# Scheduling and Power Assignments in the Physical Model

## Abstract

In the interference scheduling problem, one is given a set of *n* communication requests each of which corresponds to a sender and a receiver in a multipoint radio network. Each request must be assigned a power level and a color such that signals in each color class can be transmitted simultaneously. 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. This is commonly referred to as the “physical model” and is the established way of modeling interference in the engineering community. The objective is to minimize the schedule length corresponding to the number of colors needed to schedule all requests. We study *oblivious power assignments* in which the power value of a request only depends on the path loss between the sender and the receiver, e.g., in a linear fashion. At first, we present a *measure of interference* giving lower bounds for the schedule length with respect to linear and other power assignments. Based on this measure, we devise distributed scheduling algorithms for the linear power assignment achieving the minimal schedule length up to small factors. In addition, we study a power assignment in which the signal strength is set to the square root of the path loss. We show that this power assignment leads to improved approximation guarantees in two kinds of problem instances defined by directed and bidirectional communication request. Finally, we study the limitations of oblivious power assignments by proving lower bounds for this class of algorithms.

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