
Graph Matching with PartiallyCorrect Seeds
The graph matching problem aims to find the latent vertex correspondence...
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Seeded Graph Matching via Large Neighborhood Statistics
We study a well known noisy model of the graph isomorphism problem. In t...
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Efficient random graph matching via degree profiles
Random graph matching refers to recovering the underlying vertex corresp...
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Seedless Graph Matching via Tail of Degree Distribution for Correlated ErdosRenyi Graphs
The graph matching problem refers to recovering the nodetonode corresp...
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On the Performance of a Canonical Labeling for Matching Correlated ErdősRényi Graphs
Graph matching in two correlated random graphs refers to the task of ide...
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Linear Work Generation of RMAT Graphs
RMAT is a simple, widely used recursive model for generating `complex n...
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Stochastic Matching with Few Queries: (1ε) Approximation
Suppose that we are given an arbitrary graph G=(V, E) and know that each...
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The Power of Dhops in Matching PowerLaw Graphs
This paper studies seeded graph matching for powerlaw graphs. Assume that two edgecorrelated graphs are independently edgesampled from a common parent graph with a powerlaw degree distribution. A set of correctly matched vertexpairs is chosen at random and revealed as initial seeds. Our goal is to use the seeds to recover the remaining latent vertex correspondence between the two graphs. Departing from the existing approaches that focus on the use of highdegree seeds in 1hop neighborhoods, we develop an efficient algorithm that exploits the lowdegree seeds in suitablydefined Dhop neighborhoods. Specifically, we first match a set of vertexpairs with appropriate degrees (which we refer to as the first slice) based on the number of lowdegree seeds in their Dhop neighborhoods. This significantly reduces the number of initial seeds needed to trigger a cascading process to match the rest of the graphs. Under the ChungLu random graph model with n vertices, max degree Θ(√(n)), and the powerlaw exponent 2<β<3, we show that as soon as D> 4β/3β, by optimally choosing the first slice, with high probability our algorithm can correctly match a constant fraction of the true pairs without any error, provided with only Ω((log n)^4β) initial seeds. Our result achieves an exponential reduction in the seed size requirement, as the best previously known result requires n^1/2+ϵ seeds (for any small constant ϵ>0). Performance evaluation with synthetic and real data further corroborates the improved performance of our algorithm.
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