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Routing policies used in the Internet can be restrictive, limiting communication between source-destination pairs to one path, when often better alternatives exist. To avoid route flapping, recovery mechanisms may be dampened, making adaptation slow. Unstructured overlays have been widely proposed to mitigate the issues of path and performance failures in the Internet by routing through an indirect-path via overlay peer(s). Choice of alternate-paths in overlay networks is a challenging issue. Ensuring both availability and performance guarantees on alternate paths requires aggressive monitoring of all overlay paths using active probing; this limits scalability when the number of overlay-paths becomes large. An alternate technique to select an overlay-path is to bias its selection based on physical disjointness criteria to bypass the failure on primary-path. In this paper, we show how type-of-relationship (ToR)-Graphs can be used to select maximally-disjoint overlay-paths.