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The Computer Journal Advance Access originally published online on November 3, 2007
The Computer Journal 2008 51(1):102-121; doi:10.1093/comjnl/bxm086
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© The Author 2008. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Parameterized Complexity of Cardinality Constrained Optimization Problems

Leizhen Cai*

Department of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, China

* Corresponding author: lcai{at}cse.cuhk.edu.hk

We study the parameterized complexity of cardinality constrained optimization problems, i.e. optimization problems that require their solutions to contain specified numbers of elements to optimize solution values. For this purpose, we consider around 20 such optimization problems, as well as their parametric duals, that deal with various fundamental relations among vertices and edges in graphs. We have almost completely settled their parameterized complexity by giving either FPT algorithms or W[1]-hardness proofs. Furthermore, we obtain faster exact algorithms for several cardinality constrained optimization problems by transforming them into problems of finding maximum (minimum) weight triangles in weighted graphs.

Key Words: cardinality constrained optimization problem • exact algorithm • fixed-cardinality optimization problem • graph problem • parameterized complexity • FPT algorithm • W[1]-hardness


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