# GUB Covers and Power-Indexed formulations for Wireless Network Design

## TL;DR

This paper introduces a pure 0-1 formulation for wireless network design that uses a finite set of power levels, improving practicality and numerical stability over traditional continuous models.

## Contribution

It presents a novel GUB cover inequality-based formulation for the coverage problem, especially effective in scenarios with a single major interferer.

## Key findings

- The formulation outperforms classical models in computational tests.
- Effective for WiMAX and DVB-T network design.
- Reduces numerical issues common in continuous models.

## Abstract

We propose a pure 0-1 formulation for the wireless network design problem, i.e. the problem of configuring a set of transmitters to provide service coverage to a set of receivers. In contrast with classical mixed integer formulations, where power emissions are represented by continuous variables, we consider only a finite set of powers values. This has two major advantages: it better fits the usual practice and eliminates the sources of numerical problems which heavily affect continuous models. A crucial ingredient of our approach is an effective basic formulation for the single knapsack problem representing the coverage condition of a receiver. This formulation is based on the GUB cover inequalities introduced by Wolsey (1990) and its core is an extension of the exact formulation of the GUB knapsack polytope with two GUB constraints. This special case corresponds to the very common practical situation where only one major interferer is present. We assess the effectiveness of our formulation by comprehensive computational results over realistic instances of two typical technologies, namely WiMAX and DVB-T.