How Well Can Graphs Represent Wireless Interference?

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-tointerference-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 * ∆), where ∆ 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 * ∆)-approximation for fundamental link scheduling problems with arbitrary power control.We explore the limits of graph representations and find that our upper bound is tight: the price of graph abstraction is Ω(log * ∆). We also give strong impossibility results for general metrics, and for approximations in terms of the number of links.

Wireless Aggregation at Nearly Constant Rate

“…Below, we list some properties of the graphs above that we will use. The proofs can be found in [12,13]. We let χ(G) denote the chromatic number of a graph G, the minimum number of colors needed for coloring the vertices of G such that adjacent vertices get different colors.…”

“…that P (i) ≥ (1 + )βN l α i still holds for all links of the MST. We refer to [17] and [12] for more details. The latter assumption, which corresponds to the assumption of interference-limited networks, is a necessary one there are noise-limited networks for which only the trivial 1/n-rate is possible.…”

“…The usefulness of these conflict graphs stems from the fact that they give a good approximation for feasibility. Moreover they can be used to compute efficient schedules, as shown in [12,13].…”

“…Our results build on the approximation framework of [12,13] that captures the additive SINR interference with appropriate unweighted graphs. This results in very simple scheduling algorithms: they essentially consist of coloring a conflict graph.…”

Deterministic Digital Clustering of Wireless Ad Hoc Networks

“…In the last years the SINR model was extensively studied, both from the perspective of its structural properties [2,20,28] and algorithm design [16,4,10,18,22,35,29,21]. The first work on local broadcast in SINR model by Goussevskaia et al [16] presented an O(∆ log n) randomized algorithm under assumption that density ∆ is known to nodes.…”