Development of effective algorithm to find an optimal solution to the problem on graph matching with "disappearing" arcs
DOI:
https://doi.org/10.15587/1729-4061.2017.92226Keywords:
problem on graph matching, NP-completeness, bipartite graph, optimum algorithm, branch and bound method, the brute force methodAbstract
We performed modification of the problem on graph matching with disappearing arcs for making up a schedule at the assigned constraints. It is proven that the problem "On graph matching with disappearing arcs" is NP–complete in the strong sense.
The algorithm is developed for solving the problem about making up a schedule for taking the procedures by patients in a sanatorium. The algorithm is based on the branch and bound method and makes it possible to consider the limitations in compatibility of therapeutic procedures. The algorithm devised has a lower computational complexity in comparison with the brute force method due to the analysis of upper and lower estimates and selection of active apex for branching, which results in the reduction in the number of graph matchings, which will be analyzed.
We carried out a computational experiment, which established that the proposed optimum algorithm provides for a decrease in the time for making up a schedule by 6 to 8.87 times in comparison with the brute force method, and the time of making up a schedule directly proportionally depends on the number of apexes of the bipartite graph.
The method proposed might be used for the development and implementation of systems for calendar scheduling and operational management in the therapeutic process and when designing control systems for flexible automated systems at the enterprises with discrete character of production.
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Copyright (c) 2017 Anna Danylchenko, Vladimir Skachkov, Anatoly Panishev
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