We give a polynomial-time oracle algorithm for Tournament Canonization that accesses oracles for Tournament Isomorphism and Rigid-Tournament Canonization. Extending the Babai-Luks Tournament Canonization algorithm, we give an n n) algorithm for canonization and isomorphism testing of k-hypertournaments, where n is the number of vertices and k is the size of hyperedges.

Planar graph canonization is known to be hard for L this directly follows from L-hardness of tree-canonization [Lin92]. We give a log-space algorithm for planar graph canonization. This gives completeness for log-space under AC many-one reductions and improves the previously known upper bound of AC [MR91]. A planar graph can be decomposed into biconnected components. We give a log-space procedu...

It is known that to a planar spatial database represented by a semi algebraic set in the plane one can associate a structure here called the topological canonization such that two databases are topologically equivalent if and only if their topological canonizations are isomorphic The advantage of a topological canonization is that it contains precisely the information one needs if one is only i...

We consider the isomorphism and canonization problem for 3-connected planar graphs. The problem was known to be L -hard and in UL ∩ coUL [TW08]. In this paper, we give a deterministic log-space algorithm for 3-connected planar graph isomorphism and canonization. This gives an L -completeness result, thereby settling its complexity. The algorithm uses the notion of universal exploration sequence...

The canonization theorem says that for given m, n for some m (the first one is called ER(n;m)) we have for every function f with domain [1, . . . , m], for some A ∈ [1, . . . , m], the question of when the equality f(i1, . . . , in) = f(j1, . . . , jn) (where i1 < · · · < in and j1 < · · · jn are from A) holds has the simplest answer: for some v ⊆ {1, . . . , n} the equality holds iff ∧

We show that partial 2-tree canonization, and hence isomorphism testing for partial 2-trees, is in deterministic logspace. Our algorithm involves two steps: (a) We exploit the “tree of cycles” property of biconnected partial 2-trees to canonize them in logspace. (b) We analyze Lindell’s tree canonization algorithm and show that canonizing general partial 2-trees is also in logspace, using the a...

We show that the class of chordal claw-free graphs admits LREC=-definable canonization. LREC= is a logic that extends first-order logic with counting by an operator that allows it to formalize a limited form of recursion. This operator can be evaluated in logarithmic space. It follows that there exists a logarithmic-space canonization algorithm, and therefore a logarithmic-space isomorphism tes...

Let Lk be the k-variable fragment of first-order logic, for some k 3. We prove that equivalence of finite structures in Lk has no P-computable canonization function unless NP P=poly. The latter assumption is considered as highly unlikely; in particular it implies a collapse of the polynomial hierarchy. The question for such a canonization function came up in the context of the problem of whethe...

We show that every polynomial-time full-invariant algorithm for graphs gives rise to a polynomial-time canonization algorithm for graphs.