We show an O^*(2^k)-time polynomial space algorithm for the k-sized Graph Motif problem. We also introduce a new optimization variant of the problem, called Closest Graph Motif and solve it within the same time bound. The Closest Graph Motif problem encompasses several previously studied optimization variants, like Maximum Graph Motif, Min-Substitute, and Min-Add. Moreover, we provide a piece of evidence that our result might be essentially tight: the existence of an O^*((2-epsilon)^k)-time algorithm for the Graph Motif problem implies an ((2-epsilon')^n)-time algorithm for Set Cover.
@InProceedings{bjorklund_et_al:LIPIcs.STACS.2013.20, author = {Bj\"{o}rklund, Andreas and Kaski, Petteri and Kowalik, Lukasz}, title = {{Probably Optimal Graph Motifs}}, booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)}, pages = {20--31}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-50-7}, ISSN = {1868-8969}, year = {2013}, volume = {20}, editor = {Portier, Natacha and Wilke, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.20}, URN = {urn:nbn:de:0030-drops-39196}, doi = {10.4230/LIPIcs.STACS.2013.20}, annote = {Keywords: graph motif, FPT algorithm} }
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