Abstract
Generalized diversity coding is a promising proactive recovery scheme against single edge failures for unicast connections in transport networks. At the source node, the user data is split into two parts, and their bitwise XOR is computed as a third redundancy sub-flow. In order to guarantee instantaneous failure recovery without costly node upgrades, the network must ensure that any two of the three sub-flows reach the destination node in case of a single edge failure only by allowing flow duplication or merging identical flows, and avoiding any coding operation in the core network. In this paper, we investigate the corresponding routing problem to calculate capacity-efficient routes for these sub-flows. We propose a polynomial-time algorithm for topologies without capacity constraints on the links and without capability limitations of the nodes. We show that with node limitations the presented algorithm (as well as a minimum cost disjoint path-pair) provides a 4/3-approximation for the routing problem. Furthermore, we formulate an integer linear program to provide a minimum cost solution with arbitrary constraints in general graphs and we propose a polynomial-time algorithm in directed acyclic graphs. Our simulation results suggest that with upgrading only a small set of core network nodes with flow duplication and merging capabilities most of the benefits of generalized diversity coding can be achieved.
Highlights
D ESPITE extensive research effort focused on developing capacity-efficient survivable routing schemes in the last decades dedicated 1 + 1 path protection is still the most commonly used scheme of the current communication networks [1]
As the routing problem is NP-complete with scarce bandwidth resources in partially upgraded networks [19], in Section V we present an integer linear program for general topologies and a polynomial-time algorithm in directed acyclic graphs
This goal can be achieved either with applying three link-disjoint paths (Fig. 1a), or using three directed acyclic graphs which might share common edges (Fig. 1b), but even upon the failure of these edges all data units are received at the sink without any network reconfiguration, formally: Definition 1: The allocated bandwidth f (e) for each edge e implements a survivable routing of connection request D = (s, t, d) in G, if ∀e ∈ E : f (e) ≤ k(e), and there is an s − t flow of value at least d in G with edge capacities f, even if we delete any single edge of G
Summary
D ESPITE extensive research effort focused on developing capacity-efficient survivable routing schemes in the last decades dedicated 1 + 1 path protection is still the most commonly used scheme of the current communication networks [1]. Dedicated path protection is appealing because of its ultrafast recovery time combined with the robust and straightforward operation: it sends the user data along two disjoint paths to instantaneously recover from single edge failures [2] It consumes at least twice as much capacity as a single path, there are efficient algorithms to calculate a 1 + 1 routing solution [3] and its operation does not require to modify the operation of core network nodes. Network coding-based approaches perform algebraic operations on the data at core network nodes [4]–[6], partial path protection methods guarantee a minimum grade of service after failure using multi-path routing strategies [7], [8], and shared protection approaches pre-compute backup paths but signal them only after a failure occurs [9]–[11] They are capacity efficient, these methods did not reach the phase of widespread deployment. Our goal is to find a survivable routing f for connection D with minimum bandwidth cost, formally: min c(e) · f (e)
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