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The isomorphism problem for ktrees is complete for logspace
 PROCEEDINGS OF 34TH INTERNATIONAL SYMPOSIUM MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE (MFCS), NUMBER 5734 IN LNCS
, 2009
"... We show that ktree isomorphism can be decided in logarithmic space by giving a logspace canonical labeling algorithm. This improves over the previous StUL upper bound and matches the lower bound. As a consequence, the isomorphism, the automorphism, as well as the canonization problem for ktrees ..."
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Cited by 8 (1 self)
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We show that ktree isomorphism can be decided in logarithmic space by giving a logspace canonical labeling algorithm. This improves over the previous StUL upper bound and matches the lower bound. As a consequence, the isomorphism, the automorphism, as well as the canonization problem for ktrees are all complete for deterministic logspace. We also show that even simple structural properties of ktrees are complete for logspace.
The Complexity of Planar Graph Isomorphism
, 1997
"... The Graph Isomorphism problem restricted to planar graphs has been known to be solvable in polynomial time many years ago. In terms of complexity classes however, the exact complexity of the problem has been established only very recently. It was proved in [6] that planar graph isomorphism can be co ..."
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Cited by 3 (0 self)
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The Graph Isomorphism problem restricted to planar graphs has been known to be solvable in polynomial time many years ago. In terms of complexity classes however, the exact complexity of the problem has been established only very recently. It was proved in [6] that planar graph isomorphism can be computed within logarithmic space. Since there is a matching hardness result [12], this shows that the problem is complete for L. Although this could be considered as a result in algorithmics its proof relies on several important new developments in the area of logarithmic space complexity classes and reflects the close connections between algorithms and complexity theory. In this column we give an overview of this result mentioning the developments that led to it.