The Complexity of modular graph automorphism

Motivated by the question of the relative complexities of the Graph Isomorphism and the Graph Automorphism problems, we define and study the modular graph automorphism problems. These are the decision problems mod_k-GA which consist, for each k>1, of deciding whether the number of automorphisms o...

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Detalles Bibliográficos
Autores: Arvind, V., Beigel, Richard, Lozano Boixadors, Antoni|||0000-0002-3633-063X
Tipo de recurso: informe técnico
Fecha de publicación:1998
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/84914
Acceso en línea:https://hdl.handle.net/2117/84914
Access Level:acceso abierto
Palabra clave:Graph isomorphism
Graph automorphism
Complexity
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
Descripción
Sumario:Motivated by the question of the relative complexities of the Graph Isomorphism and the Graph Automorphism problems, we define and study the modular graph automorphism problems. These are the decision problems mod_k-GA which consist, for each k>1, of deciding whether the number of automorphisms of a graph is divisible by k. The mod_k-GA problems all turn out to be intermediate in difficulty between Graph Automorphism and Graph Isomorphism. We define an appropriate search version of mod_k-GA and design an algorithm that polynomial-time reduces the mod_k-GA search problem to the decision problem. Combining this algorithm with an IP protocol, we obtain a randomized polynomial-time checker for mod_k-GA, for all k>1.