An Evolutionary Framework for Analyzing the Distance Preserving Property of Weighted Graphs
A subgraph H of a given graph G is isometric if the distances between every pair of vertices in H are the same as the distances of those vertices in G. We say a graph G is distance preserving if there exists an isometric subgraph of every possible order up to the order of G. Distance preserving prop...
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| Vydané v: | 2017 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM) s. 577 - 584 |
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| Hlavní autori: | , , |
| Médium: | Konferenčný príspevok.. |
| Jazyk: | English |
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New York, NY, USA
ACM
31.07.2017
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| ISBN: | 1450349935, 9781450349932 |
| ISSN: | 2473-991X |
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| Abstract | A subgraph H of a given graph G is isometric if the distances between every pair of vertices in H are the same as the distances of those vertices in G. We say a graph G is distance preserving if there exists an isometric subgraph of every possible order up to the order of G. Distance preserving property has been applied to many real world problems such as route recommendation systems and all kinds of shortest-path-related applications. Here, we propose a biologically-inspired search algorithm to address the problem of finding isometric subgraphs that consequently determines if a given graph is distance preserving. In this algorithm, using a well defined fitness function, selection operator selects almost isometric subgraphs to generate the offspring for the next generation. There is a trade-off between the population size and searching speed. On one hand, the larger the population size is, the slower the search algorithm would be. On the other hand, by increasing the population size, we increase the likelihood of finding an existing isometric subgraph. Experimental results depict the performance of the proposed algorithm in finding isometric subgraphs even for challenging problems, and interestingly by these results one can see that "almost" all graphs are distance preserving. In closing, we show the smallest distance preserving graph whose product factors are not distance preserving. This graph has 80 vertices, and can be used as benchmark for algorithms in this concept. |
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| AbstractList | A subgraph H of a given graph G is isometric if the distances between every pair of vertices in H are the same as the distances of those vertices in G. We say a graph G is distance preserving if there exists an isometric subgraph of every possible order up to the order of G. Distance preserving property has been applied to many real world problems such as route recommendation systems and all kinds of shortest-path-related applications. Here, we propose a biologically-inspired search algorithm to address the problem of finding isometric subgraphs that consequently determines if a given graph is distance preserving. In this algorithm, using a well defined fitness function, selection operator selects almost isometric subgraphs to generate the offspring for the next generation. There is a trade-off between the population size and searching speed. On one hand, the larger the population size is, the slower the search algorithm would be. On the other hand, by increasing the population size, we increase the likelihood of finding an existing isometric subgraph. Experimental results depict the performance of the proposed algorithm in finding isometric subgraphs even for challenging problems, and interestingly by these results one can see that "almost" all graphs are distance preserving. In closing, we show the smallest distance preserving graph whose product factors are not distance preserving. This graph has 80 vertices, and can be used as benchmark for algorithms in this concept. |
| Author | Mirmomeni, Masoud Zahedi, Emad Esfahanian, Abdol-Hossein |
| Author_xml | – sequence: 1 givenname: Emad surname: Zahedi fullname: Zahedi, Emad email: Zahediem@msu.edu organization: Department of Mathematics, Department of Computer Science and Engineering, Michigan State University, East Lansing, MI, U.S.A – sequence: 2 givenname: Masoud surname: Mirmomeni fullname: Mirmomeni, Masoud email: Mirmomen@msu.edu organization: Department of Computer Science and Engineering, Michigan State University, East Lansing, MI, U.S.A – sequence: 3 givenname: Abdol-Hossein surname: Esfahanian fullname: Esfahanian, Abdol-Hossein email: Esfahanian@cse.msu.edu organization: Department of Computer Science and Engineering, Michigan State University, East Lansing, MI, U.S.A |
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| Editor | Diesner, Jana Ferrari, Elena Xu, Guandong |
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| Keywords | selection operator Distance preserving mutation rate evolutionary algorithm isometric subgraphs population size |
| Language | English |
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| Snippet | A subgraph H of a given graph G is isometric if the distances between every pair of vertices in H are the same as the distances of those vertices in G. We say... |
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| SubjectTerms | Computing methodologies Computing methodologies -- Artificial intelligence Computing methodologies -- Artificial intelligence -- Search methodologies Computing methodologies -- Artificial intelligence -- Search methodologies -- Discrete space search Computing methodologies -- Artificial intelligence -- Search methodologies -- Game tree search Computing methodologies -- Artificial intelligence -- Search methodologies -- Heuristic function construction Computing methodologies -- Machine learning Computing methodologies -- Machine learning -- Machine learning approaches Computing methodologies -- Machine learning -- Machine learning approaches -- Bio-inspired approaches Computing methodologies -- Machine learning -- Machine learning approaches -- Bio-inspired approaches -- Genetic algorithms Distance preserving evolutionary algorithm isometric subgraphs Mathematics of computing Mathematics of computing -- Discrete mathematics Mathematics of computing -- Discrete mathematics -- Graph theory Mathematics of computing -- Discrete mathematics -- Graph theory -- Graph algorithms mutation rate population size selection operator Theory of computation |
| Title | An Evolutionary Framework for Analyzing the Distance Preserving Property of Weighted Graphs |
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