Primal meets dual: A generalized theory of logical topology survivability in IP-over-WDM optical networks

The survivable logical topology mapping (SLTM) 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. It is assumed that both the physical and logical topologies are 2-edge connected. For this problem Kurant and Thiran [12] presented an algorithmic framework called SMART that involves successively contracting 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 [21] we presented a dual framework involving cutsets and showed that both these frameworks possess the same algorithmic structure. Algorithms CIRCUIT-SMART, CUTSET-SMART, CUTSET-SMART-SIMPLIFIED and INCIDENCE-SMART were also presented in [21]. Effectiveness of both these frameworks as well as their robustness in providing survivability against multiple failures depends on the lengths of the cutset cover and circuit cover sequences on which they are based. To improve their effectiveness and robustness, in this paper we first introduce the concept of generalized cutset cover and generalized circuit cover sequences. We present an algorithm to get a generalized cutset (circuit) cover sequence from any given cutset (circuit) cover sequence. We then present GEN-CUTSET-SMART and GEN-CUTSET-SMART-SIMPLIFIED algorithms that remove some of the shortcomings of the dual framework of [21]. We prove that there is a one-to-one correspondence between the set of generalized circuit cover sequences and the set of generalized cutset cover sequences. We then show that for each execution of GEN-CIRCUIT-SMART there exists an execution of GEN-CUTSET-SMART- SIMPLIFIED such that the groups of edges that they map into edge disjoint lightpaths are exactly the same. In other words, the distinction between the primal and dual methods disappears when they use generalized sequences. Preliminary simulation results confirm our expectation that GEN-CUTSET-SMART- SIMPLIFIED will perform better than CIRCUIT-SMART and CUTSET-SMART-SIMPLIFIED (when started with a circuit or a cutset sequence) in terms of number of additional protection edges to be added.