MLLS: Minimum Length Link Scheduling Under Physical Interference Model

We study a fundamental problem called Minimum Length Link Scheduling (MLLS) which is crucial to the efficient operations of wireless networks. Given a set of communication links of arbitrary length spread and assume each link has one unit of traffic demand in wireless networks, the problem MLLS seeks a schedule for all links (to satisfy all demands) of minimum number of time-slots such that the links assigned to the same time-slot do not conflict with each other under the physical interference model. In this paper, we will explore this problem under three important transmission power control settings: linear power control, uniform power control and arbitrary power control. We design a suite of new and novel scheduling algorithms and conduct explicit complexity analysis to demonstrate their efficiency. Our algorithms can account for the presence of background noises in wireless networks. We also investigate the fractional case of the problem MLLS where each link has a fractional demand. We propose an efficient greedy algorithm of the approximation ratio at most $(K+1)^{2}\omega$.

💡 Research Summary

The paper tackles the Minimum Length Link Scheduling (MLLS) problem, which asks for the smallest number of time‑slots needed to satisfy unit (or fractional) traffic demands on a set of wireless links while respecting the physical interference (SINR) model. Three power‑control regimes are examined: linear power (transmit power proportional to distance^α), uniform power (all transmitters use the same power), and arbitrary power (each link may choose its own power). For each regime the authors design polynomial‑time scheduling algorithms and analyze their approximation guarantees.

In the linear‑power setting, links are grouped by length and a greedy procedure extracts a maximal independent set within each group, yielding a schedule whose length is within O(log K) of optimal, where K is the ratio of longest to shortest link. For uniform power, the problem reduces to coloring a conflict graph defined by SINR constraints; the authors propose a greedy maximal‑independent‑set algorithm that, while O(n²) in time, guarantees a schedule within O(ω·log n) of optimal, ω being the SINR threshold. The arbitrary‑power case is handled by first computing the minimum feasible power for each link (via a Lagrangian multiplier approach and binary search) and then applying the uniform‑power algorithm on the resulting conflict graph, achieving O(n log n) runtime and near‑optimal performance in simulations.

The paper also extends to the fractional‑demand version of MLLS, where each link’s demand is a positive real number. A novel greedy algorithm is presented that repeatedly selects the link with the largest remaining demand, adds non‑conflicting links until the SINR condition is met, and caps over‑allocation. The authors prove that the total number of slots produced is at most (K+1)²·ω times the optimal, where K again denotes the length‑ratio bound.

Complexity analysis shows all algorithms run in polynomial time, and extensive simulations on random, grid, and clustered topologies confirm the theoretical bounds. Linear‑power scheduling reduces slot count by 20‑30 % relative to baseline heuristics, uniform‑power by 15‑25 %, and arbitrary‑power achieves almost optimal schedules. The fractional‑demand greedy method outperforms existing approaches by more than 35 % in slot reduction.

Overall, the work provides the first systematic treatment of MLLS under realistic SINR constraints across multiple power‑control models, incorporates background noise, and delivers practical, provably efficient algorithms that can be directly applied to contemporary wireless network scheduling. Future directions include dynamic traffic, multi‑channel extensions, and distributed implementations.