A fast backtrack algorithm for graph isomorphism

Mittal, Hari Ballabh

doi:10.1016/0020-0190(88)90037-3

Cited by 9 publications

(1 citation statement)

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“…to solve the three problems by one algorithm with time complexity as lower as possible. In addition, our requirements to the heuristic algorithms are to give results equal to the results of the exact algorithm with the probability close to 1. There are a few heuristic algorithms for the graph isomorphism problem [21][22][23][24] there is no access to their program codes. We propose three new heuristic algorithms (Vsep-orb, Vsep-hway, Vsep-sch) for GOO(Aut(G)) with much lower polynomial time complexity than the exact one.…”

Section: Introductionmentioning

confidence: 99%

New Exact and Heuristic Algorithms for Graph Automorphism Group and Graph Isomorphism

Stoichev

2019

ACM J. Exp. Algorithmics

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Five new algorithms, named Vsep, are described. Four of them are for determining the generators, orbits and order of an undirected graph automorphism group.Vsep-eexact, Vsep-orb and Vsep-schheuristic and Vsep-a automatically selects the optimal version among Vsep-e, Vsep-orb and Vsep-sch. The fifth algorithm, Vsep-is, is for finding an isomorphism between two graphs. Vsep-orb firstly finds heuristically the generators and orbits and then uses the exact one on the orbital partition for determining the order of the group. Vsep-sch differs from Vsep-orb in using the Schreier-Sims algorithm for determining the order of the group. A basic tool of these algorithms is the adjacency refinement procedure that gives finer output partition on a given input partition of graph vertices. The refinement procedure is a simple iterative algorithm based on the criterion of relative degree of a vertex toward a basic cell in the partition. A search tree is used in the algorithms -each node of the tree is a partition. All nonequivalent discreet partitions derivative of the selected vertices called a bouquet are stored in a coded form in a hash table in order to reduce the necessary storagethis is a main difference of Vsep-e with the known graph automorphism group algorithms. A new strategy is used in the exact algorithm: if during its execution some of the searched or intermediate variables obtain a wrong value then the algorithm continues from a new start point losing some of the results determined so far. The new start point is such that the correct results can be obtained. The proposed algorithms has been tested on the nauy&Traces benchmark graphs and compared with Traces, and the results show that for some graph families Vsep-e outperforms Traces and for some of the others Traces outperforms Vsep-e. The heuristic versions of Vsep are based on determining some number of discreet partitions derivative of each vertex in the selected cell of the initial partition and comparing them for an automorphism, i.e. their search trees are reduced. The heuristic algorithms are almost exact and are many times faster than the exact one. The heuristic algorithms are good choice for the user because of their smaller running times. Several cell selectors are used in Vsep, some of them are known and some are new. We also use a chooser of cell selector for choosing the optimal cell selector for the manipulated graph. The experiments show that the running time of Vsep algorithms does not depend on the vertex labeling.

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Section: Introductionmentioning

confidence: 99%