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.
Numerical Analysis and Scientific Computing
Intelligent Systems and Decision Analytics
Journal of Graph Algorithms and Applications
Halldorsson, Magnus M. and Lau, Hoong Chuin.
Low-degree graph partitioning via local search with applications to constraint satisfaction, max cut, and coloring. (1997). Journal of Graph Algorithms and Applications. 1, (3), 1-13. Research Collection School Of Information Systems.
Available at: http://ink.library.smu.edu.sg/sis_research/173
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