发表机构
Universidad Nacional de Rosario; CONICET; Escuela Politécnica Nacional（罗萨里奥国立大学; 国家科学技术研究委员会; 国立理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究双划分着色问题（DPCP），提出结构性质、启发式方法及增强的分支定价精确算法，并在CFCP实例上首次进行计算评估，与紧凑整数规划公式互补求解。
AI 中文摘要
双划分着色问题（DPCP）是最近提出的图与超图上若干着色问题（包括划分着色问题、列表着色问题和无冲突着色问题（CFCP））的推广。本文进一步研究了DPCP的结构与计算性质，并开发了精确与启发式求解方法。我们推导了若干结构性质，这些性质可用于检测不可行实例并缩减其规模。我们提出了单步与两步启发式方法以获得高质量解。这些过程被整合进一个基于DPCP集合覆盖公式的增强型分支定价算法中。该算法还包含了求解NP难定价问题的新策略。计算实验表明，所提出的分支定价算法与紧凑整数规划公式互为补充：紧凑公式在稀疏实例上通常更有效，而分支定价在更稠密和更大的实例上表现尤为出色。特别地，这些是首次在各种CFCP实例上进行计算评估的精确算法。
英文摘要
The Double-Partition Coloring Problem (DPCP) is a recently introduced generalization of several coloring problems on graphs and hypergraphs, including the Partition Coloring Problem, the List Coloring Problem, and the Conflict-Free Coloring Problem (CFCP). In this work, we further investigate the structural and computational properties of the DPCP and develop exact and heuristic solution approaches. We derive structural results that allow the detection of infeasible instances and the reduction of their size. We propose one-step and two-step heuristics for obtaining high-quality solutions. These procedures are incorporated into an enhanced branch-and-price algorithm based on a set covering formulation of the DPCP. The algorithm further includes new strategies for solving the NP-hard pricing problem. Computational experiments show that the proposed branch-and-price algorithm and a compact integer programming formulation complement each other: while the compact formulation is generally more effective on sparse instances, branch-and-price performs particularly well on denser and larger instances. In particular, these are the first exact algorithms to be computationally evaluated on various CFCP instances.
