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Distributed applications are commonly based on overlay networksinterconnecting their sites so that they can exchange information. For theseoverlay networks to preserve their functionality, they should be able torecover from various problems like membership changes or faults. Variousself-stabilizing overlay networks have already been proposed in recent years,which have the advantage of being able to recover from any illegal state, butnone of these networks can give any guarantees on its functionality while therecovery process is going on. We initiate research on overlay networks that arenot only self-stabilizing but that also ensure that searchability is maintainedwhile the recovery process is going on, as long as there are no corruptedmessages in the system. More precisely, once a search message from node $u$ toanother node $v$ is successfully delivered, all future search messages from $u$to $v$ succeed as well. We call this property monotonic searchability. We showthat in general it is impossible to provide monotonic searchability ifcorrupted messages are present in the system, which justifies the restrictionto system states without corrupted messages. Furthermore, we provide aself-stabilizing protocol for the line for which we can also show monotonicsearchability. It turns out that even for the line it is non-trivial to achievethis property. Additionally, we extend our protocol to deal with nodedepartures in terms of the Finite Departure Problem of Foreback et. al (SSS2014). This makes our protocol even capable of handling node dynamics.  This is the full version of a correspondent paper published at OPODIS'15.

Towards Establishing Monotonic Searchability in Self-Stabilizing Data Structures (full version)