Integer linear programming formulations for double roman domination problem

Qingqiong Cai, Neng Fan, Yongtang Shi, Shunyu Yao

Research output: Contribution to journalArticlepeer-review


For a graph G = (V, E), a double Roman dominating function (DRDF) is a function f: V → {0, 1, 2, 3} having the property that if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor u with f(u) = 3, and if f(v) = 1, then vertex v must have at least one neighbor u with f(u) ≥ 2. In this paper, we consider the double Roman domination problem (DRDP), which is an optimization problem of finding the DRDF f such that PvV f(v) is minimum. We propose several integer linear programming (ILP) formulations with a polynomial number of constraints for this combinatorial optimization problem, and present computational results for graphs of different types and sizes. Further, we prove that some of our ILP formulations are equivalent to the others regardless of the variables relaxation or usage of less number of constraints and variables. Additionally, we use one ILP formulation to give an H(2(∆ + 1))-approximation algorithm and provide an in approximability result for this problem. All proposed ILP formulations and approximation algorithm are evaluated on randomly generated graphs to compare the performance.

MSC Codes 90C10, 68W25

Original languageEnglish (US)
JournalUnknown Journal
StatePublished - Feb 20 2019


  • Approximation algorithm
  • Double Roman domination
  • Integer linear programming

ASJC Scopus subject areas

  • General

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