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The graph association problem: Mathematical models and a lagrangian heuristic

Authors

  • Gregory Tauer,

    1. Department of Industrial and Systems Engineering, 438 Bell Hall, State University of New York at Buffalo, Buffalo, New York 14260
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  • Rakesh Nagi,

    Corresponding author
    1. Department of Industrial and Systems Engineering, 438 Bell Hall, State University of New York at Buffalo, Buffalo, New York 14260
    • Department of Industrial and Systems Engineering, 438 Bell Hall, State University of New York at Buffalo, Buffalo, New York 14260
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  • Moises Sudit

    1. Department of Industrial and Systems Engineering, 438 Bell Hall, State University of New York at Buffalo, Buffalo, New York 14260
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Abstract

Graph association is the problem of merging many graphs that collectively describe a set of possibly repetitive entities and relationships into a single graph that contains unique entities and relationships. As a form of data association, graph association can be used to identify when two sensors are observing the same object so information from both sensors can be combined and analyzed in a meaningful and consistent way. Graph association between two graphs is related to the problem of graph matching, and between multiple graphs it is related to the common labeling of a graph set (also known as multiple graph matching) problem. This article contribution is to formulate graph association as a binary linear program and introduce a heuristic for solving multiple graph association using a Lagrangian relaxation approach to address issues with between-graph transitivity requirements. The algorithms are tested on a representative dataset. The developed model formulation was found to accurately solve the graph association problem. Furthermore, the Lagrangian heuristic was found to solve the developed model within 3% of optimal on many problem instances, and found better solutions to large problems than is possible by directly using CPLEX. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013

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