Logical topology augmentation for guaranteed survivability under multiple failures in IP-over-WDM optical network

The survivable logical topology mapping problem in an IP-over-WDM optical network is to map each link (u, v) in the logical topology (at the IP layer) into a lightpath between the nodes u and v in the physical topology (at the optical layer) such that failure of a physical link does not cause the logical topology to become disconnected. Kurant and Thiran presented an algorithmic framework called SMART that involves successive contracting of circuits in the logical topology and mapping the logical links in the circuits into edge disjoint lightpaths in the physical topology. In a recent work a dual framework involving cutsets was presented and it was shown that both these frameworks possess the same algorithmic structure. Algorithms CIRCUIT-SMART, CUTSET-SMART and INCIDENCE-SMART were also presented in. All these algorithms suffer from one important shortcoming, namely, disjoint lightpaths for certain groups of logical links may not exist in the physical topology. Therefore, in such cases, we will have to augment the logical graph with new logical links to guarantee survivability. In this paper we address this augmentation problem. We first show that if a logical topology is a chordal graph then it admits a survivable mapping as long as the physical topology is 3-edge connected and the logical topology is 2-edge connected. We identify one such chordal graph. We then show how to embed this chordal graph on a logical topology to guarantee survivability. We also show how this augmentation approach can be generalized to guarantee survivability under multiple failures.