Minimum-cost multicast over coded packet networks

TLDR

Minimum‑cost static multicast over routed packet networks is NP‑hard except for unicast and broadcast, highlighting the challenge that motivates studying coded networks. The paper studies how to establish minimum‑cost multicast connections over coded packet networks. The authors analyze both wireline and wireless networks, treating static multicast by reducing to a polynomial‑time optimization with decentralized algorithms, and dynamic multicast by formulating a dynamic‑programming problem. Coupling these algorithms with existing decentralized network‑coding schemes yields a fully decentralized method for achieving minimum‑cost multicast.

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.