Towards fully multivariate algorithmics: parameter ecology and the deconstruction of computational complexity. (English) Zbl 1448.68465

Fellows, Michael R.; Jansen, Bart M. P.; Rosamond, Frances

Eur. J. Comb. 34, No. 3, 541-566 (2013).

Summary: The aim of this article is to motivate and describe the parameter ecology program, which studies how different parameters contribute to the difficulty of classical problems. We call for a new type of race in parameterized analysis, with the purpose of uncovering the boundaries of tractability by finding the smallest possible parameterizations which admit FPT-algorithms or polynomial kernels.
An extensive overview of recent advances on this front is presented for the vertex cover problem. Moving even beyond the parameter ecology program we advocate the principle of model enrichment, which raises the challenge of generalizing positive results to problem definitions with greater modeling power. The computational intractability which inevitably emerges can be deconstructed by introducing additional parameters, leading towards a theory of fully multivariate algorithmics.

MSC:

68W01	General topics in the theory of algorithms
05C85	Graph algorithms (graph-theoretic aspects)
68Q25	Analysis of algorithms and problem complexity
68Q27	Parameterized complexity, tractability and kernelization

Keywords:

parameter ecology program; FPT-algorithms; polynomial kernels