Abstract
Consider a connected graph G=(V,E). For a pair of nodes u and v, denote by Muv the set of intermediate nodes of a shortest path between u and v. We are intertested in minimization of the union ∪ u,vεVMuv . We will show that this problem is NP-hard and cannot have polynomial-time ρlnδ-approximation for 0<ρ<1 unless NP ⊆ DTIME(n O(loglogn)) where δ is the maximum node degree of input graph. We will also construct a polynomial-time H(Δ(Δ-1)/2) -approximation for the problem where H(·) is the harmonic function.
| Original language | English |
|---|---|
| Pages (from-to) | 82-85 |
| Number of pages | 4 |
| Journal | Journal of Combinatorial Optimization |
| Volume | 26 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2013 Jul |
Keywords
- Greedy approximation
- Intersection of shortest paths
ASJC Scopus subject areas
- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Theory and Mathematics
- Applied Mathematics
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Cite this
Li, X., Hu, X., & Lee, W. (2013). On the union of intermediate nodes of shortest paths. Journal of Combinatorial Optimization, 26(1), 82-85. https://doi.org/10.1007/s10878-011-9436-9