem of finding the maximal bi-connected partitioning of a graph with a size constraint (MBCPG-SC). With the goal of finding approximate solutions for the MBCPG-SC, a heuristic method is developed based on the open ear decomposition of graphs. Its essential part is an adaptation of the breadth first search which makes it possible to grow bi-connected subgraphs. The proposed randomized algorithm consists of growing several subgraphs in parallel. The quality of solutions generated in this way is further improved using a local search which exploits neighboring relations between the subgraphs. In order to evaluate the performance of the method, an algorithm for generating pseudo-random unit disc graphs with known optimal solutions is created. Computational experiments have also been conducted on graphs representing electrical distribution systems for the real-world problem of dividing them into a system of fault tolerant interconnected microgrids. The experiments show that the proposed method frequently manages to find optimal solutions and has an average error of only a few percent to known optimal solutions. Further, it manages to find high quality approximate solutions for graphs having up to 10,000 nodes in reasonable time.
AB - In this paper we propose a new problem of finding the maximal bi-connected partitioning of a graph with a size constraint (MBCPG-SC). With the goal of finding approximate solutions for the MBCPG-SC, a heuristic method is developed based on the open ear decomposition of graphs. Its essential part is an adaptation of the breadth first search which makes it possible to grow bi-connected subgraphs. The proposed randomized algorithm consists of growing several subgraphs in parallel. The quality of solutions generated in this way is further improved using a local search which exploits neighboring relations between the subgraphs. In order to evaluate the performance of the method, an algorithm for generating pseudo-random unit disc graphs with known optimal solutions is created. Computational experiments have also been conducted on graphs representing electrical distribution systems for the real-world problem of dividing them into a system of fault tolerant interconnected microgrids. The experiments show that the proposed method frequently manages to find optimal solutions and has an average error of only a few percent to known optimal solutions. Further, it manages to find high quality approximate solutions for graphs having up to 10,000 nodes in reasonable time.
KW - 2-Connected
KW - Bi-connected graphs
KW - Breadth first search
KW - Graph partitioning
KW - Growth algorithm
KW - Heuristic
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U2 - 10.1007/s10732-017-9331-3
DO - 10.1007/s10732-017-9331-3
M3 - Article
VL - 23
SP - 1
EP - 26
JO - Journal of Heuristics
JF - Journal of Heuristics
SN - 1381-1231
IS - 2-3
ER -