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20
On the Hardness of Graph Isomorphism
 SIAM J. COMPUT
"... We show that the graph isomorphism problem is hard under DLOGTIME uniform AC0 manyone reductions for the complexity classes NL, PL (probabilistic logarithmic space) for every logarithmic space modular class ModkL and for the class DET of problems NC¹ reducible to the determinant. These are the stro ..."
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Cited by 33 (1 self)
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We show that the graph isomorphism problem is hard under DLOGTIME uniform AC0 manyone reductions for the complexity classes NL, PL (probabilistic logarithmic space) for every logarithmic space modular class ModkL and for the class DET of problems NC¹ reducible to the determinant. These are the strongest known hardness results for the graph isomorphism problem and imply a randomized logarithmic space reduction from the perfect matching problem to graph isomorphism. We also investigate hardness results for the graph automorphism problem.
A Logspace Algorithm for Partial 2Tree canonization
, 2008
"... We show that partial 2tree canonization, and hence isomorphism testing for partial 2trees, is in deterministic logspace. Our algorithm involves two steps: (a) We exploit the “tree of cycles ” property of biconnected partial 2trees to canonize them in logspace. (b) We analyze Lindell’s tree cano ..."
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Cited by 7 (1 self)
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We show that partial 2tree canonization, and hence isomorphism testing for partial 2trees, is in deterministic logspace. Our algorithm involves two steps: (a) We exploit the “tree of cycles ” property of biconnected partial 2trees to canonize them in logspace. (b) We analyze Lindell’s tree canonization algorithm and show that canonizing general partial 2trees is also in logspace, using the algorithm to canonize biconnected partial 2trees.
Algorithm and Experiments in Testing Planar Graphs for Isomorphism
, 2004
"... We give an algorithm for isomorphism testing of planar graphs suitable for practical implementation. The algorithm is based on the decomposition of a graph into biconnected components and further into SPQRtrees. We provide a proof of the algorithm’s correctness and a complexity analysis. We determi ..."
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Cited by 6 (0 self)
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We give an algorithm for isomorphism testing of planar graphs suitable for practical implementation. The algorithm is based on the decomposition of a graph into biconnected components and further into SPQRtrees. We provide a proof of the algorithm’s correctness and a complexity analysis. We determine the conditions in which the implemented algorithm outperforms other graph matchers, which do not impose topological restrictions on graphs. We report experiments with our planar graph matcher tested against McKay’s, Ullmann’s, and SUBDUE’s (a graphbased data mining system) graph matchers.
Colored Hypergraph Isomorphism is Fixed Paramter Tractable
 Electronic Colloquium on Computation Complexity
, 2009
"... We describe a fixed parameter tractable (fpt) algorithm for Colored Hypergraph Isomorphism which has running time 2 O(b) N O(1) , where the parameter b is the maximum size of the color classes of the given hypergraphs and N is the input size. We also describe fpt algorithms for certain permutation g ..."
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Cited by 5 (1 self)
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We describe a fixed parameter tractable (fpt) algorithm for Colored Hypergraph Isomorphism which has running time 2 O(b) N O(1) , where the parameter b is the maximum size of the color classes of the given hypergraphs and N is the input size. We also describe fpt algorithms for certain permutation group problems that are used as subroutines in our algorithm. Fixed parameter tractability, fpt algorithms, graph isomorphism, com
Restricted space algorithms for isomorphism on bounded treewidth graphs
 IN STACS
, 2010
"... The Graph Isomorphism problem restricted to graphs of bounded treewidth or bounded tree distance width are known to be solvable in polynomial time [2],[19]. We give restricted space algorithms for these problems proving the following results: • Isomorphism for bounded tree distance width graphs is i ..."
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Cited by 4 (0 self)
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The Graph Isomorphism problem restricted to graphs of bounded treewidth or bounded tree distance width are known to be solvable in polynomial time [2],[19]. 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 [8].
Progressive Solutions: A Simple but Efficient Dominance Rule for Practical RCPSP
 In Proc. of CPAIOR 2006, the 3 rd Int. Conf. on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, LNCS 3990
, 2006
"... Abstract. This paper addresses the solution of practical resourceconstrained project scheduling problems (RCPSP). We point out that such problems often contain many, in a sense similar projects, and this characteristic can be exploited well to improve the performance of current constraintbased sol ..."
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Cited by 3 (1 self)
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Abstract. This paper addresses the solution of practical resourceconstrained project scheduling problems (RCPSP). We point out that such problems often contain many, in a sense similar projects, and this characteristic can be exploited well to improve the performance of current constraintbased solvers on these problems. For that purpose, we define the straightforward but generic notion of progressive solution, in which the order of corresponding tasks of similar projects is deduced a priori. We prove that the search space can be reduced to progressive solutions. Computational experiments on two different sets of industrial problem instances are also presented. 1
Four Lessons in Versatility or How Query Languages Adapt to the Web
"... Exposing not only humancentered information, but machineprocessable data on the Web is one of the commonalities of recent Web trends. It has enabled a new kind of applications and businesses where the data is used in ways not foreseen by the data providers. Yet this exposition has fractured the W ..."
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Cited by 3 (3 self)
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Exposing not only humancentered information, but machineprocessable data on the Web is one of the commonalities of recent Web trends. It has enabled a new kind of applications and businesses where the data is used in ways not foreseen by the data providers. Yet this exposition has fractured the Web into islands of data, each in different Web formats: Some providers choose XML, others RDF, again others JSON or OWL, for their data, even in similar domains. This fracturing stifles innovation as application builders have to cope not only with one Web stack (e.g., XML technology) but with several ones, each of considerable complexity. With Xcerpt we have developed a rule and pattern based query language that aims to give shield application builders from much of this complexity: In a single query language XML and RDF data can be accessed, processed, combined, and republished. Though the need for combined access to XML and RDF data has been recognized in previous work (including the W3C’s GRDDL), our approach differs in four main aspects: (1) We provide a single language (rather than two separate or embedded languages), thus minimizing the conceptual overhead of dealing with disparate data formats. (2) Both the declarative (logicbased) and the operational semantics are unified in that they apply for querying XML and RDF in the same way. (3) We show that the resulting query language can be implemented reusing traditional database technology, if desirable. Nevertheless, we also give a unified evaluation approach based on interval labelings of graphs that is at least as fast as existing approaches for treeshaped XML data, yet provides linear time and space querying also for many RDF graphs. We believe that Web query languages are the right tool for declarative data access in Web applications and that Xcerpt is a significant step towards a more convenient, yet highly efficient data access in a “Web of Data”.
On graph isomorphism for restricted graph classes
 In
, 2006
"... Abstract. Graph isomorphism (GI) is one of the few remaining problems in NP whose complexity status couldn’t be solved by classifying it as being either NPcomplete or solvable in P. Nevertheless, efficient (polynomialtime or even NC) algorithms for restricted versions of GI have been found over th ..."
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Cited by 3 (1 self)
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Abstract. Graph isomorphism (GI) is one of the few remaining problems in NP whose complexity status couldn’t be solved by classifying it as being either NPcomplete or solvable in P. Nevertheless, efficient (polynomialtime or even NC) algorithms for restricted versions of GI have been found over the last four decades. Depending on the graph class, the design and analysis of algorithms for GI use tools from various fields, such as combinatorics, algebra and logic. In this paper, we collect several complexity results on graph isomorphism testing and related algorithmic problems for restricted graph classes from the literature. Further, we provide some new complexity bounds (as well as easier proofs of some known results) and highlight some open questions. 1
On Hypergraph and Graph Isomorphism with Bounded Color Classes ⋆
"... Abstract. Using logspace counting classes we study the computational complexity of hypergraph and graph isomorphism where the vertex sets have bounded color classes for certain specific bounds. We also give a polynomialtime algorithm for hypergraph isomorphism for bounded color classes of arbitrary ..."
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Cited by 2 (1 self)
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Abstract. Using logspace counting classes we study the computational complexity of hypergraph and graph isomorphism where the vertex sets have bounded color classes for certain specific bounds. We also give a polynomialtime algorithm for hypergraph isomorphism for bounded color classes of arbitrary size. 1