Improved algorithms for latency minimization in wireless networks

Abstract

a b s t r a c tIn the interference scheduling problem, one is given a set of n communication requests described by source-destination pairs of nodes from a metric space. The nodes correspond to devices in a wireless network. Each pair must be assigned a power level and a color such that the pairs in each color class can communicate simultaneously at the specified power levels. The feasibility of simultaneous communication within a color class is defined in terms of the Signal to Interference plus Noise Ratio (SINR) that compares the strength of a signal at a receiver to the sum of the strengths of other signals. The objective is to minimize the number of colors as this corresponds to the time needed to schedule all requests.We introduce an instance-based measure of interference, denoted by I, that enables us to improve on previous results for the interference scheduling problem. We prove the upper and lower bounds in terms of I on the number of steps needed for scheduling a set of requests. For general power assignments, we prove a lower bound of Ω(I/(log ∆ log n)) steps, where ∆ denotes the aspect ratio of the metric. When restricting to the twodimensional Euclidean space (as in the previous work) the bound improves to Ω(I/ log ∆).Alternatively, when restricting to linear power assignments, the lower bound improves even to Ω(I). The lower bounds are complemented by an efficient algorithm computing a schedule for linear power assignments using only O(I log n) steps. A more sophisticated algorithm computes a schedule using even only O(I + log 2 n) steps. For dense instances in the two-dimensional Euclidean space, this gives a constant factor approximation for scheduling under linear power assignments, which shows that the price for using linear (and, hence, energy-efficient) power assignments is bounded by a factor of O(log ∆).In addition, we extend these results for single-hop scheduling to multi-hop scheduling and combined scheduling and routing problems, where our analysis generalizes the previous results towards general metrics and improves on the previous approximation factors.

Distributed Algorithms for End-to-End Packet Scheduling in Wireless Ad Hoc Networks

“…Our results give the first distributed polylogarithmic approximation algorithms for end-to-end packet scheduling in wireless networks. Following the conference version of this article , our approach has been extended to a number of other interference models for wireless networks, including the SINR model, such as Fanghänel et al [2009], and Chafekar et al [2007]. These papers have developed a notion of congestion that allows the problem to be reduced to our approach.…”

“…Chafekar et al [2007] define a congestion measure that considers SLTs of comparable length, leading to an approximation bound that depends on the aspect ratio, that is, the ratio of the lengths of the longest to the shortest link. Fanghänel et al [2009] define a slightly different notion of congestion, which leads to better approximation bounds, which hold for other metrics than just Euclidean. A unique aspect of the SINR model is power control, which requires specifying the transmission power level for each link.…”

Efficient Link Scheduling Solutions for the Internet of Things Under Rayleigh Fading

“…Then, Goussevskaia et al gave a NP-hard proof for the link scheduling problem under the SINR model [16]. Subsequently, attentions for designing effective link scheduling algorithms shifted to a more realistic model using SINR, such as centralized (e.g., [15], [17]- [21]) and distributed algorithms (e.g., [22]- [28]).…”

Wireless Network Algorithmics

“…NP-hardness was established in [22]. Constant approximation for the One-shot Link Scheduling problem were given for uniform power [21], linear power [19,58], fixed power assignments [29], and arbitrary power control [40]. This was extended to distributed learning [4,16], admission control in cognitive radio [30], link rates [41], multiple channels [7,59], spectrum auctions [35,36], changing spectrum availability [13], jamming [14], and MIMO [61].…”