Abstract
The notion of Shared Risk Link Groups (SRLG) captures survivability issues when a set of links of a network may fail simultaneously. The theory of survivable network design relies on basic combinatorial objects that are rather easy to compute in the classical graph models: shortest paths, minimum cuts, or pairs of disjoint paths. In the SRLG context, the optimization criterion for these objects is no longer the number of edges they use, but the number of SRLGs involved. Unfortunately, computing these combinatorial objects is NP-hard and hard to approximate with this objective in general. Nevertheless some objects can be computed in polynomial time when the SRLGs satisfy certain structural properties of locality which correspond to practical ones, namely the star property (all links affected by a given SRLG are incident to a unique node) and the span 1 property (the links affected by a given SRLG form a connected component of the network). The star property is defined in a multi-colored model where a link can be affected by several SRLGs while the span property is defined only in a mono-colored model where a link can be affected by at most one SRLG. In this paper, we extend these notions to characterize new cases in which these optimization problems can be solved in polynomial time. We also investigate the computational impact of the transformation from the multi-colored model to the mono-colored one. Experimental results are presented to validate the proposed algorithms and principles.
Highlights
The motivation of this work stems from the concept of Shared Risk Link Groups (SRLG) that captures wide-spreading faults in networks
In the specific case where each edge has at most one color, we will use the terminology of mono-colored graph which is equivalent to that of labeled graphs
We consider the number of colors of span greater than 1 instead of the maximum value of the span of the colors. This allows us to prove that the MC-st-Path, MC-st-Cut, and MC-Cut problems can be solved in polynomial time when the number of colors of span > 1 is bounded by a constant
Summary
The motivation of this work stems from the concept of Shared Risk Link Groups (SRLG) that captures wide-spreading faults in networks. Two notions have been introduced to characterize polynomial cases: Coudert et al (2007) introduced the span of a SRLG, counting the number of connected components induced by this SRLG, and Luo and Wang (2005) introduced the star property, assessing whether all links impacted by a given SRLG are incident to a unique node or not. Such failure scenario corresponds to risks like the cut of a conduit containing links issued from a node, or card failures in a router node. Our experiments show that the algorithms proposed for minimum colored path and cut problems are competitive with respect to other exact methods
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