On Fundamental Bounds on Failure Identifiability by Boolean Network Tomography

Tight Bounds for Maximal Identifiability of Failure Nodes in Boolean Network Tomography

“…With the aim of optimizing the maximal identifiability of a given network many recent works on node identifiability [16,15,2] focus on heuristics/strategies toproperly increase the number monitors and to decide where to place them on the internal nodes of the network. However structural limitations due to the network topology might affect the feasibility of such approaches.…”

“…Given a graph G = (V, E) and a monitor placement χ = (m, M) we denote by P(G|χ) the set of all distinct paths from a node in m to a node in M. Let P be a set of paths over a set of nodes N . Following [16] we define: In [16], and later in [2], k-identifiability was used to localize failure within specific subsets S of V . That definition is given restricting the condition U △W = ∅ to (U ∩ S)△(W ∩ S) = ∅.…”

“…Definition 6.1. ( [9,2]) A set of paths P is routing consistent if any two distinct paths p and p ′ in P and any distinct nodes u and w traversed by both paths (if any) p and p ′ follow the same subpath between u and w.…”

Topology Agnostic Bounds on Minimum Requirements for Network Failure Identification

“…In this work, we provide topology-agnostic lower-bounds to the minimum number of measurement paths which are necessary to guarantee identifiability to a desired number of nodes. Such bounds represent the dual solution to the optimization problem studied in [4], where we introduced upper-bounds to the maximum number of identifiable nodes given a number of monitoring paths. In contrast with existing literature, we propose theoretical lower-bounds that cannot be violated, independently of the specific characteristics of the topology.…”

“…The bounds formulations are only based on the number of nodes to identify, on high level routing consistency properties (arbitrary and consistent routing), and on QoS requirements, expressed in terms of maximum allowed path length. Motivated by the need to complement the analysis of [4], our bounds are a useful tool to measure the capability of a monitored topology to efficiently identify the status of its components. Implementing a monitoring system comes with the cost of installing monitors on the nodes of a network and of traffic caused by path probing; with this work, we aim at providing fundamental guidelines and minimal requirements for achieving the desired level of network identifiability (e.g., number of identifiable nodes).…”