Low-degree graph partitioning via local search with applications to constraint satisfaction, max cut, and coloring

• Main Authors: Halldorsson, Magnus M., Lau, Hoong Chuin
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 1997
• Subjects: Numerical Analysis and Scientific Computing
• Online Access: https://ink.library.smu.edu.sg/sis_research/173; https://ink.library.smu.edu.sg/context/sis_research/article/1172/viewcontent/LauC1997LowDegree_Graph.pdf
• Institution: Singapore Management University

We present practical algorithms for constructing partitions of graphs into a fixed number of vertex-disjoint subgraphs that satisfy particular degree constraints. We use this in particular to find k-cuts of graphs of maximum degree ∆ that cut at least a k - 1/k (1 + 1/2∆+k-1 ) fraction of the edges, improving previous bounds known. The partitions also apply to constraint networks, for which we give a tight analysis of natural local search heuristics for the maximum constraint satisfaction problem. These partitions also imply efficient approximations for several problems on weighted bounded-degree graphs. In particular, we improve the best performance ratio for the weighted independent set problem to 3/∆+2 , and obtain an efficient algorithm for coloring 3-colorable graphs with at most 3∆+2/4 colors.