TY - GEN

T1 - Efficient distributed source detection with limited bandwidth

AU - Lenzen, Christoph

AU - Peleg, David

PY - 2013

Y1 - 2013

N2 - Given a simple graph G = (V, E) and a set of sources SCV, denote for each node v ε V by L(∞) the lexicographically ordered list of distance/source pairs (d(s, v), s), where s ε S. For integers d, k ε NU{∞}, we consider the source detection, or (S, d, k)-detection task, requiring each node v to learn the first k entries of L(∞) (if for all of them d(s, v) ≤ d) or all entries (d(s, v),s) ε L (∞), 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 ε 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 C(logn) 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.

AB - Given a simple graph G = (V, E) and a set of sources SCV, denote for each node v ε V by L(∞) the lexicographically ordered list of distance/source pairs (d(s, v), s), where s ε S. For integers d, k ε NU{∞}, we consider the source detection, or (S, d, k)-detection task, requiring each node v to learn the first k entries of L(∞) (if for all of them d(s, v) ≤ d) or all entries (d(s, v),s) ε L (∞), 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 ε 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 C(logn) 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.

KW - Additive spanners

KW - All-to-all shortest paths

KW - Bellmann-Ford

KW - Compact routing

KW - Concurrent incomplete breadth-first search

KW - Distance and diameter computation

UR - http://www.scopus.com/inward/record.url?scp=84883541032&partnerID=8YFLogxK

U2 - 10.1145/2484239.2484262

DO - 10.1145/2484239.2484262

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AN - SCOPUS:84883541032

SN - 9781450320658

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 375

EP - 382

BT - PODC 2013 - Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing

T2 - 2013 ACM Symposium on Principles of Distributed Computing, PODC 2013

Y2 - 22 July 2013 through 24 July 2013

ER -