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 nearlinear 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.
BibTeX  Entry
@InProceedings{halldrsson_et_al:LIPIcs:2018:9162,
author = {Magn{\'u}s M. Halld{\'o}rsson and Guy Kortsarz and Pradipta Mitra and Tigran Tonoyan},
title = {{Spanning Trees With Edge Conflicts and Wireless Connectivity}},
booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
pages = {158:1158:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770767},
ISSN = {18688969},
year = {2018},
volume = {107},
editor = {Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9162},
URN = {urn:nbn:de:0030drops91627},
doi = {10.4230/LIPIcs.ICALP.2018.158},
annote = {Keywords: spanning trees, wireless capacity, aggregation, approximation algorithms}
}
Keywords: 

spanning trees, wireless capacity, aggregation, approximation algorithms 
Collection: 

45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) 
Issue Date: 

2018 
Date of publication: 

04.07.2018 