On the union of intermediate nodes of shortest paths

Xiang Li, Xiaodong Hu, Wonjun Lee

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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 languageEnglish
Pages (from-to)82-85
Number of pages4
JournalJournal of Combinatorial Optimization
Issue number1
Publication statusPublished - 2013 Jul

Bibliographical note

Funding Information:
Acknowledgements This research was jointly sponsored by MEST, Korea under WCU (R33-2008-000-10044-0), MEST, Korea under Basic Science Research Program (2011-0012216), and MKE, Korea under ITRC NIPA-2011-(C1090-1121-0008).


  • 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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