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The broadcast median problem in heterogeneous postal model

Author

Listed:
  • Cheng-Hsiao Tsou

    (National Taiwan University)

  • Gen-Huey Chen

    (National Taiwan University)

  • Hung-I Yu

    (Academia Sinica)

  • Ching-Chi Lin

    (National Taiwan Ocean University)

Abstract

We propose the problem of finding broadcast medians in heterogeneous networks. A heterogeneous network is represented by a graph G=(V,E), in which each edge has a weight that denotes the communication time between its two end vertices. The overall delay of a vertex v∈V(G), denoted as b(v,G), is the minimum sum of the communication time required to send a message from v to all vertices in G. The broadcast median problem consists of finding the set of vertices v∈V(G) with minimum overall delay b(v,G) and determining the value of b(v,G). In this paper, we consider the broadcast median problem following the heterogeneous postal model. Assuming that the underlying graph G is a general graph, we show that computing b(v,G) for an arbitrary vertex v∈V(G) is NP-hard. On the other hand, assuming that G is a tree, we propose a linear time algorithm for the broadcast median problem in heterogeneous postal model.

Suggested Citation

  • Cheng-Hsiao Tsou & Gen-Huey Chen & Hung-I Yu & Ching-Chi Lin, 2013. "The broadcast median problem in heterogeneous postal model," Journal of Combinatorial Optimization, Springer, vol. 25(4), pages 602-616, May.
    • Handle: RePEc:spr:jcomop:v:25:y:2013:i:4:d:10.1007_s10878-012-9493-8
    DOI: 10.1007/s10878-012-9493-8
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