From Shortest-Path to All-Path: The Routing Continuum Theory and Its Applications

As a crucial operation, routing plays an important role in various communication networks. In the context of data and sensor networks, routing strategies such as shortest-path, multi-path and potential-based (“all-path”) routing have been developed. Existing results in the literature show that the shortest path and all-path routing can be obtained from
$L_{1}$
and
$L_{2}$
flow optimization, respectively. Based on this connection between routing and flow optimization in a network, in this paper we develop a unifying theoretical framework by considering flow optimization with mixed (weighted)
$L_{1}/L_{2}$
-norms. We obtain a surprising result: as we vary the trade-off parameter
$\theta$
, the routing graphs induced by the optimal flow solutions span from shortest-path to multi-path to all-path routing—this entire sequence of routing graphs is referred to as the routing continuum. We also develop an efficient iterative algorithm for computing the entire routing continuum. Several generalizations are also considered, with applications to traffic engineering, wireless sensor networks, and network robustness analysis.