2017/03/15 by David Chalupa, Chalupa, David
Computer Science · Decision Sciences · Engineering · #Computational Geometry and Mesh Generation #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Scheduling and Timetabling Solutions #Vehicle Routing Optimization Methods
paper · pdf · doi:10.48550/arxiv.1703.05129
openalex publication_date 2017/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Vertex Descent is a local search algorithm which forms the basis of a wide spectrum of tabu search, simulated annealing and hybrid evolutionary algorithms for graph colouring. These algorithms are usually treated as experimental and provide strong results on established benchmarks. As a step towards studying these heuristics analytically, an analysis of the behaviour of Vertex Descent is provided. It is shown that Vertex Descent is able to find feasible colourings for several types of instances in expected polynomial time. This includes 2-colouring of paths and 3-colouring of graphs with maximum degree 3. The same also holds for 3-colouring of a subset of 3-colourable graphs with maximum degree 4. As a consequence, Vertex Descent finds a 3-colouring in expected polynomial time for the smallest graph for which Brélaz's heuristic DSATUR needs 4 colours. On the other hand, Vertex Descent may fail for forests with maximum degree 3 with high probability.