The hardness of approximation: gap location
Computational Complexity
The hardness of approximate optima in lattices, codes, and systems of linear equations
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
Some optimal inapproximability results
Journal of the ACM (JACM)
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The Approximability of Constraint Satisfaction Problems
SIAM Journal on Computing
Packing triangles in bounded degree graphs
Information Processing Letters
Embeddings and non-approximability of geometric problems
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Rounding Techniques for the MAX 2-SAT and MAX DI-CUT Problems
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Isomorphism of graphs with bounded eigenvalue multiplicity
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Optimal Inapproximability Results for Max-Cut and Other 2-Variable CSPs?
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Polynomial-time algorithms for permutation groups
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Parallel algorithms for permutation groups and graph isomorphism
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
A survey of graph edit distance
Pattern Analysis & Applications
Approximation algorithms for graph homomorphism problems
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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We study optimization versions of Graph Isomorphism. Given two graphs G1,G2, we are interested in finding a bijection π from V(G1) to V(G2) that maximizes the number of matches (edges mapped to edges or non-edges mapped to non-edges). We give an nO(logn) time approximation scheme that for any constant factor αα-approximation. We prove this by combining the nO(logn) time additive error approximation algorithm of Arora et al. [Math. Program., 92, 2002] with a simple averaging algorithm. We also consider the corresponding minimization problem (of mismatches) and prove that it is NP-hard to α-approximate for any constant factor α. Further, we show that it is also NP-hard to approximate the maximum number of edges mapped to edges beyond a factor of 0.94. We also explore these optimization problems for bounded color class graphs which is a well studied tractable special case of Graph Isomorphism. Surprisingly, the bounded color class case turns out to be harder than the uncolored case in the approximate setting.