Broadcasting in Heterogeneous Tree Networks

Abstract

Abstract. We consider the broadcasting problem in heterogeneous tree networks. A heterogeneous tree network is represented by a weighted tree T = (V, E) such that the weight of each edge denotes the communication time between the two end vertices. The broadcasting problem is to find a broadcast center such that the maximum communication time from the broadcast center to all vertices is minimized. In this paper, we propose a linear time algorithm for the broadcasting problem in a heterogeneous tree network following the postal model. As a byproduct of the algorithm, we can compute in linear time the broadcasting time of any vertex in the tree, i.e., the maximum time required to transmit messages from the vertex to every other vertex in the tree. Furthermore, an optimal sequence by which the broadcast center broadcasts its messages to all vertices in T can also be determined in linear time.

A matheuristic approach for the minimum broadcast time problem using a biased random‐key genetic algorithm

“…In some special situations, for instance, when $$|{V}_{0}|=1$$ and the graph is a tree (Koh and Tcha, 1991; Su et al., 2010) or a complete grid (Wojciechowska and Scoy, 1999), the MBT can be optimality solved in polynomial time. For arbitrary graphs, the exact approaches include a dynamic programming algorithm (Scheuermann and Wu, 1984) and the ILP models presented by de Sousa et al.…”

“…SCHA iteratively calls function MBT‐Tree (line 5), which is an algorithm proposed by Su et al. (2010); Koh and Tcha (1991) for finding the MBT on tree graphs. Hence, SCHA finds the optimal MBT by calculating the MBT of each tree in the forest, and then returning the greatest MBT among these trees.…”

Computational Aspects of Carbon and Boron Nanotubes

“…The broadcasting problem is NP-complete for 3-regular planar graphs and a constant deadline k ≥ 2 [ 27 ]. This problem is studied almost on all kinds of architectures and systems for example, wireless sensor networks [ 28 ], cellular networks of triangular systems [ 29 ], heterogeneous tree networks [ 30 ], honeycomb networks [ 31 ], higher dimensional hexagonal networks [ 32 ], mesh architectures [ 33 ], star graphs [ 34 ], de Bruijn Networks [ 35 ], hypercubes [ 36 ].…”