A Deterministic Algorithm for Online Steiner Tree Leasing

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10389)

Abstract

We study the Online Steiner Tree Leasing (OSTL) problem, defined in a weighted undirected graph with a distinguished root node r. There is a known set \(\mathcal {L}\) of available lease types, where each type \(\ell \in \mathcal {L}\) is characterized by its duration \(D_\ell \) and cost factor \(C_\ell \). As an input, an online algorithm is given a sequence of terminals and has to connect them to the root r using leased edges. An edge of length d can be leased using lease type \(\ell \) for cost \(C_\ell \cdot d\) and remains valid for time \(D_\ell \).

The OSTL problem contains the online Steiner tree and the single-source rent-or-buy problems as specific subcases. We present the first deterministic online algorithm for OSTL, whose competitive ratio is \(O(|\mathcal {L}| \cdot \log k)\), where k is the number of different terminals in the input. The currently best randomized algorithm attains the ratio of \(O(\log |\mathcal {L}| \cdot \log n)\), where \(n \ge k\) is the number of nodes in the graph.

Keywords

Steiner tree Leasing Competitive analysis Online algorithms 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Marcin Bienkowski
    • 1
  • Artur Kraska
    • 1
  • Paweł Schmidt
    • 1
  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland

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