Core Concepts
Color-constrained subgraph problems involve finding specific subgraphs with constraints on edge colors.
Abstract
The content discusses color-constrained subgraph problems, focusing on arborescences and shortest path trees. It explores solutions for various scenarios, including NP-hardness and polynomial-time solvability based on cycle weights. Algorithms like CC-ARB-Flow are detailed for efficient computation.
Color-Constrained Subgraph Problems:
Involve finding subgraphs with color constraints.
Solutions vary based on the type of subgraph required.
Arborescences and Shortest Path Trees:
Study color-constrained arborescences and shortest path trees.
Polynomial-time solvable under certain conditions.
Algorithm Efficiency:
CC-ARB-Flow algorithm solves CC-ARB efficiently.
Dinitz's algorithm used for maximum flow computation.
Complexity Analysis:
NP-hardness discussed for general cases.
Polynomial-time solvability shown for specific scenarios.
Stats
Computing a color-constrained shortest path tree is NP-hard in general but polynomial-time solvable when cycles have positive weight.