Considering the isolation set problem

Given a network, G = [N, E] the Isolation Set Problem (ISP) finds the set of arcs, D ⊆ E, that when removed will separate a predefined set of r distinguished nodes [2]. This involves eliminating connections from a specific set of nodes to the rest of a network. In our increasingly interconnected network-centric world, this might be isolating various units from Headquarters; isolating a portion of a computer network to disrupt communications or to quarantine a virus or some other form of cyber attack; or isolating a cell or sub-group in a terrorist or “dark” network, for example.The research presented here reviews the ISP, addresses the totally unimodular character of the ISP, offers a node consolidation method, provides for the inclusion of nodes in the cut sets, and introduces resource constraints to the ISP. An example is presented to illustrate the approach.

► The Isolation Set Problem is reviewed and characteristics of the problem are addressed.
► Several approaches, including node consolidation, node inclusion, and adding resource constraints are presented.
► Approach can aid in identifying critical connections and member of a network.