Parallelization of Graph Isomorphism using OpenMP

Abstract

Advancement in computer architecture leads to parallelize the sequential algorithm to exploit the concurrency provided by multiple core on single chip. Sequential programs do not gain performance from multicore. For multicore architectures, OPENMP and MPI are application programming interfaces. They can be used for parallelization of codes. For shared memory architecture OPENMP is used, whereas for distributed memory architecture MPI is used .In this paper, analysis of the performance of parallel algorithm over sequential algorithm is done. In particular, Graph Isomorphism problem based on vertex invariants is considered and parallelized using OpenMP. We demonstrate the performance of Graph Isomorphism using variable size graphs and parallelize it using vertical tiling technique on multicore architecture. Our previous work shows, sequential implementation of modified algorithm based on vertex invariants using Euclidian vector performs better than existing algorithm of Graph Isomorphism based on vertex invariants. To analyze the performance of parallel implementation, we present practical experiments with randomly generated graphs.

A polynomial‐time algorithm for simple undirected graph isomorphism

“…László Babai in 2015 claimed that the graph isomorphism dilemma could be solved within quasi‐polynomial time 25–28 and, soon afterwards, Babai reclaimed the quasi‐polynomiality and declared a sub‐exponential time complexity bound instead 25–28 . In this paper, the time complexity of the best case is O (10 × m +4 × n +3), the worst case is O (10 × n 2 − 4 × n +12) including the storage.…”

“…László Babai in 2015 claimed that the graph isomorphism dilemma could be solved within quasi-polynomial time [25][26][27][28] and, soon afterwards, Babai reclaimed the quasi-polynomiality and declared a sub-exponential time complexity bound instead. [25][26][27][28] In this paper, the time complexity of the ), where m is the number of edges of a graph and n is the number of vertices of a graph. The complexity comparisons with other algorithms are shown in Table 29.…”

“…The authors proposed an improved version of the algorithm named VF2 20 that uses the same theory with VF and adopts suitable designed data structures to store the state space search information, thus to reduce the amount of replicated information that is passing from a state to its descendants with the memory occupation decreasing from O ( n 2 ) to O ( n ), so the algorithm is appropriate for working with large graphs. Graph invariants method using the invariant condition to verify graph isomorphism was presented in tje works of Balpande and Mahajan 24,25 . OpenMP deploys the task on a different core and then the efficiency could be boosted and the space complexity could shrink.…”

“…Graph invariants method using the invariant condition to verify graph isomorphism was presented in tje works of Balpande and Mahajan. 24,25 OpenMP deploys the task on a different core and then the efficiency could be boosted and the space complexity could shrink. It verifies graph isomorphism by utilizing the Euclidean Vector with graph invariants, while the algorithm needs more storage space due to the construction of the adjacency matrix.…”

Parallel Computation of Combinatorial Symmetries

“…However, he has subsequently not pursued this further in the last decade, and the described algorithm is based on algorithms of the first generation. The study [5] only performs comparisons against slow sequential algorithms. Overall, parallel graph isomorphism testing has not witnessed any of the ideas that characterize the second generation of algorithms.…”