We consider the problem of recovering an unknown k-factor, hidden in a weighted random graph. For k = 1 this is the planted matching problem, while the k = 2 case is closely related to the planted traveling salesman problem. The inference problem is solved by exploiting the information arising from the use of two different distributions for the weights on the edges inside and outside the planted sub-graph. We argue that, in the large size limit, a phase transition can appear between a full and a partial recovery phase as function of the signal-to-noise ratio. We give a criterion for the location of the transition.
Sicuro G., Zdeborova L. (2021). The planted k-factor problem. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 54(17), 1-22 [10.1088/1751-8121/abee9d].
The planted k-factor problem
Sicuro G.;
2021
Abstract
We consider the problem of recovering an unknown k-factor, hidden in a weighted random graph. For k = 1 this is the planted matching problem, while the k = 2 case is closely related to the planted traveling salesman problem. The inference problem is solved by exploiting the information arising from the use of two different distributions for the weights on the edges inside and outside the planted sub-graph. We argue that, in the large size limit, a phase transition can appear between a full and a partial recovery phase as function of the signal-to-noise ratio. We give a criterion for the location of the transition.File | Dimensione | Formato | |
---|---|---|---|
Sicuro_2021_J._Phys._A__Math._Theor._54_175002.pdf
accesso aperto
Tipo:
Versione (PDF) editoriale
Licenza:
Licenza per Accesso Aperto. Creative Commons Attribuzione (CCBY)
Dimensione
1.23 MB
Formato
Adobe PDF
|
1.23 MB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.