An FPTAS for the Lead-Based Multiple Video Transmission LMVT Problem

TL;DR

This paper proves the NP-hardness of the Lead-Based Multiple Video Transmission problem even with linear conversion functions and introduces a fully polynomial time approximation scheme (FPTAS) for it, linking it to the Santa Claus problem.

Contribution

The paper demonstrates NP-hardness for the LMVT problem with linear functions and develops an FPTAS, advancing approximation methods for this class of problems.

Findings

NP-hardness established for linear $$ functions

Designed an FPTAS for the LMVT problem

Linked LMVT to the Santa Claus problem

Abstract

The Lead-Based Multiple Video Transmission (LMVT) problem is motivated by applications in managing the quality of experience (QoE) of video streaming for mobile clients. In an earlier work, the LMVT problem has been shown to be NP-hard for a specific bit-to-lead conversion function $\phi$. In this work, we show the problem to be NP-hard even if the function $\phi$ is linear. We then design a fully polynomial time approximation scheme (FPTAS) for the problem. This problem is exactly equivalent to the Santa Clause Problem on which there has been a lot of work done off-late.