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How Well Can Graphs Represent Wireless Interference?

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How Well Can Graphs Represent Wireless Interference?

Content Provider	ACM Digital Library
Author	Halldorsson, Magnus M. Tonoyan, Tigran
Abstract	Efficient use of a wireless network requires that transmissions be grouped into feasible sets, where feasibility means that each transmission can be successfully decoded in spite of the interference caused by simultaneous transmissions. Feasibility is most closely modeled by a signal-to-interference-plus-noise (SINR) formula, which unfortunately is conceptually complicated, being an asymmetric, cumulative, many-to-one relationship. We re-examine how well graphs can capture wireless receptions as encoded in SINR relationships, placing them in a framework in order to understand the limits of such modelling. We seek for each wireless instance a pair of graphs that provide upper and lower bounds on the feasibility relation, while aiming to minimize the gap between the two graphs. The cost of a graph formulation is the worst gap over all instances, and the price of (graph) abstraction is the smallest cost of a graph formulation. We propose a family of conflict graphs that is parameterized by a non-decreasing sub-linear function, and show that with a judicious choice of functions, the graphs can capture feasibility with a cost of O(log* Δ), where Δ is the ratio between the longest and the shortest link length. This holds on the plane and more generally in doubling metrics. We use this to give greatly improved O(log* Δ)-approximation for fundamental link scheduling problems with arbitrary power control. We also explore the limits of graph representations and find that our upper bound is tight: the price of graph abstraction is Ω(log* Δ). In addition, we give strong impossibility results for general metrics, and for approximations in terms of the number of links.
Starting Page	635
Ending Page	644
Page Count	10
File Format	PDF
ISBN	9781450335362
DOI	10.1145/2746539.2746585
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2015-06-14
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Wireless networks Conflict graphs Scheduling Sinr
Content Type	Text
Resource Type	Article

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