Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6871969 | Discrete Applied Mathematics | 2016 | 9 Pages |
Abstract
We study the shortest-path broadcast problem in graphs and digraphs, where a message has to be transmitted from a source node s to all the nodes along shortest paths, in the classical telephone model. For both graphs and digraphs, we show that the problem is equivalent to the broadcast problem in layered directed graphs. We then prove that this latter problem is NP-hard, and therefore that the shortest-path broadcast problem is NP-hard in graphs as well as in digraphs. Nevertheless, we prove that a simple polynomial-time algorithm, called MDST-broadcast, based on min-degree spanning trees, approximates the optimal broadcast time within a multiplicative factor 32 in 3-layer digraphs, and O(lognloglogn) in arbitrary multi-layer digraphs. As a consequence, one can approximate the optimal shortest-path broadcast time in polynomial time within a multiplicative factor 32 whenever the source has eccentricity at most 2, and within a multiplicative factor O(lognloglogn) in the general case, for both graphs and digraphs. The analysis of MDST-broadcast is tight, as we prove that this algorithm cannot approximate the optimal broadcast time within a factor smaller than Ω(lognloglogn).
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Pierluigi Crescenzi, Pierre Fraigniaud, Magnus Halldórsson, Hovhannes A. Harutyunyan, Chiara Pierucci, Andrea Pietracaprina, Geppino Pucci,