Random Separation: A New Method for Solving Fixed-Cardinality Optimization Problems

  • Leizhen Cai
  • Siu Man Chan
  • Siu On Chan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4169)


We develop a new randomized method, random separation, for solving fixed-cardinality optimization problems on graphs, i.e., problems concerning solutions with exactly a fixed number k of elements (e.g., k vertices V′) that optimize solution values (e.g., the number of edges covered by V′). The key idea of the method is to partition the vertex set of a graph randomly into two disjoint sets to separate a solution from the rest of the graph into connected components, and then select appropriate components to form a solution. We can use universal sets to derandomize algorithms obtained from this method.

This new method is versatile and powerful as it can be used to solve a wide range of fixed-cardinality optimization problems for degree-bounded graphs, graphs of bounded degeneracy (a large family of graphs that contains degree-bounded graphs, planar graphs, graphs of bounded tree-width, and nontrivial minor-closed families of graphs), and even general graphs.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Leizhen Cai
    • 1
  • Siu Man Chan
    • 1
  • Siu On Chan
    • 1
  1. 1.Department of Computer Science and EngineeringThe Chinese University of Hong KongShatin, Hong Kong SARChina

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