Given a connected weighted graph G = (V, E), we consider a hypergraph H G = (V, P G) corresponding to the set of all shortest paths in G. For a given real assignment a on V satisfying 0 ≤ a(v) ≤ 1, a global rounding α with respect to H G is a binary assignment satisfying that |∑ v∈Fa(v)-α(v)| < 1 for every F ∈ P G. Asano et al  conjectured that there are at most |V|+1 global roundings for H G. In this paper, we prove that the conjecture holds if G is an outerplanar graph. Moreover, we give a polynomial time algorithm for enumerating all the global roundings of an outerplanar graph.
|Number of pages||9|
|Journal||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Publication status||Published - 2003 Dec 1|
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)