graph coloring problem

Advancing Branch-and-Price for Graph Coloring: New Pricing Strategies and Benchmark Results

  • Mingming Zheng
  • Roberto Baldacci
  • Fabio Furini
  • Qinghua Wu
    • Categories 0-1 Programming, Combinatorial Optimization, Integer Programming Tags , , ,

    This paper proposes BPCOL+, an exact branch-and-price algorithm for the Graph Coloring Problem. The algorithm is both novel and highly effective, integrating enhanced pricing strategies within Zero-Suppressed Binary Decision Diagrams (ZDDs) to efficiently solve the pricing problem associated with the maximal-stable-set-based set-covering formulation. After computing upper and lower bounds at the root node using heuristic … Read more

    Dealing with inequality constraints in large-scale semidefinite relaxations for graph coloring and maximum clique problems

  • Federico Battista
  • Marianna De Santis
    • Categories Combinatorial Optimization, Convex Optimization, Semi-definite Programming Tags , ,

    Semidefinite programs (SDPs) can be solved in polynomial time by interior point methods. However, when the dimension of the problem gets large, interior point methods become impractical in terms of both computational time and memory requirements. Certain first-order methods, such as Alternating Direction Methods of Multipliers (ADMMs), established as suitable algorithms to deal with large-scale … Read more