A Scheduling Problem in Multihop Networks
Kaoru Watanabe, Hiroshi Tamura, Keisuke Nakano, Masakazu Sengoku · Institutional Repositories DataBase (IRDB) · 1998
In a multihop network, radio packets are often relayed through inter-mediate stations (repeaters) in order to transfer a radio packet from a source to its destination. We consider a scheduling problem in a multihop network using a graphtheoretical model. Let D=(V,A) be the digraph with a vertex set V and an arc set A. Let f be a labeling of positive integers on the arcs of A. The value of f(u,v) means a frequency band assigned on the link from u to v. We call f antitransitive if f(u,v) ≠ f(v,w) for any adjacent arcs (u,v) and (v,w) of D. The minimum antitransitive-labeling problem is the problem of finding a minimum antitransitive-labeling such that the number of integers assigned in an antitransitive labeling is minimum. In this paper, we prove that this problem is NP-hard, and we propose a simple distributed approximation algorithm for it.