Spanning Trees With Edge Conflicts and Wireless Connectivity

Authors Magnús M. Halldórsson, Guy Kortsarz, Pradipta Mitra, Tigran Tonoyan



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Magnús M. Halldórsson
  • School of Computer Science, Reykjavik University, Iceland
Guy Kortsarz
  • Rutgers University, Camden, NJ, USA
Pradipta Mitra
  • Google Research, New York, USA
Tigran Tonoyan
  • School of Computer Science, Reykjavik University, Iceland

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Magnús M. Halldórsson, Guy Kortsarz, Pradipta Mitra, and Tigran Tonoyan. Spanning Trees With Edge Conflicts and Wireless Connectivity. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 158:1-158:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.ICALP.2018.158

Abstract

We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we seek to model the irregularities seen in actual wireless environments. Not all node pairs may be able to communicate, even if geographically close - thus, the available pairs are specified with a link graph {L}=(V,E). Also, signal attenuation need not follow a nice geometric formula - hence, interference is modeled by a conflict (hyper)graph {C}=(E,F) on the links. The objective is to maximize the efficiency of the communication, or equivalently, to minimize the length of a schedule of the tree edges in the form of a coloring. We find that in spite of all this generality, the problem can be approximated linearly in terms of a versatile parameter, the inductive independence of the interference graph. Specifically, we give a simple algorithm that attains a O(rho log n)-approximation, where n is the number of nodes and rho is the inductive independence, and show that near-linear dependence on rho is also necessary. We also treat an extension to Steiner trees, modeling multicasting, and obtain a comparable result. Our results suggest that several canonical assumptions of geometry, regularity and "niceness" in wireless settings can sometimes be relaxed without a significant hit in algorithm performance.

Subject Classification

ACM Subject Classification
  • Theory of computation → Routing and network design problems
  • Networks → Network design and planning algorithms
Keywords
  • spanning trees
  • wireless capacity
  • aggregation
  • approximation algorithms

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