22 research outputs found
Universal Framework for Wireless Scheduling Problems
An overarching issue in resource management of wireless networks is assessing their capacity: How much communication can be achieved in a network, utilizing all the tools available: power control, scheduling, routing, channel assignment and rate adjustment? We propose the first framework for approximation algorithms in the physical model that addresses these questions in full, including rate control. The approximations obtained are doubly logarithmic in the link length and rate diversity. Where previous bounds are known, this gives an exponential improvement.
A key contribution is showing that the complex interference relationship of the physical model can be simplified into a novel type of amenable conflict graphs, at a small cost. We also show that the approximation obtained is provably the best possible for any conflict graph formulation
The Price of Local Power Control in Wireless Scheduling
We consider the problem of scheduling wireless links in the physical model, where we seek an assignment of power levels and a partition of the given set of links into the minimum number of subsets satisfying the signal-to-interference-and-noise-ratio (SINR) constraints. Specifically, we are interested in the efficiency of local power assignment schemes, or oblivious power schemes, in approximating wireless scheduling. Oblivious power schemes are motivated by networking scenarios when power levels must be decided in advance, and not as part of the scheduling computation.
We present the first O(log log Delta)-approximation algorithm, which is known to be best possible (in terms of Delta) for oblivious power schemes, where Delta is the longest to shortest link length ratio. We achieve this by representing interference by a conflict graph, which allows the application of graph-theoretic results for a variety of related problems, including the weighted capacity problem. We explore further the contours of approximability and find the choice of power assignment matters; that not all metric spaces are equal; and that the presence of weak links makes the problem harder. Combined, our results resolve the price of local power for wireless scheduling, or the value of allowing unfettered power control
Local Conflict Coloring Revisited: Linial for Lists
Linial's famous color reduction algorithm reduces a given -coloring of a
graph with maximum degree to a -coloring, in a
single round in the LOCAL model. We show a similar result when nodes are
restricted to choose their color from a list of allowed colors: given an
-coloring in a directed graph of maximum outdegree , if every node
has a list of size from a color space then they can select a color
in two rounds in the LOCAL model. Moreover, the communication of a node
essentially consists of sending its list to the neighbors. This is obtained as
part of a framework that also contains Linial's color reduction (with an
alternative proof) as a special case. Our result also leads to a defective list
coloring algorithm. As a corollary, we improve the state-of-the-art truly local
-list coloring algorithm from Barenboim et al. [PODC'18] by slightly
reducing the runtime to and significantly
reducing the message size (from huge to roughly ). Our techniques are
inspired by the local conflict coloring framework of Fraigniaud et al.
[FOCS'16].Comment: to appear at DISC 202
Data Dissemination in Unified Dynamic Wireless Networks
We give efficient algorithms for the fundamental problems of Broadcast and
Local Broadcast in dynamic wireless networks. We propose a general model of
communication which captures and includes both fading models (like SINR) and
graph-based models (such as quasi unit disc graphs, bounded-independence
graphs, and protocol model). The only requirement is that the nodes can be
embedded in a bounded growth quasi-metric, which is the weakest condition known
to ensure distributed operability. Both the nodes and the links of the network
are dynamic: nodes can come and go, while the signal strength on links can go
up or down.
The results improve some of the known bounds even in the static setting,
including an optimal algorithm for local broadcasting in the SINR model, which
is additionally uniform (independent of network size). An essential component
is a procedure for balancing contention, which has potentially wide
applicability. The results illustrate the importance of carrier sensing, a
stock feature of wireless nodes today, which we encapsulate in primitives to
better explore its uses and usefulness.Comment: 28 pages, 2 figure