Efficient distributed source detection with limited bandwidth

Abstract

Given a simple graph G = (V, E) and a set of sources S ⊆ V , denote for each node v ∈ V by L (∞) v 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,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.

Fast Partial Distance Estimation and Applications

“…Technical Discussion. Our key tool is a generalization of the (S, h, σ)-detection problem, introduced in [10]. 2 The problem is defined as follows.…”

“…Given a graph with a distinguished set of source nodes S, the task is for each node to find the distances to its closest σ ∈ N sources within h ∈ N hops (the formal definition is given in Section 2.5). In [10] it is shown that this task can be solved in h + σ rounds on unweighted graphs. The main new ingredient in all our results is an algorithm that, within a comparable running time, produces an approximate solution to (S, h, σ)-detection in weighted graphs.…”

“…The result is (1 + ε)-approximate distances to all sources in O((h + |S|) log 2 n/ε 2 ) rounds w.h.p. We replace this part of the algorithm with the deterministic source detection algorithm from [10], obtaining a deterministic algorithm of running time O((h + |S|) log n). This, using S = V and h = σ = n, has the immediate corollary of a deterministic (1 + o(1))-approximation to APSP.…”

Algebraic Methods in the Congested Clique

“…Specifically, many algorithms and lower bounds were given for computing and approximating graph distances in this setting [23,31,39,40,45,47,48,57,61,62]. Some lower bounds apply even for graphs of small diameter; however, these lower bound constructions boil down to graphs that contain bottleneck edges limiting the amount of information that can be exchanged between different parts of the graph quickly.…”

Distributed distance computation and routing with small messages

“…At the heart of any routing protocol lies the computation of short paths between all possible node pairs, which is another This article is based on preliminary results appearing at conferences [32,34,35]. This work has been supported by the Swiss National Science Foundation (SNSF) fundamental challenge that occurs in a multitude of optimization problems.…”