**Reference**:- Erik D. Demaine, MohammadTaghi Hajiaghayi, and Dimitrios M. Thilikos, “Exponential Speedup of Fixed Parameter Algorithms on
*K*_{3,3}-minor-free or*K*_{5}-minor-free Graphs”, Technical Report MIT-LCS-TR-838, Massachusetts Institute of Technology, March 18, 2002. **Abstract**:-
We present a fixed parameter algorithm that constructively solves the
*k*-dominating set problem on graphs excluding one of the*K*_{5}or*K*_{3,3}as a minor in time*O*(3^{6 √34 k}*n*^{O(1)}). In fact, we present our algorithm for any*H*-minor-free graph where*H*is a single-crossing graph (can be drawn on the plane with at most one crossing) and obtain the algorithm for*K*_{3,3}(*K*_{5})-minor-free graphs as a special case. As a consequence, we extend our results to several other problems such as vertex cover, edge dominating set, independent set, clique-transversal set, kernels in digraphs, feedback vertex set and a series of vertex removal problems. Our work generalizes and extends the recent result of exponential speedup in designing fixed-parameter algorithms on planar graphs due to Alber et al. to other (non-planar) classes of graphs. **Length**:- The paper is 22 pages.
**Availability**:- The paper is available in PostScript (318k), gzipped PostScript (119k), and PDF (251k).
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**Related papers**:- CliqueSum_ISAAC2002 (Exponential Speedup of Fixed-Parameter Algorithms on
*K*_{3,3}-minor-free or*K*_{5}-minor-free Graphs) - CliqueSum_APPROX2002 (1.5-Approximation for Treewidth of Graphs Excluding a Graph with One Crossing as a Minor)

See also other papers by Erik Demaine.

Last updated February 26, 2024 by Erik Demaine.