Minimum-Cost Multicast over Coded Packet Networks

TL;DR

This paper addresses the challenge of establishing minimum-cost multicast connections over coded packet networks, providing polynomial-time solutions for static multicast and dynamic programming approaches for dynamic multicast, with decentralized algorithms for implementation.

Contribution

It introduces a polynomial-time optimization framework for static multicast and a dynamic programming approach for dynamic multicast in coded packet networks, enabling decentralized solutions.

Findings

Decentralized algorithms achieve minimum-cost static multicast.

Polynomial-time solvability for static multicast over coded networks.

Dynamic programming approach for dynamic multicast problems.

Abstract

We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e. packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomial-time solvable optimization problem, and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimum-cost multicast. By contrast, establishing minimum-cost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved.