The Forgiving Graph: a distributed data structure for low stretch under adversarial attack

Abstract

We consider the problem of self-healing in peer-to-peer networks that are under repeated attack by an omniscient adversary. We assume that, over a sequence of rounds, an adversary either inserts a node with arbitrary connections or deletes an arbitrary node from the network. The network responds to each such change by quick "repairs," which consist of adding or deleting a small number of edges. These repairs essentially preserve closeness of nodes after adversarial deletions, without increasing node degrees by too much, in the following sense. At any point in the algorithm, nodes v and w whose distance would have been in the graph formed by considering only the adversarial insertions (not the adversarial deletions), will be at distance at most log n in the actual graph, where n is the total number of vertices seen so far. Similarly, at any point, a node v whose degree would have been d in the graph with adversarial insertions only, will have degree at most 3d in the actual graph. Our distributed data structure, which we call the Forgiving

Local-on-Average Distributed Tasks

“…In this setting, the distributed local algorithm is allowed to add edges to the structure following adversarial removal of vertices or edges, in order to preserve certain graph properties (e.g., diameter, maximum degree, expansion) of the original network (i.e., before the attack), cf. [26,50,51]. Note that this approach requires the network to be reconfigurable, in the sense that it should be possible to change the network topology.…”

Intrusion detection and self healing model for network security

“…In each step, the adversary either deletes or adds a node [16]. After each deletion, the algorithm gets to add some new edges to the graph, as well as deleting old ones.…”

Towards a Universal Approach for the Finite Departure Problem in Overlay Networks

“…A basic prerequisite for an overlay network which allows all pairs of nodes to exchange information is that it is connected, and a fundamental problem for overlay networks is to preserve connectivity while nodes are leaving, i.e., the nodes requesting to leave the overlay network are eventually excluded from it without disconnecting any staying nodes. If the overlay is in a well-defined state, scenarios in which the rate of node departures and arrivals is limited have already been studied [1,5,7]. However, due to permanent or transient failures a distributed system may rarely be in an ideal state, so it would be desirable to find self-stabilizing protocols for the exclusion of leaving nodes, i.e., from any initial state connectivity is preserved.…”