Min-cost multicast networks in Euclidean space

Abstract

Abstract-Space information flow is a new field of research recently proposed by Li and Wu [1], [2]. It studies the transmission of information in a geometric space, where information flows can be routed along any trajectories, and can be encoded wherever they meet. The goal is to satisfy given endto-end unicast/multicast throughput demands, while minimizing a natural bandwidth-distance sum-product (network volume). Space information flow models the design of a blueprint for a minimum-cost network. We study the multicast version of the space information flow problem, in Euclidean spaces. We present a simple example that demonstrates the design of an information network is indeed different from that of a transportation network. We discuss properties of optimal multicast network embedding, prove that network coding does not make a difference in the basic case of 1-to-2 multicast, and prove upper-bounds on the number of relay nodes required in an optimal multicast network in general.

Space information flow: Multiple unicast

“…In two sibling work [3], [4], we study the multicast problem in space, with network coding explicitly considered. There we present examples that show network coding and routing are indeed different in space, prove upper-bounds on the cost advantage, analyze the achievability of optimality with finite solutions, and discuss the complexity of optimal multicast in a geometric space.…”

“…Space information flow is a new subject of study being proposed [3], [4]. It considers terminals at known locations in a geometric space, with unicast, broadcast or multicast communication demands among them.…”

“…Can network coding lead to better solutions than routing (MCF)? Recent examples show that network coding can outperform routing when the demand in space is multicast [3], [4]. What about multiple unicast?…”

On Space Information Flow: Single multicast

“…The cost advantage is defined as the ratio of minimum cost necessary for achieving a target throughput by routing over that of network coding [3]. In contrast with the multiple source examples in [4] [7], we present the first single source example, the Pentagram (Fig.2) to illustrate that the cost advantage can be strictly bigger than 1 in space. The Pentagram example (a) 6 terminal nodes in 2-D Euclidean space (b) using optimal ESMT(cost=4.64/bit) (c) using network coding(cost=4.57/bit) The Pentagram Example.…”

A geometric framework for investigating the multiple unicast network coding conjecture

“…In this work, we apply a recently proposed tool, space information flow [3]- [5], to develop a geometric framework for studying the multiple unicast network coding conjecture.…”