منابع مشابه
Graph Isomorphism is in the Low Hierarchy
The problem of determining whether two given finite graphs are isomorphic is easily seen to belong to the class NP. But up to now, no polynomial time algorithm is known. On the other hand, no NP-completeness proof is known either. That is, GRAPH ISOMORPHISM is one of the few “open problems” in NP according to Garey and Johnson’s terminology [9]. Note that GRAPH ISOMORPHISM is already mentioned ...
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In this paper we show lower bounds for a certain large class of algorithms solving the Graph Isomorphism problem, even on expander graph instances. Spielman [25] shows an algorithm for isomorphism of strongly regular expander graphs that runs in time exp{Õ(n 13 )} (this bound was recently improved to exp{Õ(n 15 )} [5]). It has since been an open question to remove the requirement that the graph...
متن کاملGraph isomorphism is polynomial
We show that the graph isomorphism problem is determined in a polynomial time. This is done by showing that that two graphs on n vertices are isomorphic if and only if a corresponding system of (4n− 1)n equations in n nonnegative variables is solvable. 2000 Mathematics Subject Classification: 03D15, 05C50, 05C60, 15A48, 15A51, 15A69, 90C05.
متن کاملGraph Isomorphism is in SPP
We show that Graph Isomorphism is in the complexity class SPP, and hence it is in ⊕P (in fact, it is in ModkP for each k ≥ 2). We derive this result as a corollary of a more general result: we show that a generic problem FIND-GROUP has an FPSPP algorithm. This general result has other consequences: for example, it follows that the hidden subgroup problem for permutation groups, studied in the c...
متن کاملGraph Isomorphism is PSPACE-complete
Combining the the results of A.R. Meyer and L.J. Stockmeyer " The Equivalence Problem for Regular Expressions with Squaring Requires Exponential Space " , and K.S. Booth " Iso-morphism testing for graphs, semigroups, and finite automata are polynomiamlly equivalent problems " shows that graph isomorphism is PSPACE-complete. The equivalence problem for regular expressions was shown to be PSPACE-...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 1988
ISSN: 0022-0000
DOI: 10.1016/0022-0000(88)90010-4