Terrorist attacks all across the world have become a major source of concern for almost all national governments. The United States Department of State's Bureau of Counter-Terrorism, maintains a list of 66 terrorist organizations spanning the entire world. Actively monitoring a large number of organizations and their members, require considerable amounts of resources on the part of law enforcement agencies. Oftentimes, the law enforcement agencies do not have adequate resources to monitor these organizations and their members effectively. On multiple incidences of terrorist attacks in recent times across Europe, it has been observed that the perpetrators of the attack were in the suspect databases of the law enforcement authorities, but weren't under active surveillance at the time of the attack, due to resource limitations on the part of the authorities. As the suspect databases in various countries are very large, and it takes significant amount of technical and human resources to monitor a suspect in the database, monitoring all the suspects in the database may be an impossible task. In this paper, we propose a novel terror network monitoring approach that will significantly reduce the resource requirement of law enforcement authorities, but still provide the capability of uniquely identifying a suspect in case the suspect becomes active in planning a terrorist attack. The approach relies on the assumption that, when an individual becomes active in planning a terrorist attack, his her friends associates will have some inkling of the individuals plan. Accordingly, even if the individual is not under active surveillance by the authorities, but the individual's friends associates are, then the individual planning the attack can be uniquely identified. We apply our techniques on various real-world terror network datasets and show the effectiveness of our approach.
A special case, where only a subset of nodes needs a unique code, can be modeled with a bipartite graph, and this version of Identifying Codes is called Discriminating Codes'' and was studied in @cite_12 . This special case is relevant for our study as, our problem formulation of individual to organization network requires us to find the unique signatures of all nodes of one side of bi-partition of a bipartite graph, by selecting only a subset of the nodes in the other side of bi-partition. This formulation corresponds directly to Discriminating Codes''.
@cite_12
2135290452 2054573207 2009380125 2107282727
In the study of deterministic distributed algorithms it is commonly assumed that each node has a unique O(log n)-bit identifier. We prove that for a general class of graph problems, local algorithms (constant-time distributed algorithms) do not need such identifiers: a port numbering and orientation is sufficient. Our result holds for so-called simple PO-checkable graph optimisation problems; this includes many classical packing and covering problems such as vertex covers, edge covers, matchings, independent sets, dominating sets, and edge dominating sets. We focus on the case of bounded-degree graphs and show that if a local algorithm finds a constant-factor approximation of a simple PO-checkable graph problem with the help of unique identifiers, then the same approximation ratio can be achieved on anonymous networks. As a corollary of our result and by prior work, we derive a tight lower bound on the local approximability of the minimum edge dominating set problem. Our main technical tool is an algebraic construction of homogeneously ordered graphs: We say that a graph is (α,r)-homogeneous if its nodes are linearly ordered so that an α fraction of nodes have pairwise isomorphic radius-r neighbourhoods. We show that there exists a finite (α,r)-homogeneous 2k-regular graph of girth at least g for any α Do unique node identifiers help in deciding whether a network G has a prescribed property P? We study this question in the context of distributed local decision, where the objective is to decide whether G has property P by having each node run a constant-time distributed decision algorithm. In a yes-instance all nodes should output yes, while in a no-instance at least one node should output no. Recently, (OPODIS 2012) gave several conditions under which identifiers are not needed, and they conjectured that identifiers are not needed in any decision problem. In the present work, we disprove the conjecture. More than that, we analyse two critical variations of the underlying model of distributed computing: (B): the size of the identifiers is bounded by a function of the size of the input network, (¬B): the identifiers are unbounded, (C): the nodes run a computable algorithm, (¬C): the nodes can compute any, possibly uncomputable function. While it is easy to see that under (¬B, ¬C) identifiers are not needed, we show that under all other combinations there are properties that can be decided locally if and only if identifiers are present. Consider a connected undirected bipartite graph G=([email protected]?A,E), with no edges inside I or A. For any vertex [email protected]?V, let N(v) be the set of neighbours of v. A code [email protected]?A is said to be discriminating if all the sets N(i)@?C, [email protected]?I, are nonempty and distinct. We study some properties of discriminating codes in particular classes of bipartite graphs, namely trees and, more generally, (bipartite) planar graphs. Given a simple graph G=(V,E) and a set of sources S ⊆ V, denote for each node ν e V by Lν(∞) the lexicographically ordered list of distance source pairs (d(s,v),s), where s ∈ S. For integers d,k ∈ N∪ ∞ , we consider the source detection, or (S,d,k)-detection task, requiring each node v to learn the first k entries of Lν(∞) (if for all of them d(s,v) ≤ d) or all entries (d(s,v),s) ∈ Lν(∞) satisfying that d(s,v) ≤ d (otherwise). Solutions to this problem provide natural generalizations of concurrent breadth-first search (BFS) tree constructions. For example, the special case of k=∞ requires each source s ∈ S to build a complete BFS tree rooted at s, whereas the special case of d=∞ and S=V requires constructing a partial BFS tree comprising at least k nodes from every node in V. In this work, we give a simple, near-optimal solution for the source detection task in the CONGEST model, where messages contain at most O(log n) bits, running in d+k rounds. We demonstrate its utility for various routing problems, exact and approximate diameter computation, and spanner construction. For those problems, we obtain algorithms in the CONGEST model that are faster and in some cases much simpler than previous solutions.