Results 1 
7 of
7
Hardness of Robust Graph Isomorphism, Lasserre Gaps, and Asymmetry of Random Graphs
, 2013
"... Building on work of Cai, Fürer, and Immerman [CFI92], we show two hardness results for the Graph Isomorphism problem. First, we show that there are pairs of nonisomorphic nvertex graphs G and H such that any sumofsquares (SOS) proof of nonisomorphism requires degree Ω(n). In other words, we sho ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Building on work of Cai, Fürer, and Immerman [CFI92], we show two hardness results for the Graph Isomorphism problem. First, we show that there are pairs of nonisomorphic nvertex graphs G and H such that any sumofsquares (SOS) proof of nonisomorphism requires degree Ω(n). In other words, we show an Ω(n)round integrality gap for the Lasserre SDP relaxation. In fact, we show this for pairs G and H which are not even (1 − 10−14)isomorphic. (Here we say that two nvertex, medge graphs G and H are αisomorphic if there is a bijection between their vertices which preserves at least αm edges.) Our second result is that under the R3XOR Hypothesis [Fei02] (and also any of a class of hypotheses which generalize the R3XOR Hypothesis), the robust Graph Isomorphism is hard. I.e. for every > 0, there is no efficient algorithm which can distinguish graph pairs which are (1 − )isomorphic from pairs which are not even (1 − 0)isomorphic for some universal constant 0. Along the way we prove a robust asymmetry result for random graphs and hypergraphs which may be of independent interest.
Reducing the Number of Fitness Evaluations in Graph Genetic Programming Using a Canonical Graph Indexed Database
 IEEE CONGRESS ON EVOLUTIONARY COMPUTATION
, 2007
"... We describe the genetic programming system GGP operating on graphs and introduce the notion of graph isomorphisms to explain how they influence the dynamics of GP. It is shown empirically how fitness databases can improve the performance of GP and how mapping graphs to a canonical form can increase ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
We describe the genetic programming system GGP operating on graphs and introduce the notion of graph isomorphisms to explain how they influence the dynamics of GP. It is shown empirically how fitness databases can improve the performance of GP and how mapping graphs to a canonical form can increase these improvements by saving considerable evaluation time.
Computational complexity of reconstruction and isomorphism testing for designs and line graphs
 ISSN 00973165. doi: 10.1016/j.jcta.2010.06.006. URL http://dx.doi.org/10.1016/j.jcta.2010
, 2011
"... ar ..."
(Show Context)
Around and Beyond the Isomorphism Problem for Interval Graphs
"... Ever since Reingold’s deterministic logspace algorithm [66] for undirected graph reachability, logspace algorithms for various combinatorial problems have been discovered and it is now a flourishing area of research. Notable examples include special cases of directed graph reachability and planar gr ..."
Abstract
 Add to MetaCart
(Show Context)
Ever since Reingold’s deterministic logspace algorithm [66] for undirected graph reachability, logspace algorithms for various combinatorial problems have been discovered and it is now a flourishing area of research. Notable examples include special cases of directed graph reachability and planar graph isomorphism [23]. In this interesting article, Johannes Köbler, Sebastian Kuhnert and Oleg Verbitsky discuss the structural properties of interval graphs and other technical ingredients that go into their recent logspace isomorphism algorithm for interval graphs, along with some generalizations and new directions.
Algorithms for Extended AlphaEquivalence and Complexity
, 2013
"... Equality of expressions in lambdacalculi, higherorder programming languages, higherorder programming calculi and process calculi is defined as alphaequivalence. Permutability of bindings in letconstructs and structural congruence axioms extend alphaequivalence. We analyse these extended alpha ..."
Abstract
 Add to MetaCart
Equality of expressions in lambdacalculi, higherorder programming languages, higherorder programming calculi and process calculi is defined as alphaequivalence. Permutability of bindings in letconstructs and structural congruence axioms extend alphaequivalence. We analyse these extended alphaequivalences and show that there are calculi with polynomial time algorithms, that a multiplebinding “let ” may make alphaequivalence as hard as finding graphisomorphisms, and that the replication operator in the picalculus may lead to an EXPSPACEhard alphaequivalence problem.