Efficient distributed source detection with limited bandwidth
Christoph Lenzen, David Peleg · 2013
Given a simple graph G=(V,E) and a set of sources S ⊆ V, denote for each node ν ε 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.