Given a connected weighted graph G = (V, E), we consider a hypergraph HG = (V, PG) corresponding to the set of all shortest paths in G. For a given real assignment a on V satisfying 0 ≤ a(υ) ≤ 1, a global rounding a with respect to HG is a binary assignment satisfying that |∑υ∈F a(υ) - α(υ)| < 1 for every F ∈ PG. We conjecture that there are at most |V| + 1 global roundings for HG, and also the set of global roundings is an affine independent set. We give several positive evidences for the conjecture.
|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|
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)