[Paper Review] Nearly Optimal Scheduling of Wireless Ad Hoc Networks in Polynomial Time

Alper Köse, Noyan Evirgen+3 more|arXiv (Cornell University)|Dec 2, 2017

Mobile Ad Hoc Networks13 references3 citations

TL;DR

This paper proposes a polynomial-time scheduling method for wireless ad hoc networks by transforming general conflict graphs into claw-free graphs through strategic edge additions, enabling throughput-optimal scheduling via maximum weighted independent set (MWIS) computation. The claw-breaking strategy achieves up to 88% of optimal performance even with 4 average neighbors per transceiver, outperforming maximal set scheduling by 33% in worst-case scenarios, especially when using directed antennas to limit interference clusters.

ABSTRACT

In this paper, we address the scheduling problem in wireless ad hoc networks by exploiting the computational advantage that comes when such scheduling problems can be represented by claw-free conflict graphs where we consider a wireless broadcast medium. It is possible to formulate a scheduling problem of network coded flows as finding maximum weighted independent set (MWIS) in the conflict graph of the network. Finding MWIS of a general graph is NP-hard leading to an NP-hard complexity of scheduling. In a claw-free conflict graph, MWIS can be found in polynomial time leading to a throughput-optimal scheduling. We show that the conflict graph of certain wireless ad hoc networks are claw-free. In order to obtain claw-free conflict graphs in general networks, we suggest introducing additional conflicts (edges) while keeping the decrease in MWIS size minimal. To this end, we introduce an iterative optimization problem to decide where to introduce edges and investigate its efficient implementation. Besides, we exemplify some physical modifications to manipulate the conflict graph of a network and also propose a mixed scheduling strategy for specific networks. We conclude that claw breaking method by adding extra edges can perform nearly optimal under the necessary assumptions.

Motivation & Objective

• To address the NP-hard complexity of throughput-optimal scheduling in wireless ad hoc networks under interference constraints.
• To enable polynomial-time scheduling by transforming general conflict graphs into claw-free graphs, where MWIS can be computed efficiently.
• To minimize performance degradation when making non-optimal modifications to conflict graphs by optimizing edge additions.
• To evaluate the effectiveness of physical network modifications (e.g., antenna direction, range adjustment) in achieving claw-freeness.
• To develop a mixed scheduling strategy that combines optimal and approximate scheduling for different network zones.

Proposed method

• Model network transmissions as vertices in a conflict graph, where edges represent interference under the protocol model.
• Use the maximum weighted independent set (MWIS) formulation to represent optimal scheduling, solvable in polynomial time for claw-free graphs.
• Introduce an iterative optimization framework to select minimal edge additions that eliminate all claws in the conflict graph.
• Apply physical modifications such as directed antennas, transmission range control, and node positioning to induce claw-free topologies.
• Design a mixed scheduling strategy that applies optimal MWIS to claw-free zones and approximate algorithms to claw-containing zones, then merge results carefully.
• Use simulations to evaluate performance under varying network density and neighbor counts, comparing against maximal set scheduling.

Experimental results

Research questions

• RQ1 Can the NP-hard scheduling problem in wireless ad hoc networks be solved in polynomial time by transforming the conflict graph into a claw-free structure?
• RQ2 How can edge additions be optimally selected to minimize throughput degradation while eliminating all claws in the conflict graph?
• RQ3 To what extent does the use of directed antennas reduce the number of claws and improve the performance of the claw-breaking strategy?
• RQ4 How does the performance of the proposed claw-breaking strategy compare to maximal set scheduling under varying network densities?
• RQ5 Can a mixed scheduling strategy combining optimal and approximate scheduling achieve near-optimal throughput in general networks?

Key findings

• The claw-breaking strategy achieves up to 88% of the optimal throughput when the average number of neighbors per transceiver reaches 4, significantly outperforming maximal set scheduling.
• For networks with up to 2 neighbors per transceiver, the claw-breaking strategy achieves optimal performance, demonstrating near-ideal efficiency.
• The strategy improves performance by 33% over maximal set scheduling in the worst-case scenario, even with high interference density.
• The number of edges added to eliminate claws increases concavely with network size, indicating scalability and efficiency of the optimization process.
• Directed antennas are crucial: with omnidirectional antennas, the number of claws grows rapidly, degrading performance and increasing complexity.
• Physical modifications such as antenna orientation and range adjustment can induce claw-free conflict graphs, but require expert intervention and are not fully automatable.