Abstract
Given a connected weighted graph G = (V, E), we consider a hypergraph HG = (V, script P sign 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 a with respect to HG is a binary assignment satisfying that |Σu∈Fa(v) - α(v)| - < 1 for every F ∈ script P sign G. 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.
Original language | English |
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Pages (from-to) | 425-437 |
Number of pages | 13 |
Journal | Theoretical Computer Science |
Volume | 325 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2004 Oct 6 |
Event | Selected Papers from COCOON 2003 - Big Sky, United States Duration: 2003 Jul 25 → 2003 Jul 28 |
Keywords
- Combinatorics
- Discrepancy
- Graph
- Hypergraph
- Rounding
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)