On the consistent path problem

Leonardo Lozano, David Bergman, J. Cole Smith

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


The application of decision diagrams in combinatorial optimization has proliferated in the last decade. In recent years, authors have begun to investigate how to use not one, but a set of diagrams, to model constraints and objective function terms. Optimizing over a collection of decision diagrams, the problem we refer to as the consistent path problem (CPP) can be addressed by associating a network-flow model with each decision diagram, jointly linked through channeling constraints. A direct application of integer programming to the ensuing model has already been shown to result in algorithms that provide orders-of-magnitude performance gains over classical methods. Lacking, however, is a careful study of dedicated solution methods designed to solve the CPP. This paper provides a detailed study of the CPP, including a discussion on complexity results and a complete polyhedral analysis. We propose a cut-generation algorithm, which, under a structured ordering property, finds a cut, if one exists, through an application of the classical maximum flow problem, albeit in an exponentially sized network. We use this procedure to fuel a cutting-plane algorithm that is applied to unconstrained binary cubic optimization and a variant of the market split problem, resulting in an algorithm that compares favorably with CPLEX, using standard integer programming formulations for both problems.

Original languageEnglish (US)
Pages (from-to)1913-1931
Number of pages19
JournalOperations Research
Issue number6
StatePublished - Nov 2020


  • Algorithms
  • Networks/graphs: flow algorithms
  • Networks/graphs: generalized networks
  • Programming: integer

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research


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