53 research outputs found

    Canonizing Graphs of Bounded Tree Width in Logspace

    Get PDF
    Graph canonization is the problem of computing a unique representative, a canon, from the isomorphism class of a given graph. This implies that two graphs are isomorphic exactly if their canons are equal. We show that graphs of bounded tree width can be canonized by logarithmic-space (logspace) algorithms. This implies that the isomorphism problem for graphs of bounded tree width can be decided in logspace. In the light of isomorphism for trees being hard for the complexity class logspace, this makes the ubiquitous class of graphs of bounded tree width one of the few classes of graphs for which the complexity of the isomorphism problem has been exactly determined.Comment: 26 page

    Restricted Space Algorithms for Isomorphism on Bounded Treewidth Graphs

    Get PDF
    The Graph Isomorphism problem restricted to graphs of bounded treewidth or bounded tree distance width are known to be solvable in polynomial time [Bod90],[YBFT99]. We give restricted space algorithms for these problems proving the following results: - Isomorphism for bounded tree distance width graphs is in L and thus complete for the class. We also show that for this kind of graphs a canon can be computed within logspace. - For bounded treewidth graphs, when both input graphs are given together with a tree decomposition, the problem of whether there is an isomorphism which respects the decompositions (i.e. considering only isomorphisms mapping bags in one decomposition blockwise onto bags in the other decomposition) is in L. - For bounded treewidth graphs, when one of the input graphs is given with a tree decomposition the isomorphism problem is in LogCFL. - As a corollary the isomorphism problem for bounded treewidth graphs is in LogCFL. This improves the known TC1 upper bound for the problem given by Grohe and Verbitsky [GroVer06].Comment: STACS conference 2010, 12 page

    The Complexity of Bisimulation and Simulation on Finite Systems

    Full text link
    In this paper the computational complexity of the (bi)simulation problem over restricted graph classes is studied. For trees given as pointer structures or terms the (bi)simulation problem is complete for logarithmic space or NC1^1, respectively. This solves an open problem from Balc\'azar, Gabarr\'o, and S\'antha. Furthermore, if only one of the input graphs is required to be a tree, the bisimulation (simulation) problem is contained in AC1^1 (LogCFL). In contrast, it is also shown that the simulation problem is P-complete already for graphs of bounded path-width

    3-connected Planar Graph Isomorphism is in Log-space

    Get PDF
    We show that the isomorphism of 3-connected planar graphs can be decided in deterministic log-space. This improves the previously known bound UL∩\capcoUL of Thierauf and Wagner

    On the Parallel Complexity of Bisimulation on Finite Systems

    Get PDF

    Isomorphism testing of read-once functions and polynomials

    Get PDF
    In this paper, we study the isomorphism testing problem of formulas in the Boolean and arithmetic settings. We show that isomorphism testing of Boolean formulas in which a variable is read at most once (known as read-once formulas) is complete for log-space. In contrast, we observe that the problem becomes polynomial time equivalent to the graph isomorphism problem, when the input formulas can be represented as OR of two or more monotone read-once formulas. This classifies the complexity of the problem in terms of the number of reads, as read-3 formula isomorphism problem is hard for coNP. We address the polynomial isomorphism problem, a special case of polynomial equivalence problem which in turn is important from a cryptographic perspective[Patarin EUROCRYPT\u2796, and Kayal SODA\u2711]. As our main result, we propose a deterministic polynomial time canonization scheme for polynomials computed by constant-free read-once arithmetic formulas. In contrast, we show that when the arithmetic formula is allowed to read a variable twice, this problem is as hard as the graph isomorphism problem
    • …
    corecore