Paper Info
Title
An Analysis of a Simple Local Search Algorithm for Graph Colouring.
Abstract
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 Bru0027elazu0027s heuristic DSATUR needs 4 colours. On the other hand, Vertex Descent may fail for forests with maximum degree 3 with high probability.
Year
Venue
Field
2017
arXiv: Discrete Mathematics
Simulated annealing,Discrete mathematics,Combinatorics,Circulant graph,Loop (graph theory),Vertex (graph theory),Cycle graph,Degree (graph theory),Bidirectional search,Mathematics,Feedback vertex set
DocType
Volume
Citations 
Journal
abs/1703.05129
0
PageRank 
References 
Authors
0.34
32
1
Name
Order
Citations
PageRank
David Chalupa1246.84