On the Tree Search Problem with Non-uniform Costs

  • Ferdinando CicaleseEmail author
  • Balázs Keszegh
  • Bernard Lidický
  • Dömötör Pálvölgyi
  • Tomáš Valla
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9224)


Searching in partially ordered structures has been considered in the context of information retrieval and efficient tree-like indices, as well as in hierarchy based knowledge representation. In this paper we focus on tree-like partial orders and consider the problem of identifying an initially unknown vertex in a tree by asking edge queries: an edge query e returns the component of \(T-e\) containing the vertex sought for, while incurring some known cost c(e).

The Tree Search Problem with Non-Uniform Cost is the following: given a tree T on n vertices, each edge having an associated cost, construct a strategy that minimizes the total cost of the identification in the worst case.

Finding the strategy guaranteeing the minimum possible cost is an NP-complete problem already for input trees of degree 3 or diameter 6. The best known approximation guarantee was an \(O(\log n/\log \log \log n)\)-approximation algorithm of [Cicalese et al. TCS 2012].

We improve upon the above results both from the algorithmic and the computational complexity point of view: We provide a novel algorithm that provides an \(O(\frac{\log n}{\log \log n})\)-approximation of the cost of the optimal strategy. In addition, we show that finding an optimal strategy is NP-hard even when the input tree is a spider of diameter 6, i.e., at most one vertex has degree larger than 2.



We are very grateful to Balázs Patkós for organizing \(5^{\mathrm {th}}\) Emléktábla Workshop where we collaborated on this paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Ferdinando Cicalese
    • 1
    Email author
  • Balázs Keszegh
    • 2
  • Bernard Lidický
    • 3
  • Dömötör Pálvölgyi
    • 4
  • Tomáš Valla
    • 5
  1. 1.Department of Computer ScienceUniversity of VeronaVeronaItaly
  2. 2.Rényi InstituteBudapestHungary
  3. 3.Department of MathematicsIowa State UniversityAmesUSA
  4. 4.Eötvös UniversityBudapestHungary
  5. 5.Faculty of Information TechnologyCzech Technical UniversityPragueCzech Republic

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