arXiv subjects

Boyue Lin

Publications and source records attributed to Boyue Lin.

2 recordsLinked to original sources

arXiv2026

Convex Recoloring of General Graphs: Formulations, Polyhedra, and Computational Experiments

A vertex coloring of a graph is convex if the vertices of each color induce a connected subgraph. In the convex recoloring problem (CR), the goal is to find a convex coloring while minimizing the weight of recolored vertices, i.e., vertices assigned a color different from their original one. This problem was originally motivated by the study of phylogenetic trees in bioinformatics and is NP-hard even on paths. Most existing research focuses on trees, with only limited results available for general graphs. We advance the state of the art by developing exact solution methods for CR on general graphs. In particular, we propose four mixed-integer linear programming formulations, including a compact flow-based model and a representatives model, and design corresponding solution methods. We compare the polytopes associated with the linear relaxation of the proposed formulations. Computational experiments on benchmark instances and on new synthetic instances show that a branch-and-cut algorithm based on the representatives formulation performs best overall.

cs.DM↗

arXiv2023

Algorithmic Solutions for Maximizing Shareable Costs

This paper addresses the optimization problem to maximize the total costs that can be shared among a group of agents, while maintaining stability in the sense of the core constraints of a cooperative transferable utility game, or TU game. When maximizing total shareable costs, the cost shares must satisfy all constraints that define the core of a TU game, except for being budget balanced. The paper first gives a fairly complete picture of the computational complexity of this optimization problem, its relation to optimiztion over the core itself, and its equivalence to other, minimal core relaxations that have been proposed earlier. We then address minimum cost spanning tree (MST) games as an example for a class of cost sharing games with non-empty core. While submodular cost functions yield efficient algorithms to maximize shareable costs, MST games have cost functions that are subadditive, but generally not submodular. Nevertheless, it is well known that cost shares in the core of MST games can be found efficiently. In contrast, we show that the maximization of shareable costs is NP-hard for MST games and derive a 2-approximation algorithm. Our work opens several directions for future research.

cs.GT↗