منابع مشابه
On convex relaxation of graph isomorphism.
We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a convex quadratic program, in which the space of permutations is replaced by the space of doubly stochastic matrices. However, the applicability of such a rela...
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In this work a convex relaxation of a subgraph isomorphism problem is proposed, which leads to a new lower bound that can provide a proof that a subgraph isomorphism between two graphs can not be found. The bound is based on a semidefinite programming relaxation of a combinatorial optimisation formulation for subgraph isomorphism and is explained in detail. We consider subgraph isomorphism prob...
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We show that a nontrivial graph isomorphism problem of two undirected graphs, and more generally, the permutation similarity of two given n × n matrices, is equivalent to equalities of volumes of the induced three convex bounded polytopes intersected with a given sequence of balls, centered at the origin with radii ti ∈ (0, √ n − 1), where {ti} is an increasing sequence converging to √ n − 1. T...
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In this paper we propose a concavely regularized convex relaxation based graph matching algorithm. The graph matching problem is firstly formulated as a constrained convex quadratic program by relaxing the feasible set from the permutation matrices to doubly stochastic matrices. To gradually push the doubly stochastic matrix back to be a permutation one, an objective function is constructed by ...
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Graph isomorphism (GI) is one of the few remaining problems in NP whose complexity status couldn’t be solved by classifying it as being either NP-complete or solvable in P. Nevertheless, efficient (polynomial-time or even NC) algorithms for restricted versions of GI have been found over the last four decades. Depending on the graph class, the design and analysis of algorithms for GI use tools f...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 2015
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.1401651112