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The graph association problem: Mathematical models and a lagrangian heuristic

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  • Gregory Tauer
  • Rakesh Nagi
  • Moises Sudit

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

Suggested Citation

  • Gregory Tauer & Rakesh Nagi & Moises Sudit, 2013. "The graph association problem: Mathematical models and a lagrangian heuristic," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(3), pages 251-268, April.
    • Handle: RePEc:wly:navres:v:60:y:2013:i:3:p:251-268
    DOI: 10.1002/nav.21532
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