Abstract
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 [1] 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.
| Original language | English |
|---|---|
| Pages (from-to) | 425-433 |
| Number of pages | 9 |
| Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
| Volume | 2906 |
| Publication status | Published - 2003 Dec 1 |
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)