Results 1  10
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22
Completeness results for Graph Isomorphism
, 2002
"... We prove that the graph isomorphism problem restricted to trees and to colored graphs with color multiplicities 2 and 3 is manyone complete for several complexity classes within NC². In particular we show that tree isomorphism, when trees are encoded as strings, is NC¹hard under AC0reductions ..."
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Cited by 20 (9 self)
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We prove that the graph isomorphism problem restricted to trees and to colored graphs with color multiplicities 2 and 3 is manyone complete for several complexity classes within NC². In particular we show that tree isomorphism, when trees are encoded as strings, is NC¹hard under AC0reductions. NC¹completeness thus follows from Buss's NC¹ upper bound. By contrast, we prove that testing isomorphism of two trees encoded as pointer lists is Lcomplete. Concerning colored graphs we show that the isomorphism problem for graphs with color multiplicities 2 and 3 is complete for symmetric logarithmic space SL under manyone reductions. This result improves the existing upper bounds for the problem. We also show that the graph automorphism problem for colored graphs with color classes of size 2 is equivalent to deciding whether a graph has more than a single connected component and we prove that for color classes of size 3 the graph automorphism problem is contained in SL.
Engineering an Efficient Canonical Labeling Tool for Large and Sparse Graphs
"... The problem of canonically labeling a graph is studied. Within the general framework of backtracking algorithms based on individualization and refinement, data structures, subroutines, and pruning heuristics especially for fast handling of large and sparse graphs are developed. Experiments indicate ..."
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Cited by 13 (1 self)
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The problem of canonically labeling a graph is studied. Within the general framework of backtracking algorithms based on individualization and refinement, data structures, subroutines, and pruning heuristics especially for fast handling of large and sparse graphs are developed. Experiments indicate that the algorithm implementation in most cases clearly outperforms existing stateoftheart tools.
Equivalence and isomorphism for Boolean constraint satisfaction
 In Proceedings of the 16th Annual Conference of the EACSL (CSL 2002
, 2002
"... Abstract. A Boolean constraint satisfaction instance is a conjunction of constraint applications, where the allowed constraints are drawn from a fixed set C of Boolean functions. We consider the problem of determining whether two given constraint satisfaction instances are equivalent and prove a Dic ..."
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Cited by 12 (6 self)
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Abstract. A Boolean constraint satisfaction instance is a conjunction of constraint applications, where the allowed constraints are drawn from a fixed set C of Boolean functions. We consider the problem of determining whether two given constraint satisfaction instances are equivalent and prove a Dichotomy Theorem by showing that for all sets C of allowed constraints, this problem is either polynomialtime solvable or coNPcomplete, and we give a simple criterion to determine which case holds. A more general problem addressed in this paper is the isomorphism problem, the problem of determining whether there exists a renaming of the variables that makes two given constraint satisfaction instances equivalent in the above sense. We prove that this problem is coNPhard if the corresponding equivalence problem is coNPhard, and polynomialtime manyone reducible to the graph isomorphism problem in all other cases.
Planar graph isomorphism is in logspace
 In IEEE Conference on Computational Complexity
, 2009
"... Abstract. We show that the isomorphism of 3connected planar graphs can be decided in deterministic logspace. This improves the previously known bound UL ∩ coUL of [13]. 1 ..."
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Cited by 8 (1 self)
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Abstract. We show that the isomorphism of 3connected planar graphs can be decided in deterministic logspace. This improves the previously known bound UL ∩ coUL of [13]. 1
Equivalence Problems for Boolean Constraint Satisfaction
, 2001
"... A Boolean constraint satisfaction instance is a conjunction of constraint applications, where the allowed constraints are drawn from a fi xed set C of Boolean functions. We consider the problem of determining whether two given constraint satisfaction instances are equivalent in the sense that they p ..."
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Cited by 5 (2 self)
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A Boolean constraint satisfaction instance is a conjunction of constraint applications, where the allowed constraints are drawn from a fi xed set C of Boolean functions. We consider the problem of determining whether two given constraint satisfaction instances are equivalent in the sense that they possess the same sets of satisfying assignments. We prove a Dichotomy Theorem by showing that for all sets C of allowed constraints, this problem is either polynomialtime solvable or coNPcomplete, and we give a simple criterion to determine which case holds. Another equivalence problem...
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 4 (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 Graph Isomorphism for Colored Graphs with Color Classes of Size 2 and 3
"... We prove that the graph isomorphism problem restricted to colored graphs with color multiplicities 2 and 3 is complete for symmetric logarithmic space SL under manyone reductions. This result improves the existing upper bounds for the problem. We also ..."
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Cited by 2 (2 self)
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We prove that the graph isomorphism problem restricted to colored graphs with color multiplicities 2 and 3 is complete for symmetric logarithmic space SL under manyone reductions. This result improves the existing upper bounds for the problem. We also
Privacy Problems with Anonymized Transaction Databases
"... In this paper we consider privacy problems with anonymized transaction databases, i.e., transaction databases where the items are renamed in order to hide sensitive information. In particular, we show how an anonymized transaction database can be deanonymized using nonanonymized frequent itemse ..."
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Cited by 2 (0 self)
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In this paper we consider privacy problems with anonymized transaction databases, i.e., transaction databases where the items are renamed in order to hide sensitive information. In particular, we show how an anonymized transaction database can be deanonymized using nonanonymized frequent itemsets. We describe how the problem can be formulated as an integer programming task, study the computational complexity of the problem, discuss how the computations could be done more e#ciently in practice and experimentally examine the feasibility of the proposed approach.
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