Scheduling Wireless Ad Hoc Networks in Polynomial Time Using Claw-free Conflict Graphs

TL;DR

This paper demonstrates that scheduling in certain wireless ad hoc networks can be efficiently solved in polynomial time by leveraging the properties of claw-free conflict graphs, enabling optimal scheduling algorithms.

Contribution

It shows that the conflict graphs of specific wireless ad hoc networks are claw-free, allowing polynomial-time solutions for maximum weighted independent set problems.

Findings

Claw-free conflict graphs enable polynomial-time scheduling algorithms.

Certain wireless ad hoc networks have claw-free conflict graphs.

Application of known algorithms yields efficient scheduling solutions.

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. 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. We consider activation of hyperedges in a hypergraph to model a wireless broadcast medium. We show that the conflict graph of certain wireless ad hoc networks are claw-free. It is known that finding MWIS of a general graph is NP-hard, but in a claw-free conflict graph, it is possible to apply Minty's or Faenza et al.'s algorithms in polynomial time. We discuss our approach on some sample networks.