49 research outputs found
How to Wake up Your Neighbors: Safe and Nearly Optimal Generic Energy Conservation in Radio Networks
Recent work [Chang et al., 2018; Chang et al., 2020; Varsha Dani et al., 2021] has shown that it is sometimes feasible to significantly reduce the energy usage of some radio-network algorithms by adaptively powering down the radio receiver when it is not needed. Although past work has focused on modifying specific network algorithms in this way, we now ask the question of whether this problem can be solved in a generic way, treating the algorithm as a kind of black box.
We are able to answer this question in the affirmative, presenting a new general way to modify arbitrary radio-network algorithms in an attempt to save energy. At the expense of a small increase in the time complexity, we can provably reduce the energy usage to an extent that is provably nearly optimal within a certain class of general-purpose algorithms.
As an application, we show that our algorithm reduces the energy cost of breadth-first search in radio networks from the previous best bound of 2^O(?{log n}) to polylog(n), where n is the number of nodes in the network
A key ingredient in our algorithm is hierarchical clustering based on additive Voronoi decomposition done at multiple scales. Similar clustering algorithms have been used in other recent work on energy-aware computation in radio networks, but we believe the specific approach presented here may be of independent interest
On the Power of Choice for k-Colorability of Random Graphs
In an r-choice Achlioptas process, random edges are generated r at a time, and an online strategy is used to select one of them for inclusion in a graph. We investigate the problem of whether such a selection strategy can shift the k-colorability transition; that is, the number of edges at which the graph goes from being k-colorable to non-k-colorable.
We show that, for k ? 9, two choices suffice to delay the k-colorability threshold, and that for every k ? 2, six choices suffice
The Energy Complexity of Broadcast
Energy is often the most constrained resource in networks of battery-powered
devices, and as devices become smaller, they spend a larger fraction of their
energy on communication (transceiver usage) not computation. As an imperfect
proxy for true energy usage, we define energy complexity to be the number of
time slots a device transmits/listens; idle time and computation are free.
In this paper we investigate the energy complexity of fundamental
communication primitives such as broadcast in multi-hop radio networks. We
consider models with collision detection (CD) and without (No-CD), as well as
both randomized and deterministic algorithms. Some take-away messages from this
work include:
1. The energy complexity of broadcast in a multi-hop network is intimately
connected to the time complexity of leader election in a single-hop (clique)
network. Many existing lower bounds on time complexity immediately transfer to
energy complexity. For example, in the CD and No-CD models, we need
and energy, respectively.
2. The energy lower bounds above can almost be achieved, given sufficient
() time. In the CD and No-CD models we can solve broadcast using
energy and energy,
respectively.
3. The complexity measures of Energy and Time are in conflict, and it is an
open problem whether both can be minimized simultaneously. We give a tradeoff
showing it is possible to be nearly optimal in both measures simultaneously.
For any constant , broadcast can be solved in
time with
energy, where is the diameter of the network
Wake Up and Join Me! An Energy-Efficient Algorithm for Maximal Matching in Radio Networks
We consider networks of small, autonomous devices that communicate with each
other wirelessly. Minimizing energy usage is an important consideration in
designing algorithms for such networks, as battery life is a crucial and
limited resource. Working in a model where both sending and listening for
messages deplete energy, we consider the problem of finding a maximal matching
of the nodes in a radio network of arbitrary and unknown topology.
We present a distributed randomized algorithm that produces, with high
probability, a maximal matching. The maximum energy cost per node is , where is the size of the network. The total latency of our algorithm
is time steps. We observe that there exist families of network
topologies for which both of these bounds are simultaneously optimal up to
polylog factors, so any significant improvement will require additional
assumptions about the network topology.
We also consider the related problem of assigning, for each node in the
network, a neighbor to back up its data in case of node failure. Here, a key
goal is to minimize the maximum load, defined as the number of nodes assigned
to a single node. We present a decentralized low-energy algorithm that finds a
neighbor assignment whose maximum load is at most a polylog() factor bigger
that the optimum.Comment: 14 pages, 2 figures, 3 algorithm